2580 papers
This paper establishes that finite chains within the two-branching countable ultrahomogeneous pseudotree possess finite big Ramsey degrees, specifically determining the degree for chains of length two to be seven, thereby presenting the first example of a countable ultrahomogeneous structure in a finite language where some finite substructures have finite big Ramsey degrees while others have infinite ones.
This paper constructs a finite-dimensional Kan simplicial manifold that integrates the universal Lie -algebroid of a singular foliation admitting a geometric resolution, utilizing a recursive application of bi-submersions to generalize the Androulidakis-Skandalis holonomy groupoid to a higher Lie groupoid setting.
This paper characterizes Martin-Löf and Schnorr randomness by establishing that these notions correspond to the weak merging of computable probability measures under the summable Kullback-Leibler divergence, a result derived by linking the divergence to the incremental growth of the Doob decomposition of a specific submartingale.
This paper constructs and provides a complete classification of all differential symmetry breaking operators between specific vector and line bundles over the 3-sphere and 2-sphere, respectively, in the special case where the rank parameter equals the absolute value of the integer .
This paper investigates the inverse problem of determining the properties of a quadratic number field based on the growth of an elliptic curve's torsion subgroup defined over the rationals, establishing an explicit relationship between the primes dividing the curve's conductor and the conductor of the field extension.
This paper establishes new results on robust Diophantine tuples with property and their applications to product sets within shifted perfect powers, significantly improving prior work by combining sieve methods, Diophantine approximation, and extremal graph theory.
This paper investigates the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms between groupoid and coarse-geometric models, demonstrating that strong phases are detected by position spectral triples while phases arising from stacking along Delone sets are inherently weak in the coarse-geometric sense.
This paper introduces a novel transformation-based, doubly-adaptive quasi-Milstein scheme for jump-diffusion SDEs with discontinuous drift and degenerate diffusion, achieving a strong convergence rate of order 1 in under assumptions weaker than those in existing literature.
This paper introduces WG-IDENT, a robust framework that combines weak formulations, B-spline representations with spectrally optimized knots, and a novel group feature trimming technique to accurately identify Partial Differential Equations with spatially varying coefficients from heavily noisy spatiotemporal data.
This paper introduces CVQP, an open-source operator splitting method that efficiently solves large-scale quadratic programs with Conditional Value-at-Risk (CVaR) constraints by combining a specialized projection algorithm with parallel computations, achieving performance orders of magnitude faster than general-purpose solvers for problems involving millions of scenarios.
This paper establishes a unified framework for proving the almost everywhere pointwise convergence of sparse ergodic averages in for both deterministic and random sequences within specific parameter ranges, while providing new quantitative convergence estimates that improve upon previous non-quantitative results.
This paper introduces a general forward-backward splitting framework utilizing coefficient matrices to solve monotone inclusion problems with non-cocoercive operators, unifying existing algorithms while enabling new flexible and distributed implementations.
This paper introduces an adaptive replication strategy within a trust-region Bayesian optimization framework that dynamically allocates repeated evaluations to effectively manage high-variance stochastic functions, significantly improving both solution accuracy and computational efficiency compared to baseline methods.
This paper investigates the monodromy representations of compact Lagrangian fibrations, proving their irreducibility over when the period map is generically immersive and characterizing the structure of these representations as a direct sum of two irreducible local systems in the isotrivial case.
This paper establishes an exact recursive equation for the covariation measures of the two-dimensional stochastic heat equation at criticality, explicitly expressing the quadratic variations of its martingale parts in terms of the equation's solutions and two-body delta-Bose gas semigroups through asymptotic analysis and new fourth-order moment bounds.
This paper establishes a correspondence between multiplicity-free, self-dual fusion rings and digraph-hypergraph pairs to characterize these rings via graphical properties and to classify all non-isomorphic instances of rank at most 8.
This paper investigates the bifiltration of bracket ideals and the associated bivariate Hilbert polynomial for complex finite-dimensional filiform Lie algebras, demonstrating that this polynomial serves as a refined invariant capable of distinguishing isomorphism classes that remain indistinguishable by traditional numerical invariants related to centralizers and abelian ideal dimensions.
This paper extends Suzuki's approach to Kannan and Chatterjea type contractions by utilizing the CJM condition to establish the weakest possible conditions that ensure the convergence of all Picard sequences to a fixed point, thereby proving the optimality of these conditions.
This paper proves that the infinite system-size free energy of quantum -spin glasses in a transverse magnetic field converges to that of the quantum random energy model as , achieved by combining non-commutative analytical techniques with the geometry of extreme negative deviations in classical -spin glasses.
This paper characterizes the Cohen-Macaulay property of the square of an edge ideal by constructing the Stanley-Reisner complex of its polarization and applying Reisner's criterion, proving that for several important classes of graphs, is Cohen-Macaulay if and only if is either a pentagon or a single edge.