2660 papers
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.
This paper classifies all local connected components of non-discriminant sets near parabolic function singularities, thereby proving and refining previous conjectures, enumerating local Petrovskii lacunas for hyperbolic PDE wavefronts, and demonstrating that certain parabolic singularities possess nontrivial one-dimensional homology groups in their discriminant complements, all achieved through a novel method combining Picard–Lefschetz theory with computer-assisted Morse surgery analysis.
This paper establishes a combinatorial-cut characterization of minimal forts in trees to derive new bounds on their cardinality and count, while providing a four-part classification of trees that achieve the lower bound on the number of minimal forts.
This paper computes Raja's covering index for infinite-dimensional Hilbert spaces, establishes sharp asymptotic estimates for scalar-valued spaces under renormability conditions, provides uniform upper bounds for Bochner spaces that partially resolve a question by Raja, and derives power-type lower bounds for non-commutative spaces using non-commutative Clarkson inequalities.
This paper clarifies the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces used in Cartan Neural Networks by proving that only Kähler spaces support Gibbs distributions, explicitly characterizing their generalized temperature spaces via adjoint orbits, and demonstrating the equivalence between various information and thermodynamical geometries while establishing the covariance of these distributions under the full symmetry group.
This paper investigates the conditions under which smooth maps are modulary dense on compact manifolds, specifically analyzing the validity and failure of this property in the context of the Lavrentiev gap.
This paper establishes a formula for the Euclidean distance degree of curves parameterized by rational functions and applies it to resolve conjectures regarding the ED degree of one-dimensional line multiview varieties in computer vision.
This paper provides the first systematic treatment of the measure-theoretic properties of nonlinear Lebesgue spaces, unifying scattered literature results and extending classical theorems on completeness, separability, and the density of simple, continuous, and smooth mappings to this broader nonlinear framework.
This paper proposes a deep reinforcement learning-based approach using proximal policy optimisation to enhance physical layer security in indoor visible light communication systems by leveraging realistic IRS-induced time delays to constructively boost signals for legitimate users while intentionally creating intersymbol interference for both colluding and non-colluding eavesdroppers.
This paper proves the Fourier extension conjecture for the paraboloid in all dimensions greater than two by decomposing smooth Alpert projections into localized pieces and establishing a key local inequality through a bilinear approach that transforms difficult exponential sums into controllable oscillatory integrals with periodic amplitudes.
This paper resolves the Peterson hit problem for five variables in generic degrees to prove that the fifth Singer algebraic transfer is an isomorphism in an infinite family of degrees, validates a localized version of Kameko's conjecture, and distinguishes the homotopy types of specific complex projective space quotients via their Steenrod module structures.
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and initial displacement in a damped biharmonic wave equation by proving the forward problem's well-posedness via contraction semigroups and deriving explicit stability estimates that highlight the enhanced stability provided by the biharmonic structure and its dependence on the damping coefficient.
This paper constructs smooth affine algebras of dimension over an algebraically closed field of characteristic zero that admit nontrivial projective modules of rank with trivial total Chern classes, thereby demonstrating the existence of nontrivial vector bundles whose topological invariants vanish.
This paper constructs a transitive symmetric model of ZF + DC + PP + AC_wo + ¬AC by performing an Ord-length countable-support symmetric iteration over a Cohen seed model, utilizing a diagonal-lift scheme and Ryan–Smith localization to separate the partition principle from the axiom of choice while preserving dependent choice and the non-well-orderability of a specific set.
This paper establishes the existence and uniqueness of solutions to backward stochastic differential equations driven by G-Brownian motion under time-varying monotonicity and Lipschitz conditions by utilizing the Yosida approximation method.
This paper introduces the Pretrained Finite Element Method (PFEM), a framework that combines a physics-informed neural operator pretraining stage with a conventional FEM warm-start stage to achieve highly efficient and accurate solutions for partial differential equations across complex geometries and material properties.
This paper analyzes the finite sampling map for free-tail canonical systems, establishing that while local identifiability and inversion are achievable for specific finite-dimensional families via a weighted Fourier-Laplace linearization, the full free-tail class suffers from nontrivial first-order invisible directions at the free Hamiltonian that preclude any local inverse-Lipschitz estimate.