Minimization of λ2(Ω)\lambda_2(\Omega) with a perimeter constraint

We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two points where the curvature vanishes. In $N$ dimensions, we prove a more general existence theorem for a class of functionals which is decreasing with respect to set inclusion and $\gamma$ lower semicontinuous.Comment: Indiana University Mathematics Journal (2009) to appea

On the quantitative isoperimetric inequality in the plane with the barycentric distance

In this paper we study the following quantitative isoperimetric inequality in the plane: $\lambda_0^2(\Omega) \leq C \delta(\Omega)$ where $\delta$ is the isoperimetric deficit and $\lambda_0$ is the barycentric asymmetry. Our aim is to generalize some results obtained by B. Fuglede in \cite{Fu93Geometriae}. For that purpose, we consider the shape optimization problem: minimize the ratio $\delta(\Omega)/\lambda_0^2(\Omega)$ in the class of compact connected sets and in the class of convex sets

Dynamical spectral unmixing of multitemporal hyperspectral images

In this paper, we consider the problem of unmixing a time series of hyperspectral images. We propose a dynamical model based on linear mixing processes at each time instant. The spectral signatures and fractional abundances of the pure materials in the scene are seen as latent variables, and assumed to follow a general dynamical structure. Based on a simplified version of this model, we derive an efficient spectral unmixing algorithm to estimate the latent variables by performing alternating minimizations. The performance of the proposed approach is demonstrated on synthetic and real multitemporal hyperspectral images.Comment: 13 pages, 10 figure

Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

This paper deals with the eigenvalue problem for the operator $L=-\Delta -x\cdot \nabla$ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue $\lambda_k$ of $L$ under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any $c>0$ and $k\in \mathbb{N}$ the following minimization problem \min\left\{\lambda_k(\Omega): \> \Omega \>\mbox{quasi-open} \>\mbox{set}, \> \int_\Omega e^{|x|^2/2}dx\le c\right\} has a solution

A reproducible approach with R markdown to automatic classification of medical certificates in French

In this paper, we report the ongoing developments of our first participation to the Cross-Language Evaluation Forum (CLEF) eHealth Task 1: “Multilingual Information Extraction - ICD10 coding” (Névéol et al., 2017). The task consists in labelling death certificates, in French with international standard codes. In particular, we wanted to accomplish the goal of the ‘Replication track’ of this Task which promotes the sharing of tools and the dissemination of solid, reproducible results.In questo articolo presentiamo gli sviluppi del lavoro iniziato con la partecipazione al Laboratorio CrossLanguage Evaluation Forum (CLEF) eHealth denominato: “Multilingual Information Extraction - ICD10 coding” (Névéol et al., 2017) che ha come obiettivo quello di classificare certificati di morte in lingua francese con dei codici standard internazionali. In particolare, abbiamo come obiettivo quello proposto dalla ‘Replication track’ di questo Task, che promuove la condivisione di strumenti e la diffusione di risultati riproducibili

Enfers du Nom dans A la recherche du temps perdu

D\ue9signer (en contexte) n\u2019est pas d\ue9nommer (stablement). Les \uab \ueatres de papiers \ubb de la Recherche acqui\ue8rent leur statut de personnage dans le jeu et la tension qui s\u2019instaurent entre ces deux modalit\ue9s r\ue9f\ue9rentielles : le pr\ue9nom, le nom de famille, les titres, les surnoms, sobriquets et diminutifs, les d\ue9formations injurieuses constituent le paradigme dont tant\uf4t la progression tant\uf4t l\u2019alternance file la chaine r\ue9f\ue9rentielle du personnage tout au long du roman. Que le nom puisse \ueatre malmen\ue9 ou concurrenc\ue9 permet au paysage social du roman de se transformer par endroits et pas \ue0-coups. Deux tendances oppos\ue9es poussent \ue0 modifier un nom propre : un d\ue9sir d\u2019ascension sociale, ou sym\ue9triquement, et bien plus fr\ue9quemment, un geste de rejet, un verdict d\u2019exclusion du groupe, qui trace pour la victime le seuil m\ueame de l\u2019enfer social : l\u2019isolement. Cet article analyse les divers proc\ue9d\ue9s phon\ue9tiques, morphologiques et syntaxiques mis en \u153uvre par les personnages pour d\ue9figurer le nom d\u2019autrui