4965 papers
This paper introduces the -TF equivalence for objects in an abelian length category to coarsen the standard TF equivalence, demonstrating that the resulting structure forms a finite, complete rational generalized fan in the dual real Grothendieck group that corresponds to the normal fan of the object's Newton polytope.
This paper establishes simple necessary and sufficient conditions for information cost functions to be monotone with respect to Blackwell and Lehmann informativeness orders, grounded in their garbling characterizations, and applies these criteria to evaluate several well-known cost functions from the literature.
This paper enumerates and classifies the isotopy classes of degree three Morse polynomials from to , proving there are exactly 37 classes with nonsingular principal homogeneous parts and 2,258 classes of strictly Morse polynomials with eight real critical points, utilizing a combinatorial computer program based on Morse surgeries and Picard-Lefschetz theory.
This paper introduces a new, general approach to proving strong convergence of random matrices using soft arguments, rational function asymptotics, and elementary Fourier analysis, which is then applied to provide short proofs and extensions of key results regarding random regular graphs, random permutation matrices, and symmetric group representations.
This paper initiates a systematic study of modular representations of symmetric groups arising from braiding in tensor categories over fields of positive characteristic, establishing their equivalence to the classification of polynomial functors and the extension of strict polynomial functors to arbitrary tensor categories.
This paper establishes that for any positive integer , there exists a constant such that if a skew circuit in a binary matroid with circumference is contained in a sufficiently large set (where ), then the sum of the sizes of and any other skew circuit is strictly less than $2c - k$.
This paper introduces a Partitioned Optimization Framework (POf) that reformulates complex optimization problems by identifying variable subsets that render subproblems tractable, and proposes a Derivative-Free Partitioned Optimization method (DFPOm) that efficiently solves these reformulated problems to find global solutions, demonstrating its effectiveness in both infinite-dimensional optimal control and finite-dimensional composite greybox applications.
This paper introduces a new class of Liouville polarizations for open symplectic manifolds to establish symplectic embedding results, demonstrate non-removable Lagrangian intersections at small scales, and reveal a novel phenomenon of Legendrian barriers in contact geometry.
This paper proves that the partial sums of Rademacher random multiplicative functions evaluated at specific polynomial arguments converge in distribution to a standard Gaussian, confirming a conjecture by Najnudel and establishing that the fluctuations of sums over quadratic arguments almost surely reach the magnitude predicted by the law of the iterated logarithm.
This paper presents formal proofs in Lean 4 of Farkas-like theorems over linearly ordered fields and extends duality theory to linear optimization problems where coefficients may take infinite values.
This paper generalizes colour algebras from fields of odd characteristic to unital commutative associative rings containing , demonstrating their canonical construction via nondegenerate ternary hermitian forms with trivial determinant and exploring their structural properties, automorphism groups, derivations, and close relationship with octonion algebras.
This paper provides axiomatic characterizations of generalized and standard -estimators by establishing that symmetry, (strong) internality, and asymptotic idempotency are the defining properties, utilizing a separation theorem for Abelian subsemigroups in the proofs.
This paper investigates which four-dimensional real Lie superalgebras, as classified by Backhouse, can be realized as Lagrangian extensions and analyzes their left-symmetric structures, finding that all but two of them are Novikov superalgebras.
This paper revisits the partial regularity theory for minimizers of variational integrals with Morrey-Hölder zero-order terms to establish the sharp dependence of the Hölder exponent on structural assumptions, thereby confirming optimal regularity up to the limit exponent in Massari's theorem for prescribed-mean-curvature hypersurfaces.
This paper investigates fluctuations in Coulomb gases under specific external potentials, proving that particle counts near spectral outposts follow an asymptotic Heine distribution while those near disconnected droplet components exhibit discrete normal fluctuations, ultimately characterizing general linear statistics as a sum of Gaussian and oscillatory discrete Gaussian fields.
This book serves as a pedagogical resource that unifies scattered research on conformal prediction and distribution-free inference by curating key results and presenting their proofs in a coherent framework to help readers understand the fundamental technical arguments behind these uncertainty quantification methods.
This paper investigates a Lotka-Volterra type model of two competing populations driven by Brownian motions and spectrally positive -stable random measures, establishing nearly sharp conditions under which one of the populations becomes extinct.
This paper establishes an upper bound for the sum of powers of the ratio between positive integers and their Euler's totient function values under specific constraints, and applies this result to derive an upper bound for the count of integers in a given range where this ratio exceeds a specified threshold.
This paper establishes Allard-Michael-Simon-type -Sobolev inequalities with explicit, asymptotically sharp, and codimension-free constants for Euclidean minimal submanifolds of arbitrary codimension by utilizing optimal mass transport theory, while also providing a unified proof of recent isoperimetric inequalities by Brendle and Eichmair.
This paper introduces a massively parallel heuristic that approximates Graver basis directions by solving nonconvex continuous problems, thereby overcoming the computational bottlenecks of the augmentation scheme and achieving performance comparable to advanced solvers on nonlinear integer optimization instances.