7189 papers
This paper determines the minimum total perimeter for an axis-aligned rectangular tiling of a flat torus and proves that this optimal value is always achieved by a tiling consisting of either exactly one or exactly two rectangles.
This paper demonstrates that the conjugacy relation on one-sided subshifts over the binary alphabet is neither treeable nor amenable from the perspective of descriptive set theory.
This paper defines and analyzes the asymptotic behavior of the Archimedean height pairing for fiberwise cohomologically trivial differential forms on one-parameter degenerations of Riemann surfaces, utilizing Dai--Yoshikawa's results on small eigenvalues to extend the current-valued pairing of Filip--Tosatti to broader geometric settings.
This paper introduces a multilevel training framework for Kolmogorov-Arnold Networks (KANs) that leverages their structural equivalence to multichannel MLPs and the properties of spline basis functions to create a properly nested hierarchy of models, resulting in orders-of-magnitude improvements in training accuracy and speed, particularly for physics-informed neural networks.
This paper establishes a BBP phase transition for a doubly sparse deformed Wigner ensemble, proving that sparse signal vectors with strength greater than one generate outlier eigenvalues and correlate with top eigenvectors in the supercritical sparsity regime, thereby generalizing previous results to models where both the noise matrix and signal vectors are sparse without requiring specific relationships between their sparsity levels.
This paper proves that the Hochschild cohomology ring of any self-injective Nakayama algebra is a Batalin-Vilkovisky algebra, thereby demonstrating that the semisimplicity condition on the Nakayama automorphism required in previous results is not necessary, while also correcting inaccuracies found in existing literature.
This paper establishes that the Bergman kernel of a finite-volume quotient of a Hermitian manifold with bounded geometry is the average of the kernel over the discrete isometry group, and applies this result to Hermitian symmetric spaces to prove the non-vanishing of a broad class of relative Poincaré series, thereby extending previous findings to general locally symmetric spaces of finite volume.
This paper establishes that mixed H2/H-infinity control exhibits benign nonconvexity where every stationary point is globally optimal, by characterizing the feasible set's topology and employing an Extended Convex Lifting framework to bridge nonconvex policy optimization with convex reformulations for scalable, data-driven applications.
This paper introduces one-sided --Gorenstein categories as a generalization of Gorenstein categories, establishes equivalent characterizations based on relative projective and injective dimensions, and derives a necessary condition for the validity of the Wakamatsu tilting conjecture.
This paper constructs a mutation cone and a corresponding wall-and-chamber structure for maximal modifying modules over 3-dimensional Gorenstein isolated singularities, proving that the tilting-noetherian property holds if and only if all such modules are mutation-connected, and establishing a regular covering map from a specific subspace of Bridgeland stability conditions to the complexified mutation cone to describe the associated autoequivalence group.
This paper addresses the problem of set-membership localization using noisy range measurements by characterizing the nonconvex set of consistent points and developing efficient convex programming methods to compute tight, guaranteed outer-bounding boxes or ellipsoids, as well as inner approximations, without relying on semidefinite programming relaxations.
This paper investigates transformations on the interval and functions that preserve the asymptotic mean of digits in the ternary (or -adic) representation of numbers, establishing the necessary and sufficient conditions for such transformations to belong to this class.
This paper investigates the set of lattice points formed by pairs of Castelnuovo-Mumford regularity and v-number for edge ideals of connected graphs, establishing general bounds and explicitly characterizing these pairs for whisker and Cameron-Walker graphs while proposing a conjecture for connected chordal graphs.
This paper establishes the conditions for the existence of the asymptotic mean value of ternary digits and identifies an infinite, everywhere dense set of numbers that possess this mean despite lacking a well-defined frequency for their digits.
This paper establishes a comprehensive potential-theoretic framework for the fractional-logarithmic Laplacian by deriving explicit kernel representations and sharp asymptotics, defining associated logarithmic Bessel spaces, and proving global regularity results alongside critical compact embeddings that exhibit a strict logarithmic gain.
This paper presents a probabilistic solution for linear-quadratic optimal control problems with state constraints, providing a representation for the value function and an explicit optimal control that keeps the system within a specified domain while minimizing quadratic control costs.
This paper constructs higher Chow cycles of type on a family of degree abelian covers of branched over points and proves that for a very general member, these cycles generate a subgroup of the indecomposable part of rank at least by computing their images under the transcendental regulator map.
This paper demonstrates that for high-dimensional random data, gradient descent on shallow ReLU networks exhibits an implicit bias that approximates the minimum -norm solution with high probability, bridging the gap between worst-case non-existence and exact orthogonality results through a novel primal-dual analysis.
This paper presents methods for constructing two types of non-Runge Fatou-Bieberbach domains—proper open subsets biholomorphic to either or the ambient Stein manifold itself—within Stein manifolds possessing the density property, and provides concrete examples where these constructions are applicable.
This paper initiates the study of the hat guessing number under the constraint that the adversary must provide a proper coloring, establishing that complete graphs have a guessing number of , all trees on vertices have a guessing number of $4$, and providing general bounds, exact results for small graphs, and new conjectures for this variation.