diffusion models

Capital Flight and Regional Divergence in a Spatial Model of Financial Contagion

ABSTRACT This paper investigates a reaction–diffusion–chemotaxis model describing the interaction between financial instability and spatial economic differentiation. The model incorporates a herding mechanism that amplifies speculative behavior and a chemotactic flux representing capital reallocation in response to exp...

A few-shot learning framework using multimodal rheological features for local prepreg thickness prediction in multilayer PCBs

As multilayer printed circuit boards (PCBs) move toward high-frequency and high-speed applications, back-drilling stub control and impedance matching have become critical for signal integrity. Their accuracy is strongly governed by the micrometer-level stability of prepreg (PP) dielectric thickness during lamination. H...

Diffusion Models for Advances in Manufacturing Quality Abrasive Grains

La résolution spectrale de Turing dans le vide actif / The Turing spectral resolution in the active vacuum.

DESCRIPTION — VERSION WORD (FRANÇAIS, MCDS v3.1) Ce dépôt présente le manuscrit de référence « La résolution spectrale de Turing dans le vide actif », consacré à la formulation analytique de l’instabilité de Turing spectrale pure dans le cadre du continuum MCDS (Modified Continuity Disformal Structure). Contrairement a...

Synthèse exécutive IA de luxe 2025

Abstract ENThis document, produced with the assistance of ChatGPT o3 and ChatGPT 5 Thinking, is released under the Apache 2.0 licence. It is a voluntary defensive publication (prior art) and therefore enters the prior art upon release under the applicable patent statutes: art. L 611-11 CPI (French Intellectual Property...

HDSI-YOLO: Hierarchical-semantics Driven Insulator Defect Detection with Cross-domain Generalization

Insulator defect detection is a core task of intelligent inspection of power transmission lines, but existing deep-learning detectors face two bottlenecks: severe semantic ambiguity among rare defect classes (broken vs. pollution-flashover) under flat classification heads, and poor cross-domain generalization across da...

A Technical Comment on the Finite-Time Stability Analysis of a Discrete-Time Generalized Reaction–Diffusion System

This technical note examines the impulsive model and finite-time stability proof in O. A. Almatroud and A. Ouannas, Mathematics 12 (2024), article 3679 (DOI: 10.3390/math12233679). It shows that the published error impulse omits an affine term after translation by the stated nonzero equilibrium; both numerical targets...

Multimodal Magnetic Resonance Imaging and Machine Learning Uncovers Distinct Progression Patterns in Friedreich Ataxia.

Longitudinal multimodal MRI shows distinct neurodegenerative progression patterns in FRDA that are not fully captured by conventional clinical measures, and provides a basis for investigating imaging-derived disease heterogeneity and its potential relevance to participant stratification in clinical trials.

stochastic-rs: quantitative finance and stochastic process simulation in Rust

stochastic-rs is an open-source Rust library for quantitative finance and stochastic process simulation. It provides 120+ stochastic processes (diffusion, jump, fractional and rough volatility, short-rate, HJM, LMM), option pricing and model calibration (Black-Scholes-Merton, Heston, SABR, rough Bergomi, Lévy, double H...

Y101. A Dream-Born Paradigm: Behavioral Resonance Gravitation Reshaping the Future Mode of Human Production

This paper proposes the A Dream-Born Paradigm, a new underlying operating logic for the information age that fundamentally subverts the industrial-era information dissemination model of "imposing information on people". Different from the traditional push-based production and communication system relying on capital and...

Beyond the Data Paradigm — Freedom Intelligence and the Structural Laws of Navigability

Machine learning's dominant paradigm—whether model-centric or data-centric—treats intelligence as the extraction of statistical patterns from behavioral records. This approach has delivered remarkable engineering feats. Yet something foundational is missing. Data is not reality: it is a finite record of trajectories th...

A Technical Comment on the Finite-Time Stability Analysis of a Discrete-Time Generalized Reaction–Diffusion System

This technical note examines the impulsive model and finite-time stability proof in O. A. Almatroud and A. Ouannas, Mathematics 12 (2024), article 3679 (DOI: 10.3390/math12233679). It shows that the published error impulse omits an affine term after translation by the stated nonzero equilibrium; both numerical targets...