## Comportement en temps grand de solutions de systèmes intégrables sur le tore

Type:
Site:
Date:
11/10/2012 - 13:30 - 14:30
Salle:
P1 - 012
Orateur:
FERMANIAN Clotilde

## WANG Guofang

Date:
Mer, 03/10/2012 - Ven, 05/10/2012
Site:
Nom:
WANG
Prénom:
Guofang
Origine:
Université de Freiburg
Origine:
Allemagne
Invitant:
GE Yuxin

## ZHANG Ping

Date:
Lun, 01/10/2012 - Mer, 31/10/2012
Site:
Nom:
ZHANG
Prénom:
Ping
Origine:
Academy of Mathematics and System sciences, Beijing
Origine:
République populaire de Chine
Invitant:
DANCHIN Raphaël

## RODIAC Rémy

Situation:
Non permanent
Nom:
RODIAC
Prénom:
Rémy
Site:
Site:
Statut:
Équipe de recherche:
Équations aux dérivées partielles
Courriel:
remy [dot] rodiac [at] u-pec [dot] fr
Téléphone:
01 45 17 14 24

## YASSINE Zeina

Situation:
Non permanent
Nom:
YASSINE
Prénom:
Zeina
Site:
Site:
Statut:
Équipe de recherche:
Géométrie et courbure
Courriel:
zeina [dot] yassine [at] u-pec [dot] fr
Téléphone:
01 45 17 65 72

## BETERMIN Laurent

Situation:
Non permanent
Nom:
BETERMIN
Prénom:
Laurent
Site:
Site:
Statut:
Équipe de recherche:
Équations aux dérivées partielles
Courriel:
laurent [dot] betermin [at] u-pec [dot] fr
Téléphone:
01 45 17 14 24

## Pattern generation problems arising in multiplicative integer systems

Type:
Type:
Site:
Date:
07/09/2012 - 11:00 - 12:00
Salle:
P1-02
Orateur:
BAN Jung-Chao
Localisation:
Université de Dong Hwa
Localisation:
République populaire de Chine
Résumé:

This talk investigates a multiplicative integer system using a method that was developed for studying pattern generation problems. The entropy and the Minkowski dimensions of general multiplicative systems can thus be computed. A multi-dimensional decoupled system is investigated in three main steps. (I) Identify the admissible lattices of the system; (II) compute the density of copies of admissible lattices of the same length, and (III) compute the number of admissible patterns on the admissible lattices. A coupled system can be decoupled by removing the multiplicative relation set and then performing procedures similar to those applied to a decoupled system. The admissible lattices are chosen to be the maximum graphs of different degrees which are mutually independent. The entropy can be obtained after the remaining error term is shown to approach zero as the degree of the admissible lattice tends to infinity.

## On control of Sobolev norms of solutions of semilinear wave equations with localized data

Type:
Site:
Date:
19/06/2012 - 15:30 - 16:30
Salle:
à préciser
Orateur:
Tristan Roy
Localisation:
Université de Princeton
Localisation:
États-Unis
Résumé:

Abstract: We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the $H^s$, $s<1$, closure of compactly supported data inside a ball of radius $R$, with $R$ a fixed but positive number. In order to do that we perform an analysis in the neighborhood of the cone, using an almost Shatah-Struwe estimate, an almost conservation law and some estimates for localized functions: this allows to prove a decay estimate and establish a low frequency estimate of the position of the solution. Then, in order to establish a high frequency estimate of the solution, we use this decay estimate and another almost conservation law.

## Asymptotic behavior of critical points of an energy involving a "circular-well" potential"

Type:
Site:
Date:
19/06/2012 - 14:00 - 15:00
Salle:
à préciser
Orateur:
Itaï Shafrir
Localisation:
Université de Haïfa
Localisation:
Israël

## Gradient matching approaches for parameter estimation in biological models defined by Ordinary Differential

Type:
Site:
Date:
13/06/2012 - 14:00 - 15:00
Salle:
P1 05
Orateur:
Clairon Quentin
Résumé:

Biological processes are commonly described Ordinary Differential Equation (ODE) taking a
general form, :
$$̇ X'=f(X,t,\theta)$$

as it gives the ability to have a mechanistic descripion of biological systems. These ODE critically
rely on a set of parameter θ which have to be estimated from sparse and noisy data. Classical
statistical estimators (such as least squares, maximum likelihood) often fail to give proper estimation
due to the implicit nature of the model, heavy computation and the presence of local minima in
the objective function. New methods have been proposed to circumvent these difficulties. Among
them, two step estimators use classical nonparametric technics in order to “regularize” the estimation
problem. These estimators use:
1. A first preliminary smoothing step to obtain an estimator of the solution $\varphi^∗$ (called $\hat{X_n}$ )
directly from the data,
2. A second step of parametric estimation by optimizing a functional criteria constructed from
$\hat{X_n}$ .
Our aim here will be to describe these methods theoritically and through a simple example coming
from biological modeling.