2652 papers
This paper establishes that a discrete-time stochastic clustering model on , where points move halfway toward randomly chosen neighbors and merge, converges to a unique weak limit with exponential gap tails when initialized as a renewal process, and further characterizes the scaling limit of its time-reversed dynamics as a random distribution function.
This paper establishes the global well-posedness and long-time behavior of stochastic forced 3D Navier-Stokes equations in the critical -space by leveraging the regularization effect of transport and nonlocal turbulent noise through Lyapunov functions, bootstrap estimates, and stopping time arguments.
This paper investigates the Chow group of zero-cycles on bielliptic surfaces over arbitrary fields of characteristic not 2 or 3, proving that the kernel of the Albanese map is a torsion group with a specific exponent and providing explicit examples over -adic fields where this kernel contains nontrivial elements arising from abelian surfaces.
This paper extends fractional linear transformations from Banach algebras to general rings via Wedderburn's continued fractions, establishing a connection to the projective elementary group PE(2,R) to define a length function and prove structural results regarding the perfectness and simplicity of its commutator subgroup.
This paper empirically demonstrates that while the runtime of local greedy search for optimizing Sherrington-Kirkpatrick spin glass Hamiltonians is universal across various coupling distributions, the performance of Parisi's local reluctant search is surprisingly non-universal and sensitive to the specific entry distribution, particularly when couplings have discrete support.
This paper establishes several inequalities comparing formal slopes with p-adic slopes of solvable differential modules over the punctured open unit disc by analyzing Newton polygons and the log-convexity of generic radius functions.
This paper presents a numerical benchmark of stabilized and self-stabilized p-version Virtual Element Methods, demonstrating that while self-stabilized formulations achieve optimal accuracy at the cost of worse conditioning, a newly introduced projection operator accounting for variable coefficients significantly enhances robustness for high polynomial degrees.
This paper introduces Sigmoid-FTRL, an adaptive experimental design that overcomes the non-convexity challenges of AIPW estimators to achieve the minimax optimal Neyman Regret rate of while providing valid asymptotic inference.
This paper investigates the Cauchy problem for a nonlinear damped Schrödinger equation involving the Riemann zeta function, establishing the uniqueness of distributional solutions, proving the existence of global solutions via regularization and compactness arguments, and demonstrating that solutions in the one-dimensional case vanish in finite time.
This paper investigates higher property T by providing new operator-algebraic characterizations and exploring its relationship with cohomological, rigidity, and geometric phenomena in lattices of semisimple Lie groups below their real rank, culminating in a unifying conjectural framework.
This paper establishes that Riemannian manifolds admitting a connection with closed, covariantly constant torsion decompose locally into a product of a semisimple Lie group and a torsion-free manifold, a result used to simplify proofs for special geometries like KT and HKT manifolds and to fully characterize the geometry of complete, simply connected , , and compact 8-dimensional HKT manifolds under these conditions.
This paper revisits the HED Method for Mullins-Sekerka evolution in the plane to establish not only the algebraic rate but also the sharp leading-order constant for convergence to a flat interface by introducing an intrinsic distance and deriving natural assumptions on the flow.
This paper investigates the 2-switch-degree of a graph, defined as the degree of the graph within its realization graph, by analyzing active and inactive vertices, deriving explicit computation formulas, and examining the property's behavior in specific graph families like trees and unicyclic graphs.
This survey article explores the universal decay rate for approximating smooth convex bodies by polytopes with faces, tracing the concept from classical circle approximations to modern results on random polytopes, projection-based distances, and open problems regarding sharp constants and dimension dependence.
This paper establishes the tightness of known convergence rates for the Polyak stepsize in gradient descent by constructing worst-case functions, demonstrates its ability to escape worst-case scenarios via floating-point errors, and proves its universality across diverse function classes including those with Hölder smoothness and growth conditions.
This paper introduces FEALPy, a modular, cross-platform numerical simulation engine built on a unified tensor abstraction that seamlessly integrates diverse numerical methods with deep learning workflows across multiple computational backends and hardware systems.
This paper presents a comprehensive taxonomy and practical guide for selecting numerical differentiation methods suited to various scientific applications, accompanied by the open-source Python package PyNumDiff for differentiating noisy data.
This paper introduces a conductance-weighted fractional arboricity for graphs, establishing sharp global bounds, deriving new conductance-resistance inequalities using effective resistances, and characterizing its algebraic structure as a max-invariant within a commutative idempotent monoid under edge-disjoint unions.
This paper investigates the state complexity of automata recognizing relations and operations on -automatic sequences, establishing a link between the subword complexity of interior sequences and the state complexity of their linear subsequences while resolving a recent question by Zantema and Bosma regarding most-significant-digit-first inputs.
This paper formalizes the Galois correspondence between covering spaces and subgroups of fundamental groups within homotopy type theory, extends the concept to n-dimensional generalizations, and applies the framework to classify lens space coverings and construct the Poincaré homology sphere.