Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

SesIndexCreatoR: An R Package for Socioeconomic Indices Computation and Visualization

Abstract: In order to study social inequalities, indices can be used to summarize the multiple dimensions of the socioeconomic status. As a part of the Equit’Area Project, a public health program focused on social and environmental health inequalities; a statistical procedure to create (neighborhood) socioeconomic indices was developed. This procedure uses successive principal components analyses to select variables and create the index. In order to simplify the application of the procedure for non-specialists, the R package SesIndexCreatoR was created. It allows the creation of the index with all the possible options of the procedure, the classification of the resulting index in categories using several classical methods, the visualization of the results, and the generation of automatic reports.

ODE-based Double-preconditioning for Solving Linear Systems $A^{\alpha}x = b$ and $f(A)x=b$

Abstract: This paper is devoted to the computation of the solution to fractional linear algebraic systems using a differential-based strategy to evaluate matrix-vector products $A^\alpha x$, with $\alpha \in \mathbb{R}^{*}_{+}$. More specifically, we propose ODE-based preconditioners for efficiently solving fractional linear systems in combination with traditional sparse linear system preconditioners. Different types of preconditioners are derived (Jacobi, Incomplete LU, Pade) and numerically compared. The extension to systems $f (A)x = b$ is finally considered.

Growth of a population of bacteria in a dynamical hostile environment

Abstract: We study the growth of a population of bacteria in a dynamical hostile environment corresponding to the immune system of the colonised organism. The immune cells evolve as subcritical open clusters of oriented percolation and are perpetually reinforced by an immigration process, while the bacteria try to grow as a supercritical oriented percolation in the remaining empty space. For appropriate values of the parameters, we prove that the population of bacteria grows linearly. In this perspective, we build general tools to study dependent percolation models issued from renormalization processes.

A probabilistic approach to Dirac concentration in nonlocal models of adaptation with several resources

Abstract: This work is devoted to the study of scaling limits in small mutations and large time of the solutions u^e of two deterministic models of phenotypic adaptation, where the parameter e > 0 scales the size of mutations. The first model is the so-called Lotka-Volterra parabolic PDE in R d with an arbitrary number of resources and the second one is an adaptation of the first model to a finite phenotype space. The solutions of such systems typically concentrate as Dirac masses in the limit e → 0. Our main results are, in both cases, the representation of the limits of e log u^e as solutions of variational problems and regularity results for these limits. The method mainly relies on Feynman-Kac type representations of u e and Varadhan's Lemma. Our probabilistic approach applies to multi-resources situations not covered by standard analytical methods and makes the link between variational limit problems and Hamilton-Jacobi equations with irregular Hamiltonians that arise naturally from analytical methods. The finite case presents substantial difficulties since the rate function of the associated large deviation principle has non-compact level sets. In that case, we are also able to obtain uniqueness of the solution of the variational problem and of the associated differential problem which can be interpreted as a Hamilton-Jacobi equation in finite state space.