2549 papers
This paper establishes a Galois connection framework for morphisms of neural codes using binary matrices to characterize boolean matrix factorization, define a partial order on codes based on free neurons, and introduce the concept of code defect to analyze covering relations in this poset.
This paper establishes new, improved upper bounds for the classical Ramsey numbers , , and , surpassing the previous limits derived from the standard recursive inequality.
This paper establishes finite-horizon mean-square strong and weak error bounds for Euler--Maruyama simulations of current-based leaky integrate-and-fire networks by employing a path-space pruning-and-balance strategy that accounts for the unique concentration of numerical error at stochastic threshold-crossing events.
This paper establishes the global well-posedness and constructs self-similar solutions for a semilinear elliptic equation with a nonlinear dynamic boundary condition in the half-space by utilizing the broader framework of Morrey spaces to accommodate rough, non-decaying initial data and deriving key estimates for associated interior and boundary operators.
This paper introduces a physics-informed neural particle method (PINN-PM) for the spatially homogeneous Landau equation that utilizes a continuous-time, mesh-free formulation to eliminate time-discretization errors, while providing rigorous stability analysis and error bounds that demonstrate superior accuracy and macroscopic invariant preservation compared to traditional time-stepping methods.
This paper disproves the Perälä–Virtanen conjecture by constructing explicit radial symbols on Bergman and Fock spaces where a positive limit inferior of the Berezin transform fails to guarantee essential positivity, demonstrating that the Berezin liminf criterion is insufficient for radial Toeplitz operators in all complex dimensions.
This paper establishes the monotonicity of simplicial volume and dilatation under ribbon concordance for fibered knots, proves the finiteness of their ribbon predecessors, and provides an algorithm to enumerate minimal compressions of surface homeomorphisms to identify strongly homotopy-ribbon concordant knots.
This paper establishes that the Chow motive of a specific smooth compactification of the Lagrangian fibration associated with a smooth cubic fourfold is a direct summand of the motive of the fifth power of the fourfold, thereby proving it is of abelian type for a general family of such cubics.
This paper provides a simple proof of the FKG inequality for random interlacements on transient weighted graphs and establishes 0-1 laws for non-local events, including a general result for increasing non-local events without additional assumptions.
This paper analyzes Boolean-valued random forcing in bounded arithmetic from a set-theoretic perspective, demonstrating that under specific saturation assumptions, the forcing algebra is isomorphic to the probability algebra on $2^{\omega_1}$ and establishing the structural relationship between the original model and its generic extensions while offering an alternative framework to axiomatic approaches.
This paper introduces the concept of F-convexity as a generalization of power convexity and characterizes which specific F-convexities are preserved under both the standard heat flow in Euclidean space and the Dirichlet heat flow in convex domains.
This paper investigates the long-time dynamics of a bulk-surface convective Cahn--Hilliard system by establishing instantaneous regularization, proving the existence of a minimal pullback attractor for the resulting non-autonomous system, and demonstrating convergence to a single steady state under decay assumptions on the velocity fields using the Łojasiewicz–Simon inequality.
This paper establishes the first sharp bounds for eigenfunctions of the Laplacian on the square torus for with , proving the discrete restriction conjecture without loss by refining the circle method and extending these sharp results to spectral projectors and additive energy.
This paper presents a constructive formalization of Abstract Rewriting Systems in Agda that eliminates classical logic from standard proofs, refines termination and confluence criteria, and demonstrates its applicability through a formalization of the lambda calculus.
This paper establishes the sharp finite-time Type-I blowup for the three-dimensional incompressible Euler equations in the axisymmetric no-swirl class with initial velocity in for every , utilizing a novel Lagrangian framework to prove that the quadratic strain term dominates the pressure Hessian uniformly below the critical regularity threshold of .
This paper establishes uniform Hölder bounds and analyzes the strong competition limit of variational reaction-diffusion systems driven by -wise interactions (), proving that minimizers converge to partially segregated configurations that satisfy specific regularity and extremality conditions.
The paper proves that for any fixed maximum degree and any , every sufficiently large oriented graph with minimum semidegree at least contains every oriented tree on vertices with maximum degree at most , a bound that is asymptotically optimal.
This paper extends Turán problems to the spectral domain of digraphs by determining the maximum Laplacian energy and characterizing the extremal digraphs for the class of -free digraphs.
This paper argues that the Gelfand–Naimark duality between compact Hausdorff spaces and unital commutative C*-algebras offers profound insights into the structure of compact Hausdorff spaces, particularly regarding Čech–Stone remainders and their autohomeomorphisms.
This paper establishes the first time-uniform error estimate for a fully discrete Luenberger observer applied to the one-dimensional barotropic Euler equations using mixed finite elements and implicit Euler time integration, demonstrating convergence that depends on initial errors, discretization parameters, and measurement noise via a modified relative energy technique.