2842 papers
This paper provides a comprehensive review of the Partial Information Decomposition (PID) framework by integrating diverse formalisms into a unified language, systematically evaluating their adherence to known properties, mapping theorems that reveal relationships and incompatibilities between these properties, and charting a path for future theoretical and empirical advancements.
This paper investigates the analytic continuation and prime-restricted theory of arctanh sums , establishing their meromorphic extension with specific poles and zeros, deriving Laurent expansions and Mittag-Leffler decompositions, and proving the unconditional transcendence of their prime-restricted analogues via a -cancellation mechanism.
This paper employs the AlphaEvolve computational engine to explore three combinatorial problems—graph reconstruction, the Alon-Tarsi parity problem, and Rota's Basis Conjecture—by iteratively refining local correcting steps to generate explicit algorithms and structural patterns that serve as foundations for future traditional mathematical proofs.
This paper utilizes Markov models and Monte Carlo simulations to analyze how the average duration of Chutes and Ladders changes as die roll probabilities approach certainty and to evaluate the impact of six distinct strategies involving optional coin-flip moves on game length.
This paper introduces a unified recursive framework that constructs elliptic extensions of Clausen-type functions by replacing trigonometric seeds with Jacobi theta functions, thereby establishing a structural correspondence between circular and elliptic settings while organizing the hierarchy into a single analytic object.
This numerically driven study establishes a robust multi-scale framework demonstrating that the inverse eigenvalue loci of generalized Lucas sequences exhibit a striking low-distortion geometric and potential-theoretic correspondence with the boundary of the Mandelbrot set, revealing shared structural organization across geometric, harmonic, and statistical levels.
This paper reformulates Constructal evolution as a nonsmooth dynamical system governed by Filippov differential inclusions, proving that irreversible transport constraints and resistance dissipation guarantee the existence, uniqueness, and global exponential stability of optimal flow architectures without relying on static optimization.
This paper establishes a framework for defining self-adjoint realizations of 2d-dimensional canonical systems through symplectic geometry and Lagrangian boundary conditions, demonstrating their critical application in analyzing the spectral stability of traveling waves and solitons in nonlinear partial differential equations.
This paper serves as a corrigendum and addendum to the authors' 2024 work on categoricity-like properties in first-order logic, providing necessary corrections and supplementary insights to the original study.
This paper investigates linear preserver problems on the space of Toeplitz matrices over real or complex fields, providing characterizations for preservers of rank-one matrices and determinants while also discussing related results for other structured matrices.
This paper analyzes a normalized two-dimensional competitive Lotka-Volterra model of state-society interaction, demonstrating that as parameters approach a critical coexistence threshold, the system exhibits slow convergence and prolonged transient dynamics organized within a narrow corridor around a balance manifold, even in the absence of bistability.
This paper compares three fixed-dimension satisfiability semantics for quantum logic—standard Hilbert-lattice, global commuting-projector, and local partial-Boolean—proving a strict hierarchy where the standard semantics is strictly more expressive than the others, as demonstrated by an explicit formula that is satisfiable in the standard semantics but unsatisfiable under the other two for all dimensions .
This paper characterizes graphs with an Alon-Tarsi number of 2 and investigates the relationship between the Alon-Tarsi number and degeneracy under -sum operations.
This paper presents an age-structured PDE model of the cell cycle to analyze how the availability of population summary data, such as FACS and FUCCI measurements, influences the identifiability of model parameters and determines the minimum data requirements for successfully fitting structured population models.
This paper proposes a new goodness-of-fit test for multivariate normality that leverages -nearest neighbor estimators of Shannon entropy and Kullback-Leibler divergence to demonstrate superior power and accurate Type I error control, particularly in medium to high dimensions, compared to conventional tests.
This paper establishes necessary and sufficient conditions for the Markov property of a coupled virus-like evolving population model driven by mutually-exciting Hawkes processes, utilizing this property to derive convergence results and demonstrate a phase transition at a critical fitness level.
This paper demonstrates that pure SU(3) Yang--Mills theory on a punctured three-ball generates a finite, hadronic-scale spectral gap through a gauge-invariant quantum rotor mechanism driven by a Berry-shifted holonomy angle, thereby realizing "mass without mass" without introducing explicit mass terms or Higgs fields.
This paper extends the theory of ambidexterity by proving that the norm square induced from a weakly ambidextrous morphism commutes under Beck-Chevalley fibrations, thereby generalizing the naturality of the norm established by Hopkins and Lurie and recovering specific results on local systems and equivariant powers by Carmeli, Schlank, and Yanovski.
This paper integrates Chemical Reaction Network theory and Mathematical Epidemiology to generalize the Next Generation Matrix theorem and apply a symbolic-numeric approach, utilizing the Epid-CRN Mathematica package, for analyzing the stability and bifurcation of positive ordinary differential equations.
The paper proves the existence of a partial -system whose Ramsey number with colors exhibits tower-type growth of height .