7012 papers
This paper establishes necessary and sufficient conditions for the input-to-state stability (ISS) of impulsive switched systems with both stable and unstable modes by introducing time-varying ISS-Lyapunov functions under relaxed mode-dependent average dwell and leave time constraints, while also providing methods to construct decreasing Lyapunov functions and guarantee ISS even with unknown switching signals.
This paper investigates separable commutative algebras in equivariant homotopy theory, establishing conditions under which they are "standard" (arising from finite -sets) and demonstrating that while all such algebras are standard for -groups, non-standard examples exist for general finite groups, with the classification further refined by the presence of multiplicative norms and the solvability of the group.
This paper establishes the minimax rate optimality of three popular matrix completion estimators by leveraging advanced matrix concentration inequalities to eliminate the dimensional factor in their convergence rates.
This paper introduces the concept of "zippers" as a novel and streamlined method for constructing universal circles—key dynamical structures associated with hyperbolic 3-manifolds—by deriving them directly from uniform quasimorphisms or uniform left orders.
This paper analyzes a two-player permutation game inspired by the Erdős-Szekeres Theorem, determining the winner and providing a winning strategy for cases where the parameter is greater than or equal to and is an integer between 2 and 5.
This paper introduces the concept of uniformly dominant local rings, establishes sufficient conditions for their existence in various classes such as Burch rings, and derives upper bounds for the Orlov spectrum of their singularity categories while demonstrating the preservation of this property under basic operations.
This paper establishes the minimax rates for robust mean estimation under star-shaped constraints in the presence of adversarial corruption and Gaussian or sub-Gaussian noise, characterizing the optimal error bounds in terms of the local entropy of the constraint set, the noise variance, and the corruption fraction.
This paper establishes the convergence properties and rates of projected subgradient methods for paraconvex optimization under various step-size rules and error bound conditions, demonstrating their effectiveness through numerical experiments on diverse robust low-rank matrix recovery problems.
This paper establishes the equivalence between the existence of a specific divisor and a non-degenerate harmonic morphism on 3-edge connected tropical curves to define their moduli spaces, ultimately proving that the dimension of the moduli space of tropical trigonal curves matches that of their algebraic counterparts.
This paper computes the first and second moments of sums of normalised Hecke eigenvalues over holomorphic cusp forms of large weight, demonstrating that in the range , the second moment scales between and , a sharp contrast to the linear growth observed in the lower range .
This paper establishes Runge-type approximation results for solutions to linear partial differential equations with constant coefficients on spaces of smooth Whitney jets, providing geometric characterizations of density conditions for elliptic, parabolic, and wave operators, and applying these findings to the approximation of holomorphic functions on specific planar domains.
This paper demonstrates that training shallow neural networks with Lipschitz continuous activation functions to approximate smooth target functions suffers from the curse of dimensionality, as the population risk decays at a rate bounded by a power of time that depends inversely on the input dimension, regardless of whether the optimization is analyzed via empirical or population risk or through 2-Wasserstein gradient flow dynamics.
This paper proves that the Beilinson conjecture holds for specific K3 surfaces over equipped with an involution, provided their quotient by the involution is a projective plane branched along a sextic curve.
This paper introduces Clip21-SGD2M, a novel federated learning algorithm that combines clipping, heavy-ball momentum, and error feedback to achieve both optimal convergence rates for non-convex problems with heterogeneous data and near-optimal differential privacy guarantees without restrictive assumptions.
This paper proposes a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noises that significantly reduces computational costs through volume-preserving characteristics and domain adaptation, while providing a first-order convergence analysis that partially resolves a recent conjecture on numerical convergence.
This paper introduces an optimal uniform mean estimator that, by combining Talagrand's generic chaining with single-variable mean estimation, achieves a near-optimal error bound for classes of mean-zero functions under minimal assumptions, thereby resolving key challenges in high-dimensional probability and statistics.
This paper proposes two-stage sequential estimators for relative risk, odds ratio, and their logarithms that guarantee a target mean-square error for any population parameters while maintaining a controlled sample size ratio and achieving high efficiency near the Cramér-Rao bound.
This paper introduces two variations of setwise climbability properties, demonstrating that the first type is equivalent to known principles and consistent with the Proper Forcing Axiom (PFA), while the second type characterizes Martin-type axioms via generalized Banach-Mazur games and is inconsistent with PFA, alongside an analysis of their compatibility with large fragments of PFA.
This paper formulates p-adic analogues of three fundamental results in functional analysis and geometry: the Grothendieck Inequality, the Johnson-Lindenstrauss Flattening Lemma, and the Bourgain-Tzafriri Restricted Invertibility Theorem.
This paper establishes that central extensions of certain separable hyperbolic and double coset separable groups inherit product and double coset separability properties, provided they are subgroup separable, and demonstrates that double coset separability is preserved under direct products with finitely generated nilpotent groups.