Université Paris-Est Université Paris-Est - Marne-la-Vallée Université Paris-Est - Créteil Val-de-Marne Centre National de la Recherche Scientifique

UPEC

SOHIER Julien

Situation: 
Permanent
Nom: 
SOHIER
Prénom: 
Julien
Site: 
Site: 
Équipe de recherche: 
Probabilités et statistiques
Courriel: 
julien [dot] sohier [at] u-pec [dot] fr
Téléphone: 
01 45 17 65 99

SHMERKIN Pablo

Date: 
Mer, 16/09/2015 - Mar, 06/10/2015
Site: 
Nom: 
SHMERKIN
Prénom: 
Pablo
Origine: 
Université Torcuato di Tella
Origine: 
Argentine
Thème: 
Analyse multi-fractale
Invitant: 
SEURET Stéphane

Gradient Holder continuity for the parabolic homogeneous p-Laplacian equation

Site: 
Date: 
09/07/2015 - 14:00 - 15:00
Salle: 
P1-011
Orateur: 
SYLVESTRE Luis
Localisation: 
Université de Chicago
Localisation: 
États-Unis
Résumé: 

It is well known that p-harmonic functions are $C^{1,\alpha}$ regular, for some $\alpha>0$. The classical proofs of this fact use variational methods. In a recent work, Peres and Sheffield construct p-Harmonic functions from the value of a stochastic game. This construction also leads to a parabolic versions of the problem.
However, the parabolic equation derived from the stochastic game is not the classical parabolic p-Laplace equation, but a homogeneous of degree one version. This equation is not in divergence form and variational methods are inapplicable. We prove that solutions to this equation are also $C^{1,\alpha}$ regular in space. This is joint work with Tianling Jin.

Reaching nonlinear consensus: quadratic stochastic operators

Site: 
Date: 
03/07/2015 - 14:00 - 15:00
Salle: 
P1 018
Orateur: 
SABUROV Mansoor
Localisation: 
Université islamique internationale de Malaisie
Localisation: 
Malaisie
Résumé: 

A Multi-Agent System (MAS) gives a complete description for large-scale systems consisting of small subunits, called agents. The behavior of MAS is particularly interesting because the agents may fulfill certain tasks as a group, even the individual agent does not know about the overall task. A lot of examples come from nature, such as schooling fishes or fireflies flashing in unison. A collective behavior is also interesting for engineers when solving problems such as flocking or synchronization. This is mainly due to its important applications, including the cooperative control of unmanned air vehicles, autonomous underwater vehicles, congestion control in communication networks, swarms of autonomous vehicles or robots, autonomous formation fight, etc. In all cases the goal is to control a group of agents connected through a communication network to reach an agreement on certain quantities of interest. This problem is called the consensus problem.

Many results have been achieved on this problem. Most researches in MAS consider a linear rule of an information exchanging. However, many systems, such as for instance the well-known Kuramoto oscillator exhibit nonlinear, locally passive dynamics.

In this work, we have considered a nonlinear protocol for a structured time-invariant multi-agent system. In the multi-agent system, we present an opinion sharing dynamics as a trajectory of a cubic triple stochastic matrix. We showed that the multi-agent system eventually reaches to a consensus if either one of the following two conditions is satisfied: (i) every member of the group people has a positive subjective opinion on the given task after some revision steps or (ii) all entries of the given cubic triple stochastic matrix are positive.

We know from the theory of Markov chains that if all entries of a doubly stochastic matrix are positive then its trajectory starting from any initial point taken from the simplex converges to the center of the simplex. The similar problem was open for cubic triple stochastic matrices. In this work, we gave an affirmative answer. To the best of our knowledge, this is a pioneering result for higher dimensional stochastic matrices.

