7116 papers
This paper presents complete diagrammatic axiomatisations for Kullback-Leibler and Rényi divergences by characterizing them as quantitative enrichments of stochastic matrix categories under both Kronecker product and direct sum monoidal structures within a graphical string diagram framework.
This paper proposes a fast and provably correct method for approximating the persistence diagrams of sliding window embeddings of quasiperiodic functions by integrating the Three Gap Theorem from number theory with the Persistent Künneth formula from topological data analysis.
This paper establishes that for any integer and any greater than the unique positive root of a specific polynomial, the restricted -fold sumset of a subset in a finite abelian group of sufficiently large odd order equals the entire group whenever , thereby generalizing previous results on cyclic groups and identifying as the optimal asymptotic density threshold.
This paper resolves a long-standing open problem by establishing a universal central limit theorem for both smooth and numerical statistics of intersection currents arising from independent Gaussian holomorphic sections in arbitrary codimensions, thereby fully extending the 2010 Shiffman–Zelditch theorem through a novel geometric framework that adapts Wiener chaos and Feynman diagram techniques to random currents on complex manifolds.
This paper characterizes fractional Malliavin-Watanabe-Sobolev spaces for all by establishing a criterion based on the integrability and fractional differentiability properties of the -transform's Bargmann-Segal norm, thereby bridging Malliavin calculus with white noise analysis and providing practical tools for analyzing objects like Donsker's delta and self-intersection local times.
The authors resolve an open question regarding the fragility of Tennenbaum's theorem by constructing a sequence of definitionally equivalent theories for fragments of arithmetic that admit computable nonstandard models, utilizing a new general-purpose strong jump inversion theorem that also unifies several known results.
This paper demonstrates that while BSD invariants themselves do not exhibit murmuration oscillations, the analytic order of the Tate-Shafarevich group uniquely modulates Frobenius trace murmurations and low-lying L-function zero distributions through a pure mean shift concentrated at small primes, revealing information not captured by other standard invariants.
The paper introduces KRAFTY, a novel multi-view clustering framework that utilizes a transposed Khatri-Rao matrix to represent joint clusters in orthogonal subspaces, enabling accurate recovery of true cluster structures and effective model selection even when the number of joint clusters exceeds the sum of clusters in individual views.
This paper provides combinatorial characterizations of virtually torsion-free and virtually free groups by utilizing canonical graph decomposition theory to establish necessary and sufficient conditions involving the structural properties of -local covers and their associated tree-decompositions.
This paper establishes two-sided heat kernel estimates for "book-like" graphs, which are formed by gluing together multiple pieces satisfying the parabolic Harnack inequality along a common set of vertices, with results robust enough to accommodate various structural perturbations.
This paper introduces dynamic curvature-set persistent homology, a computationally tractable and stable method for distinguishing dynamic data by extending Kim and Mémoli's spatiotemporal framework to curvature sets, proving the resulting modules are antichain-decomposable to enable efficient erosion distance computation and successfully demonstrating its ability to detect parameter changes in the Boids model.
This paper establishes a rigorous variational and gradient-based equivalence between K-Means and differentiable Radial Basis Function networks, proving that the latter converges to the former as temperature vanishes and proposing Entmax-1.5 to ensure stable training for end-to-end differentiable clustering.
This paper introduces an induction-free notion of completeness for topological spaces equipped with a graded base by redefining net convergence as an approach relation, thereby extending classical completeness results from uniform spaces to a broader class of locally symmetric base spaces.
This paper investigates the structure and properties of a new rearrangement-invariant quasi-Banach space that generalizes Arias-de-Reyna's classical space and explores its relationship with other rearrangement-invariant Banach spaces.
This paper introduces a non-separable progressive multivariate WENO scheme tailored for cell-average data that achieves high-order accuracy and non-oscillatory stability in image processing, demonstrating superior performance over linear Lagrange reconstruction through theoretical analysis and numerical experiments.
This paper derives new elliptic integral identities by embedding Coxeter's classical integrals into a one-parameter family, differentiating with respect to the parameter to express the result in terms of incomplete elliptic integrals, and integrating back to establish a direct connection between Coxeter's original evaluations and elliptic functions.
This paper establishes quantitative bounds on the size of dense subsets of hypercubes that can be embedded into other metric spaces with specific distortion constraints, while also deriving geometric applications regarding nonpositive Alexandrov curvature targets and improving bounds for embeddings of paths and trees.
This paper demonstrates that Riesz energies with exponents differing by one emerge as the limiting cases of a one-parameter family of infinite-strip energies under Neumann boundary conditions as the strip thickness varies from zero to infinity, offering a potential approach to a capacity conjecture by Pólya and Szegő.
This paper disproves the 2007 conjecture by Huang and Tam that the Frobenius norm of the self-commutator is contractive under the -Aluthge transform by providing a counterexample and establishing quantitative bounds on the ratio of the transformed to the original self-commutator norms.
This paper investigates the limitations of plane substructures in drawings of the -dimensional hypercube graph by constructing drawings with restricted plane paths, matchings, and subgraphs, while also establishing existence guarantees for specific rectilinear configurations and characterizing universal plane subgraphs as forests of caterpillars.