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Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping
arXiv:2502.19947v3 Announce Type: replace-cross Abstract: In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite Volume Method (FVM) and we are interested in deriving the stability estimates and the convergence of the numerical solution to the continuous one. Numerical experiments are performed to confirm the...
Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators
Announce Type: replace Abstract: Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equations. Substantial computational issues arise from the treatment of the physically most relevant three-dimensional case with Coulomb-type interaction. This work is concerned with the introduction and numerical comparison of novel approaches for the reliable and efficient evaluation...
A machine-learning-assisted progressive digit-randomness screening framework for detecting non-random patterns in raw numerical research data
Announce Type: new Abstract: Raw numerical datasets remain less systematically examined in integrity screening than images, plagiarism, or summary-statistic inconsistencies. We developed the Fabrication-risk Digit Randomness Screening model (FDRS), a statistical and machine-learning framework for detecting non-random digit-pattern irregularities in numerical research data. FDRS integrates single- and joint-decimal-digit tests, Cramer's V, entropy metrics, Kullback-Leibler divergence,...
Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators
arXiv:2402.02247v3 Announce Type: replace Abstract: Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equations. Substantial computational issues arise from the treatment of the physically most relevant three-dimensional case with Coulomb-type interaction. This work is concerned with the introduction and numerical comparison of novel approaches for the reliable and...
Nonlinear numerical schemes using specular differentiation for initial value problems of first-order ordinary differential equations
arXiv:2601.09900v4 Announce Type: replace Abstract: This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical schemes for solving initial value problems for first-order ordinary differential equations. Based on numerical simulations, we select one scheme and prove its second-order consistency and convergence.
Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
arXiv:2606.08203v1 Announce Type: new Abstract: Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this...
Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
arXiv:2606.03606v1 Announce Type: new Abstract: Large language models achieve strong performance on arithmetic reasoning benchmarks, and one common response to arithmetic brittleness is to delegate computation to code. Yet models are still often used in settings where they must reason directly from natural language, and trustworthy models should solve small-number arithmetic word problems without external tools. Prior work shows that LLMs are sensitive to numerical variation: a model may...
Testing LLM Arithmetic Reasoning Generalization with Automatic Numeric-Remapping Attacks
arXiv:2606.03606v2 Announce Type: replace Abstract: Large language models achieve strong performance on arithmetic reasoning benchmarks, and one common response to arithmetic brittleness is to delegate computation to code. Yet models are still often used in settings where they must reason directly from natural language, and trustworthy models should solve small-number arithmetic word problems without external tools. Prior work shows that LLMs are sensitive to numerical variation: a model may...
Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time
arXiv:2401.02878v5 Announce Type: replace-cross Abstract: Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the $L^{q}$ sense.
Utility-Preserving De-Identification for Math Tutoring: Investigating Numeric Ambiguity in the MathEd-PII Benchmark Dataset
arXiv:2602.16571v3 Announce Type: replace Abstract: Large-scale sharing of dialogue data is key to advancing the science of teaching and learning, yet rigorous de-identification remains a major barrier. In mathematics tutoring transcripts, numeric expressions frequently resemble structured identifiers (e.g., dates or IDs), leading generic Personally Identifiable Information (PII) detection systems to over-redact core instructional content and reduce data utility. This work asks how to detect...