7189 papers
This paper generalizes Hopf's theorem to thermostats by establishing that non-positive total curvature characterizes systems without conjugate points, proving the equivalence between transverse Green bundles and projective Anosov flows, and providing a counterexample to Hopf's rigidity on the 2-torus via the first known instance of a projectively Anosov thermostat that is not Anosov.
This paper proposes a novel Linear Parameter-Varying (LPV) framework utilizing Integral Quadratic Constraints (IQCs) to analyze and establish quantitative tracking error bounds for iterative first-order optimization algorithms applied to time-varying convex problems, where the bounds depend on specific measures of temporal variability such as function value and gradient rates of change.
This paper investigates generalized -support dual norms derived from arbitrary source norms to enforce a strict -sparsity budget, establishing conditions for their effectiveness through the analysis of exposed faces and revealing that their unit ball faces are structurally hypersimplices when the source norm is an -norm.
This paper establishes a dimension-free Gehring-Hayman inequality for quasigeodesics in infinite-dimensional spaces by developing a new approach that relaxes previous constraints on geodesics and quasiconformal equivalence, thereby affirmatively resolving a long-standing open problem regarding the relationship between uniformity and Gromov hyperbolicity in Banach spaces.
This paper establishes that for typical self-affine sets and measures generated by contractive affine iterated function systems, the Hausdorff and box-counting dimensions of their orthogonal projections coincide and are determined by a specific pressure function, while also characterizing the conditions under which the projected measures possess exact dimensionality.
This paper introduces a parsimonious Levy-driven graph supOU process for modeling high-dimensional time series with both short- and long-range dependence, develops a consistent generalized method of moments estimator for it, and validates the approach through simulations and an empirical study of European wind capacity factors.
This paper introduces the Morse parametric qualification condition to establish a relevant intermediate class for bilevel programming and analyzes two gradient-based solution strategies: a biased single-step multi-step method with rich theoretical properties and a simpler, though less stable, differentiable programming approach.
This paper establishes closed formulae for the orbifold Euler characteristics of double ramification loci and their higher-rank generalizations in genus one, utilizing a recurrence relation to derive a polynomial result for rank one and a formula involving greatest common divisors of matrix minors for higher ranks.
This paper provides a geometric interpretation of virtual knotoids as arcs in thickened surfaces, demonstrating that virtual knotoid theory generalizes classical knotoid theory and thereby proving a conjecture by Kauffman and the first author.
This paper establishes the Fujita-type critical exponents for semilinear heat equations driven by mixed local-nonlocal operators, demonstrating that the critical threshold is governed solely by the nonlocal component and thereby refining existing results for both forced and unforced cases.
This paper establishes a complete characterization of the compactness of Sobolev embeddings for radially symmetric functions on and weighted balls within the general framework of rearrangement-invariant function spaces by developing novel techniques that overcome the limitations of previous methods restricted to domains of finite measure.
This paper proposes a fix-and-propagate heuristic that leverages low-precision, GPU-accelerated first-order LP solutions to efficiently solve large-scale mixed-integer linear optimization problems, demonstrating superior performance over state-of-the-art commercial solvers on massive unit commitment instances.
This paper further investigates the function used to construct a canonical connected fundamental domain for , establishing identities to match its cusps with known classes and detailing the domain's boundary arcs and gluing patterns to aid in understanding the modular curve .
This paper establishes two explicit formulas for counting -points of orbital varieties in ad-nilpotent ideals of type using Hall-Littlewood functions and -weighted tableaux, while providing new proofs and applications for results concerning nilpotent Hessenberg varieties, square-zero matrices, and double coset counts.
This paper proposes and analyzes a new filtered two-step variational integrator for charged-particle dynamics in moderate to strong magnetic fields, establishing its second-order accuracy, uniform convergence properties, and long-time near-conservation of energy and momentum through backward error analysis and modulated Fourier expansions.
This paper extends dilation results, characterizations, and decomposition theorems for operators in the class and quantum annulus to the setting of doubly commuting tuples of such operators.
This paper proposes a correlation-based metric and a simple common-neighbor clustering algorithm to achieve exact, almost exact, and weak recovery of small, heterogeneously-sized communities in the planted partition model, overcoming the limitations of traditional methods in highly unbalanced settings.
This paper derives asymptotic formulas for the sums of the smallest integer such that is divisible by , considering both all integers up to and the subset of -free integers.
This paper extends the classical sharp upper bound on central hyperplane sections of a regular simplex to a probabilistic framework involving negative moments of centered log-concave random variables, revealing a phase transition in the extremizing distributions for new sharp reverse Hölder-type inequalities.
This paper introduces a distribution-free framework for formalizing identifiability in ill-posed linear regression by defining a constrained least-squares solution and establishing sharp error bounds for statistically interpretable dimensionality reduction algorithms that outperform traditional minimax rates under heavy-tailed features and low effective rank.