Pour modéliser les systèmes complexes, nous proposons la théorie de la prétopologie, qui est un outil de modélisation quant au concept de proximité (Belmandt (1993)). Ce puissant outil permet l’analyse et la classification de structures complexes (Le et al. (2008)). Afin de suivre les processus de développement du modèle, il permet des opérations de dilatation, d’alliance, d’adhérence, de ferme...

— The paper consists of two parts. In the first part, we explain an excellent idea, due to mathematicians of the 19-th century, of naturally developing classical Galois theory of algebraic equations to an infinite dimensional Galois theory of nonlinear differential equations. We show with an instructive example how we can realize the idea of the 19-th century in a rigorous framework. In the sec...

The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We approach the associahedron from the point of view of discrete homotopy theory, that is we consider 5-cycles in the 1-skeleton of the associahedron to be combinat...

1. IRIT Université Toulouse Capitole France @irit.fr 2. CEDRIC – CNAM Paris – France @cnam.fr 3. CBI Sté TRIMANE Saint Germain en Laye – France @gmail.com RESUME : La transformation digitale des entreprises et plus largement celle de la société, entraine une évolution des bases de données vers le Big Data. Nos travaux s’inscrivent dans cette mutation et conce...

Abstract We show that some classical identities about multiplicative functions, and the Riemann zeta-function, may conveniently be interpreted in terms of the addition of ±1 to some alphabets. Résumé Nous montrons que des identités classiques concernant des fonctions multiplicatives de la théorie des nombres, et la fonction zeta de Riemann, s’interprètent commodément en terme de l’opération : “...

Considering probability theory in which the semifield of positive real numbers is replaced by the idempotent semifield of real numbers (union infinity) endowed with the min and plus laws leads to a new formalism for optimization. Probability measures correspond to minimums of functions that we call cost measures, whereas random variables correspond to constraints on these optimization problems ...

In this paper, we provide a convergence analysis of a projection semi-implicit scheme for the simulation of fluid-structure systems involving an incompressible viscous fluid. The error analysis is performed on a fully discretized linear coupled problem: a finite element approximation and a semiimplicit time-stepping strategy are respectively used for space and time discretization. The fluid is ...

English version: We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q = 0. This numerical method is tested on analytical tests. Version Française :...

In this paper, we study the rate of convergence of a symmetrized version of the classical Euler scheme, applied to the discretisation of the solution of a stochastic differential equation with a diffusion coefficient function of the form |x|, α ∈ [1/2, 1). For smooth test functions, we show that the weak error is of order one as for the classical Euler scheme. More over, the symmetrized version...

La notion de graphes augmentés a été introduite dans le but d’analyser le phénomène des ”six degrés de séparation entre individus” observé empiriquement par le psychologue Milgram dans les années 60. De façon formelle, un graphe augmenté est une paire (G,φ), où G est un graphe et φ une collection de distributions de probabilité {φu,u∈V (G)}. Un lien supplémentaire est attribué à chaque noeud u ...