projet ANR PIECE

Transcription

projet ANR PIECE

PROGRAMME
Projet : PIECE
JEUNES CHERCHEUSES ET
JEUNES CHERCHEURS
DOCUMENT SCIENTIFIQUE
EDITION 2012
Nom et prénom du
coordinateur /
Coordinator’s name
MALRIEU Florent
Acronyme /
Acronym
PIECE
Titre de la
proposition de
projet
PDMP : inférence, évolution, contrôle et ergodicité
PDMP: Inference, Evolution, Control and Ergodicity
Proposal title
Comité
d’évaluation /
Evaluation
committee
SIMI1 – Mathématiques et interactions
Type de recherche /
Type of research
x Recherche Fondamentale / Basic Research
 Recherche Industrielle / Industrial Research
 Développement Expérimental : Experimental
Development
Aide totale
demandée /
Grant
requested
155854,40 €
ANR-GUI-AAP-05 – Doc Scientifique 2012 – V2
Durée du
projet / Projet
duration
48 mois
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PROGRAMME
Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
1. RÉSUME DE LA PROPOSITION DE PROJET / EXECUTIVE SUMMARY...........................3
2. CONTEXTE, POSITIONNEMENT ET OBJECTIFS DE LA PROPOSITION / CONTEXT, POSITION AND
OBJECTIVES OF THE PROPOSAL............................................................3
2.1. Contexte et enjeux économiques et sociétaux / Context, social and economic
issues ............................................................................................. 3
2.2. Positionnement du projet / Position of the project.....................................3
2.3. État de l'art / State of the art................................................................. 4
2.4. Objectifs et caractère ambitieux/novateur du projet / Objectives, originality
and novelty of the project.................................................................. 5
3. PROGRAMME
SCIENTIFIQUE ET TECHNIQUE, ORGANISATION DU PROJET
TECHNICAL PROGRAMME,
PROJECT
/ SCIENTIFIC AND
ORGANISATION........................................ 6
3.1. Programme scientifique et structuration du projet / Scientific programme,
project structure............................................................................... 6
3.2. Management du projet / Project management..........................................6
3.3. Description des travaux par tâche / Description by task.............................6
3.3.1 Tâche 1 / Task 1 : Limits and Scalings
3.3.2 Tâche 2 / Task 2 : Control and Regularity
3.3.3 Tâche 3 / Task 3 : Estimation and Simulation
6
7
7
3.4. Calendrier des tâches, livrables et jalons / Tasks schedule, deliverables and
milestones........................................................................................9
4. STRATÉGIE DE VALORISATION, DE PROTECTION ET D’EXPLOITATION DES RÉSULTATS /
DISSEMINATION AND EXPLOITATION OF RESULTS. INTELLECTUAL PROPERTY..............10
4.1. Communication to the mathematical community.....................................10
4.2. Communication to the scientific community at large................................11
4.3. Communication to the general public..................................................... 11
5. DESCRIPTION
DE L’EQUIPE
/ TEAM
DESCRIPTION
........................................11
5.1. Description, adéquation et complémentarité des participants / Partners
description & relevance, complementarity...........................................11
5.2. Qualification du coordinateur du projet / Qualification of the project
coordinator..................................................................................... 11
5.3. Qualification, rôle et implication des participants / Qualification and
contribution of each partner..............................................................11
6. JUSTIFICATION
/ SCIENTIFIC JUSTIFICATION OF
REQUESTED RESSOURCES............................................................... 13
7. RÉFÉRENCES BIBLIOGRAPHIQUES / REFERENCES..........................................15
8. FICHES INDIVIDUELLES ..................................................................21
8.1.
8.2.
8.3.
8.4.
8.5.
8.6.
8.7.
8.8.
SCIENTIFIQUE DES MOYENS DEMANDÉS
Florent MALRIEU................................................................................. 21
Jean-Baptiste BARDET......................................................................... 22
Benoîte De SAPORTA........................................................................... 22
Marie DOUMIC.................................................................................... 23
Dan GOREAC...................................................................................... 23
Nathalie Krell...................................................................................... 24
Gilles Wainrib......................................................................................24
Pierre-André Zitt................................................................................. 24
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PROGRAMME
Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
1. RÉSUME
DE LA PROPOSITION DE PROJET
/ EXECUTIVE
SUMMARY
The Piecewise Deterministic Markov Processes (PDMP) are non-diffusive
stochastic processes which naturally appear in many areas of applications as
communication networks, neuron activities, biological populations or reliability of
complex systems. Their mathematical study has been intensively carried out in
the past two decades but many challenging problems remain completely open.
This project aims at federating a group of experts with different backgrounds
(probability, statistics, analysis, partial derivative equations, modelling) in order
to pool everyone's knowledge and create new tools to study PDMPs. The main
lines of the project relate to estimation, simulation and asymptotic behaviors
