Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Local limit theorems, like the famous deMoivre-Laplace theorem, have inspired similar results for ergodic sums $S_nf=\sum_{0\le i<n} f\circ T^i$ in dynamical systems $T:X\to X$ and for measurable functions $f:X\to\mathbb R$.
The talk will provide exact formulations of such results and discuss applications to Fuchsian groups, continued fractions and local times for fractal Gaussian noise.

We present several parameter estimation problems dealing with situations when the model depends on the unknown parameter in a non-regular way. The problems correspond to observations of different natures, but all have the same type of singularity: a cusp. We will see that all the considered models give rise to the same limiting likelihood ratio process.

A weighted Shiryaev-Roberts change detection procedure is shown to approximately minimize the

expected delay to detection as well as higher moments of the detection delay among all

change-point detection procedures with the given low maximal local probability of a false alarm

In this talk we will give some dynamical properties of group actions on
local dendrites. A local dendrite is a continuum for which every point has a
neighborhood which is a dendrite (a locally connected continuum containing
no homeomorphic copy to the circle).
In the first part, we will review some results concerning the structure of
minimal sets and give some new results in this context obtained in joint
work with El Houcein El Abdalaoui. In the second part of the talk, we will

Ce travail est motivé par l'étude d'un modèle de croissance de plante mécaniste dont les paramètres peuvent dépendre du génotype. L'échelle de l'étude étant celle de la population, nous introduisons alors un modèle à effets mixtes pour décrire les variabilités inter- et intra-génotyptiques. Puis, l'objectif est de déterminer les paramètres qui sont communs à tous les génotypes, et ceux qui dépendent du génotype. Les premiers sont appelés effets fixeset les seconds effets aléatoires.

Gene regulatory networks (GRNs) are powerful tools to represent and analyse complex biological systems and enable the modelling of functional relationships between elements of these systems. In this talk, I will focus on theoretical analysis and the use of statistical and optimization methods in the context of GRN inference. The first part will be dedicated to the study of statistical learning methods to infer networks from sparse linear regressions in a high-dimensional setting.