DE MAIO Umberto

Date: 
Dim, 05/07/2015 - Sam, 11/07/2015
Site: 
Nom: 
DE MAIO
Prénom: 
Umberto
Origine: 
Université de Naples Frédéric II
Origine: 
Italie
Thème: 
Analyse des EDP
Invitant: 
HADIJI Rejeb

SABUROV Mansoor

Date: 
Jeu, 02/07/2015 - Lun, 06/07/2015
Site: 
Nom: 
SABUROV
Prénom: 
Mansoor
Origine: 
Université islamique internationale de Malaisie
Origine: 
Malaisie
Thème: 
Nombres $p$-adiques
Invitant: 
LIAO Lingmin

Points doubles des processus stables au sens des opérateurs

Site: 
Date: 
22/06/2015 - 15:00 - 16:00
Salle: 
P2 131
Orateur: 
LUKS Tomasz
Localisation: 
Ecole Centrale de Marseille
Localisation: 
France
Résumé: 

Un point $x\in\mathbb{R}^d$ est appelé un point de multiplicité $k$ pour un processus $X(t)$ s’il existe $k$ temps distincts $t_1,t_2, ..., t_k \in\mathbb{R}_+$ tels que
$$X(t_1) = X(t_2) = \cdots = X(t_k) = x.$$

Dans cet exposé, nous nous intéresserons à l’ensemble des points multiples $M_k$ pour les processus de Lévy symétriques. Nous présenterons dans un premier temps une formule pour la dimension de Hausdorff de $M_k$ comme une fonction de l’exposant de Lévy. Ce résultat nous permettra ensuite d’obtenir une forme explicite de la dimension de Hausdorff de l’ensemble des points doubles $M_2$ pour les processus stables au sens des opérateurs. Un processus de Lévy $d$-dimensionnel $X(t)$ est dit stable au sens des opérateurs s’il existe une matrice carrée non singulière $B$ telle que $\{X(ct), t\ge0\}$ a la même loi que $\{c^B X(t), t\ge0\}$ pour tout $c > 0$. Dans ce cas, la dimension de Hausdorff de $M_2$ ne dépendra que des valeurs propres de $B$.

The modeling of operator self-similarity

Site: 
Date: 
22/06/2015 - 13:45 - 14:45
Salle: 
P2 131
Orateur: 
DIDIER Gustavo
Localisation: 
Université Tulane
Localisation: 
États-Unis
Résumé: 

A multivariate random process or field is called operator self-similar (o.s.s.) when its law satisfies an (operator) scaling relation according to a matrix Hurst parameter. In particular, the so-named operator fractional Brownian motion (OFBM) is the natural multivariate extension of the univariate fractional Brownian motion.

The construction of inferential methods for o.s.s. processes turns out to be rather challenging due to the presence of mixed power laws. In this talk, we will provide a broad description of the problem of modeling operator self-similarity and illustrate how operator scaling laws naturally appear in physical applications. The discussion will be centered on the wavelet estimator for OFBMs recently put forward in Abry and Didier (2015).

Mathématiques pour le grand écran (what we do in the shadows)

Site: 
Date: 
22/06/2015 - 11:00 - 12:00
Salle: 
P2 131
Orateur: 
AUBRY Jean-Marie
Résumé: 

L’industrie des effets spéciaux numériques pour le cinéma utilise d’immenses ressources informatiques et la recherche de toujours plus de réalisme conduit à une complexité sans cesse croissante. Le rendu 3D et la simulation dynamique en sont les exemples les plus coûteux. Je présenterai un solveur implicite rapide pour arbres flexibles, utilisé pour la simulation des plantes dans certains films récents.

Quelques propriétés des déplacements "SBD"

Site: 
Date: 
18/06/2015 - 14:00 - 15:00
Salle: 
P1-008
Orateur: 
CHAMBOLLE Antonin
Localisation: 
École polytechnique
Localisation: 
France
Résumé: 

On s'intéressera à des propriétés fines des déplacements de la classe "SBD" (special bounded deformation functions) dont le gradient symétrisé est une mesure absolument continue plus une partie de saut (pouvant modéliser une fracture). On discutera quelques propriétés fines de ces fonctions (inégalités de type Poincaré-Korn, approximation par des fonctions plus régulières).

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