5124 papers
This paper proposes randomized stochastic gradient schemes with smoothing techniques to solve nonconvex nonsmooth stochastic potential games under uncertainty, achieving optimal sample complexity and asymptotic convergence without relying on stringent growth conditions or local convexity.
StochasticBarrier.jl is an open-source Julia toolbox that efficiently synthesizes Stochastic Barrier Functions for verifying the safety of discrete-time stochastic systems using Sum-of-Squares and piecewise constant optimization methods, demonstrating superior speed, scalability, and safety bounds compared to state-of-the-art tools across over 30 case studies.
This paper investigates the homotopy types and connectivity of total cut complexes and their Alexander duals for various graph families, including powers of cycles, complete multipartite graphs, and Cartesian products, thereby resolving specific conjectures regarding these structures.
This paper establishes a general mathematical framework for variational problems in quantum thermodynamics with measurement constraints, leveraging non-commutative optimal transport to analyze dual formulations and zero-temperature limits while tailoring the approach to quantum state tomography and developing convergent computational algorithms.
This paper improves the known bounds for the constant , which represents the minimum proportion of a Sidon subset guaranteed within any -set of size , by establishing that through a reformulated extremal problem and an explicit construction.
This paper establishes that the inversion walk on tournaments exhibits total-variation cutoff at time and characterizes the state space of the -restricted inversion walk as a coset of a subgroup whose codimension depends solely on .
This paper proves that for a smooth complex projective curve of genus , the Fourier–Mukai transform of a semistable vector bundle with slope greater than $2g-2\mathrm{IT}_0$ property.
This paper investigates the finite-one structure within the many-one degrees of -rigid sets, demonstrating that such degrees typically contain a least finite-one degree and infinitely many pairwise incomparable finite-one degrees, thereby providing partial solutions to open problems posed by Richter, Stephan, and Zhang.
This paper introduces a notion of semistability for intrinsic reductions of non-archimedean rational functions at non-classical points in the Berkovich projective line and computes the resulting loci for quadratic rational iterations via a slope formula, demonstrating that these loci exhibit precise stationarity analogous to the polynomial case.
This paper establishes that for most parameter sets, the symmetry group of Markoff-type equations acts transitively on the majority of solutions modulo for a density one set of primes, with specific applications proving near-complete transitivity results for the -classification conjecture in and for solutions arising from generalized cluster algebras.
This paper introduces the concept of marking data-informativity and develops corresponding algorithms to design valid nonblocking supervisors for unknown discrete-event systems using available behavioral data, while also addressing cases where data is insufficient through restricted informativity and informatizability frameworks.
This paper presents the fourth known primitive solution to the Diophantine equation , detailing the methodology used to discover it.
This paper proves that every sufficiently large odd integer can be expressed as the sum of one square and fourteen fifth powers of primes, while every sufficiently large even integer can be written as the sum of one square, one biquadrate, and twelve fifth powers of primes.
This paper demonstrates that any parahoric group scheme over a henselian discretely valued field becomes reductive after a finite Galois extension, allowing it to be recovered as the smoothening of Galois invariants of a reductive model, a result that extends prior work to the wildly ramified case and confirms the Grothendieck–Serre conjecture for generically trivial parahoric torsors in sufficiently good residue characteristics.
This paper establishes the Sobolev regularity of a nonlinear function of the symmetric gradient for weak solutions to -Laplacian systems with Lipschitz coefficients and Orlicz-Sobolev data, utilizing uniform higher differentiability estimates derived from approximating problems with singular perturbations.
This paper investigates the convergence properties of M.V. Berry's superoscillating approximation to the truncated Weierstrass function, providing sharp error estimates and analyzing the associated double limits.
This paper proves a conjecture by Michel and Venkatesh regarding the joinings of distinct Linnik problems through simultaneous quaternionic embeddings of imaginary quadratic fields, while also addressing a related non-equivariant conjecture by Aka, Einsiedler, and Shapira.
This paper proposes a distributionally robust framework for standard quadratic optimization under Wasserstein ambiguity, demonstrating its equivalence to a modified deterministic StQP instance while providing out-of-sample performance guarantees and empirical validation.
This paper establishes the existence of equilibria for non-Markovian mean-field games with unbounded controls and quadratic running costs using a weak formulation approach grounded in new stability results for quadratic-growth generalized McKean-Vlasov BSDEs, thereby removing previous restrictions on model parameter boundedness and time horizons.
This study demonstrates that neglecting vaccine unwillingness in epidemiological models introduces significant errors in both long-term equilibrium predictions and short-term epidemic wave simulations, with the magnitude of error depending on the disease's infectivity and the speed of vaccination programs.