We present a discretization strategy for compressible fluids systems for unstrutctured grids based a Lagrange-Remap approach that does not involve any moving mesh. We present the stability properties of this solver and present a natural semi-implicit extension of the method that allows to remain stable under a CFL condition involving only the material velocity. We present another modification of the solver that allows to provide an accurate and stable solver for simulation involving low-Mach regions in the flow. This work is a collaboration with Christophe CHALONS and Mathieu GIRARDIN.

Among the numerous practical application of Statistical Process Control (SPC) is the monitoring of the number of defecting (non-conforming) items that are produced from a manufacturing company or the number of the incidents of a disease in a specic area. The basic aim is to detect any kind of change (e.g., an increase in the number of non-conforming items) quickly and accurately. In such cases, the available data are usually discrete (counts) and for process monitoring, the ordinary control charts for attributes (e.g., np-, p-, c- and u-charts) are used in practice. The main assumption is that the data come from the Poisson or the binomial distribution.

Due to technological advancements and automation progress, many processes are now characterized by a low fraction of non-conforming items. That kind of processes are known as high-yield processes and it is very common to have an excessive number of samples with zero non-conforming items. Consequently, due to the inherent over-dispersion of data, the ordinary schemes for attributes cannot be eactively used because of the high false alarm rates and the low statistical power in the detection of changes in the parameters of the process.

In this talk, new control charts, which are suitable for the monitoring of high-yield processes, are proposed and studied. Instead of the ordinary Poisson and binomial distributions, we assume that a proper parametric model for the process is the zero-inaged Poisson (ZIP) or the zero-inated Binomial (ZIB) distribution. We provide the Markov chain methodology for the theoretical study of each chart as well as aspects of their statistical design. Also, numerical comparisons between the dievent control charting techniques are given. Finally, the practical application of the proposed techniques is discussed.
(joint work with Prof. Philippe Castagliola and Prof. Petros Maravelakis)

Chemotaxis is the phenomenon in which cells direct their motion according to a chemical present in their environment. Since experimental observations have shown that the motion of bacteria (e.g. Escherichia Coli) is due to the alternation of 'runs and tumbles', mathematical modelling thanks to a kinetic description has been proposed. The starting point of the study is the so-called Othmer-Dunbar-Alt model governing the dynamics of the distribution function of cells. From this system, macroscopic model can be derived after rescaling. When the taxis is small compared to the unbiased movement of cells, the scaling must be of diffusive type.

In this presentation, we focus on a theoretical analysis and the use of statistical and optimization methods in the context of sparse linear regressions in a high-dimensional setting. The first part of this work is dedicated to the study of statistical learning methods, more precisely penalized methods and greedy algorithms. The second part concerns the application of these methods for gene regulatory networks inference. Gene regulatory networks are powerful tools to represent and analyse complex biological systems, and enable the modelling of functional relationships between elements of these systems. We thus propose to develop optimization methods to estimate relationships in such networks.

On commencera par un rappel sur les structures auto-distributives (quandles, racks etc.), leurs homologies et leurs applications aux théories des nœuds et des tresses. Ensuite on présentera une théorie homologique des opérateurs de Yang-Baxter, où le flot d’idées va changer de sens : c’est la théorie des tresses qui va donner des méthodes et des inspirations pour une étude algébrique. La 3ème partie de l’exposé fermera la boucle : on munira diverses structures algébriques (quandle, algèbre associative, algèbre de Lie, bigèbre etc.) d'opérateurs de Yang-Baxter, de telle sorte que la théorie homologique associée contienne les homologies usuelles des structures en question. Comme application, on obtient une explication conceptuelle des parallèles entre les théories homologiques des structures auto-distributives et associatives, mis en évidence par J.Przytycki.

Dans cet exposé je vais présenter un travail fait en collaboration avec R. Mazzeo et F. Pacard sur la construction de sous-variétés de courbure moyenne constante en codimension quelconque dans les variétés riemanniennes munies de métriques génériques. Notre résultat est une généralisation du théorème de R. Ye qui construit des familles d'hypersurfaces de courbure moyenne constante qui sont des petites déformations de sphères géodésiques centrées en des points critiques non-dégénérés de la courbure scalaire et d'un travail plus récent de F. Pacard et X. Xu où de telles hypersurfaces sont obtenues autours de points critiques d'un autre invariant de courbure.

En codimension quelconque, on définit les sous-variétés de courbure moyenne constante comme les bords des sous-variétés qui sont des points critiques d'une certaine énergie. En utilisant des techniques développées par Pacard et Xu, on construit telles sous-variétés autours des points critiques d'une fonctionnelle, qu'on appelle la courbure scalaire partielle, qui est définie sur le fibré grassmanien de la variété ambiante et coïncide avec la courbure scalaire dans le cas de codimension 1.