273 papers
This paper establishes a quantitative boundary-aware stability theorem for nonlocal proximity sublevel sets of finitely sampled curves, combining it with Hermite interpolation and interval arithmetic to derive sufficient sampling conditions ensuring that the curve and its interpolant deformation retract onto a common core.
This paper presents a positive, stable, and first-order convergent discontinuous Galerkin method for variable-order advection-diffusion equations that utilizes backward-Euler generalized convolution quadrature with composite Gaussian compression to efficiently handle time-dependent fractional orders on arbitrary grids.
This paper presents a governance-aware nonlinear reservoir model that establishes rigorous stability conditions for neural network policies, demonstrating through a synthetic drought benchmark that while certified networks trained only on nominal data fail under distribution shifts, a hybrid policy combining networks trained on diverse conditions achieves superior robustness and performance across varying drought scenarios.
This paper presents a robust, parallel C++ algorithm that combines adaptive zero-counting, two-dimensional bisection, and Newton-Kantorovich methods to efficiently compute and certify millions of zeros for analytic functions, including exponential polynomials and partial sums of the Riemann zeta function, with high precision.
This paper introduces a residual-certified Volterra predictor–corrector framework that combines Adams–Bashforth–Moulton discretization with Gauss–Legendre quadrature to provide reliable numerical solutions and a posteriori error diagnostics for nonlinear fractional differential equations and their stochastic financial applications.
This paper presents a unified set of Gaussian-type quadrature formulas with common nodes and weights for integrals over semi-infinite intervals involving power-law weights and various kernels, which are validated through the successful numerical solution of a singular integral equation arising from a two-dimensional elasticity problem.
This paper introduces the Intersection Euler Characteristic Profile, a stable and canonical invariant for analyzing the topological interaction of multiple colored point clouds via Euler calculus, which can be computed efficiently using Alpha-complex sweeps and refined via relative homology to consistently recover the underlying shape properties.
This paper introduces a unified fuzzy centrality profile framework for -fuzzy graphs that integrates diverse centrality measures to enable comprehensive vertex comparison and assess ranking stability through profile dominance and overlap metrics.
This paper develops a discounted dynamic Trust-Building Game to characterize a pure stationary Markov equilibrium, demonstrating that the trust builder's optimal signaling policy follows a unique activation-band structure over intermediate public states rather than a simple monotone threshold, while providing exact analytical bounds and numerical validations for cooperation dynamics.
The paper introduces pCHA, a novel reconstruction framework utilizing p-adic ultrametric geometry and categorical layers to achieve robust forecasting of chaotic dynamics under extreme data scarcity, significantly outperforming existing machine learning and dynamical system baselines across synthetic, real-world, and experimental benchmarks.