On the excision of Brownian bridge paths
Motivated by Pitman and Yor's construction of the 3-dimensional Bessel process, this paper demonstrates that applying a similar excision procedure to a Brownian bridge yields a 3-dimensional Bessel bridge.
🔢 Category
math
4730 papers
A characterization of interval nest digraphs
This paper provides a complete characterization of interval nest digraphs by introducing "nest orderings," a specific type of vertex linear ordering defined by forbidden patterns, thereby completing the set of vertex-ordering characterizations for major subclasses of interval digraphs.
Informational Cardinality: A Unifying Framework for Set Theory, Fractal Geometry, and Analytic Number Theory
This paper introduces a deterministic fractal constructed from prime numbers modulo 4, analyzes its Hausdorff dimension to distinguish its geometric complexity from the classical Cantor set, and proposes a novel framework linking the density of this prime-driven fractal to the distribution of zeros of the Riemann zeta function.
Pinching Antennas-Assisted Low-Latency Federated Learning Over Multi-User Wireless Networks
This paper proposes FedPASS, a novel framework that leverages pinching-antenna systems to dynamically optimize physical-layer connectivity, thereby jointly minimizing end-to-end latency and convergence gaps in multi-user wireless federated learning through a specialized two-tier iterative algorithm.
The -adjacency graph for knots
This paper introduces the -adjacency graph to visualize relationships between knots connected by sets of crossing circles and establishes several fundamental properties of this new mathematical structure.
Asymptotic Tail of the Product of Independent Poisson Random Variables
This paper derives an explicit Laplace-type asymptotic approximation with vanishing relative error for the tail probability of the product of independent Poisson random variables, utilizing Stirling's approximation, a constrained saddle-point method, and the Lambert function.
On the concatenability of solutions of partial differential equations
This paper establishes that the space of continuous distribution-valued solutions to a linear partial differential equation with polynomial coefficients possesses the concatenation property if and only if the equation is first-order in the time derivative.
Context-Free Trees
This paper investigates bona fide context-free trees by demonstrating their finite-state description via multi-edge NFAs and proving that the isomorphism problem for deterministic context-free trees is NL-complete in both rooted and non-rooted cases.
Congruences between Klingen-Eisenstein series and cusp forms on
This paper investigates congruences between Hecke eigenvalues of Hermitian Klingen-Eisenstein series and cusp forms on the unitary group over , while also establishing the rationality of the space of Hermitian automorphic forms and the integrality of their Hecke eigenvalues.
Mass and rigidity in almost Kähler geometry
This paper establishes an explicit formula for the ADM mass of asymptotically locally Euclidean almost Kähler manifolds using a spin adaptation of Witten's proof, and subsequently derives positive mass theorems, Penrose-type inequalities, and rigidity results showing that certain almost Kähler-Einstein manifolds are necessarily Kähler-Einstein.
Secondary gravitational waves against a strong gravitational wave in the Bianchi VI universe
This paper presents a proper-time method to analytically construct and demonstrate the stability of secondary gravitational waves as perturbative solutions against a strong gravitational wave background in the Bianchi VI universe.
Observables in Chern-Simons theory
This paper computes the expectation values of Wilson loop observables in Chern-Simons theory on closed oriented 3-manifolds, demonstrating their topological invariance, analyzing the impact of topological sectors, exhibiting CS duality, and determining the theory's zero modes and equations of motion.
CONVOLVED NUMBERS OF K-SECTION OF THE FIBONACCI SEQUENCE: PROPERTIES, CONSEQUENCES Convolved Numbers of -sections of the Fibonacci Sequence
This paper introduces and analyzes convolved numbers of -sections of the Fibonacci sequence, deriving an explicit Binet-type formula for these generalized sequences and establishing their connections to Chebyshev polynomials and Lucas numbers while noting their absence from the OEIS encyclopedia.
Low order maximally single-trace graphs as the first counterexamples to large N factorization in random tensors
This paper presents the first and lowest-order examples of 3-regular 3-edge-colored graphs that violate large factorization in Gaussian random tensor models, contrasting with the well-established factorization behavior observed in random matrices.
Coherence-Aware Over-the-Air Distributed Learning under Heterogeneous Link Impairments
This paper proposes a coherence-aware federated learning framework that mitigates heterogeneous link impairments by employing product superposition for efficient downlink delivery and partial model reception with local filling for robust uplink aggregation, thereby achieving improved communication efficiency and learning accuracy under varying channel conditions.
On the expressive power of inquisitive team logic and inquisitive first-order logic
This paper demonstrates that while inquisitive team logic is expressively equivalent to first-order logic for sentences, its open formulas possess strictly greater expressive power, a finding that extends to standard inquisitive first-order logic where certain sentences can express non-first-order properties.
Theorem of the heart for Weibel's homotopy -theory
This paper establishes the theorem of the heart for Weibel's homotopy -theory (), proving that the realization functor induces an equivalence for small stable -categories with bounded -structures, a result derived from a strengthened version of Barwick's theorem that provides precise isomorphism ranges for classical -theory and demonstrates the sharpness of these bounds.
Structure-preserving model reduction on manifolds of port-Hamiltonian systems
This paper proposes a non-intrusive, structure-preserving model order reduction method based on generalized manifold Galerkin reduction that generates reduced-order port-Hamiltonian models for both linear and nonlinear systems while maintaining stability and passivity, demonstrating superior accuracy compared to existing techniques.
Optimal Savings under Transition Uncertainty and Learning Dynamics
This paper establishes the existence and structural properties of optimal consumption and saving policies under transition uncertainty with Bayesian learning, demonstrating how uncertainty about regime persistence shapes precautionary motives and long-run wealth accumulation through a newly identified dynamic mechanism.
Monge-Ampère measures on balanced polyhedral spaces
This paper establishes a framework for constructing Monge-Ampère measures and solving associated variational equations on balanced polyhedral spaces by leveraging convex function theory and tropical intersection, while also connecting these results to non-archimedean pluripotential theory.