(long time, large populations, multi-scale problems) in the various contexts of
application.
2. CONTEXTE, POSITIONNEMENT ET OBJECTIFS DE LA PROPOSITION /
CONTEXT, POSITION AND OBJECTIVES OF THE PROPOSAL
2.1. CONTEXTE
ET ENJEUX ÉCONOMIQUES ET SOCIÉTAUX
/ CONTEXT,
SOCIAL AND ECONOMIC ISSUES
This project of fundamental research deals with the advanced mathematical
study of PDMPs in connection with complex system modelling applications. In
particular, the members of this proposal intend to design new algorithms for the
simulation of neuron activation and to develop efficient inference procedures to
calibrate the models in the numerous fields of application of PDMPs (biology,
reliability of complex systems, communications networks).
2.2. POSITIONNEMENT
DU PROJET
/ POSITION
OF THE PROJECT
The mathematical study of PDMP and their applications has been very active in
the last two decades. In particular, several ANR projects have been dedicated to
this subject.
The ANR project MANDy (2009-2012), which gathers mathematicians and
neuroscientists, aims at developping mathematically rigorous approaches to
neuroscience considering single neurons as well as interconnected neuronal
populations. Classical models in this area turn out to be PDMPs such as the
Hodgkin-Huxley model. The main goal of the project is twofold: to conduct the
mathematical analysis of existing models and to enrich the modelling by
proposing new ones. Several works as [PTW09] and [WTP09] are dedicated to
the relation between PDMPs and neuron activity.
The objectives of ANR FAUTOCOES (2009-2013) coordinated by F. Dufour and in
collaboration with EADS Astrium are to use the framework of PDMP to model
complex physical systems and phenomena such as crack propagation in
mechanical structures of embedded systems, to compute expectations of
functionals of the process in order to evaluate the performance of the system
and to develop theoretical and numerical control tools for PDMP’s to optimize the
performance and/or to maintain system function when a failure has occurred.
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PROGRAMME
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Projet : PIECE
EDITION 2012
First results have been published in peer-reviewed journals [dSDG10, CD10a,
CD10b, CD11, BdSD12a, BdSD12b, dSD12, dSDZE12] and presented in
conferences [AGTE10, AGT10, BdSDE11, dSDZ11].
Moreover the ANR project EVOL (2009-2012) brought great improvements in the
study of the long time behavior of nonlinear PDEs or hypo-elliptic diffusions. Most
of the tools that have been developed in this project fail to describe PDMPs
evolution. Nevertheless, some of them should be adapted in our non-diffusive
framework.
The different research groups involved in the proposal PIECE have already been
connected for one year: they met and debated during an informal one-day
session in January 2011; a more formal 3-day meeting is planned in March 2012.
The point is now to perpetuate these interactions by launching a long term
program in order to enable theoretical and algorithmic discoveries in the different
contexts of application.
2.3. ÉTAT
DE L'ART
/ STATE
OF THE ART
Piecewise deterministic Markov processes (PDMPs) were introduced rigorously in
the mathematical literature by Davis [Dav84] (see also the books [Dav93] and
[Jac06]) as a general class of non-diffusive stochastic models. PDMPs evolution is
made of deterministic motion punctuated by random jumps. The motion of the
PDMP depends on three local characteristics, namely, a flow of deterministic
continuous-time dynamic system, a state-dependent jump rate and a jump
kernel. Starting from an initial point, the motion of the process follows the flow
until the first jump time which occurs in a Poisson-like fashion according to the
jump rate. Then, the location of the process at the jump time is selected by the
jump kernel and the motion restarts from this new point as before.
These processes appear in a very natural way in the modelling of various
evolutions and have been already widely studied from both applied and
theoretical points of view. Let us briefly mention several areas of applications :
the famous transmission protocol TCP/IP control congestion in communication
networks (see for example [DGR02],[GRZ04]), the Hodgkin-Huxley model of
neuronal activity (see in particular [PTW09] and [WTP09]), or the movement of
populations of bacteria (see the reviews [EO05] and [ODA88]).
One of the most motivating issues is to get a precise description of the long time
behavior of ergodic PDMPs. Several works have been dedicated to this problem
starting from [Dav93] (see also [Cos90], [DC99] or [CD98]). In particular,
equivalence results are obtained regarding irreducibility, existence of invariant
measures, and (positive) recurrence and (positive) Harris recurrence between a
time-continous PDMP and a discrete time Markov chain. Sufficient conditions in
terms of a modified Foster-Lyapunov criterion are also presented to ensure
positive Harris recurrence and ergodicity of the PDMP as in the classical theory of
Meyn and Tweedie (see [MT93]). In [Las04], stability and ergodicity via Meyn-
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Projet : PIECE
EDITION 2012
Tweedie arguments are established for one dimensional PDMPs as AIMD (Additive
Increase Multiplicative Decrease) processes. Most of these results are essentially
of qualitative type i.e. no practical information can be obtained on the rate of
convergence to equilibrium. The papers [CMP10] and [FGM11] are first attempts
to get quantitative results for the long time behavior of PDMPs.
In many applications, one has to deal with processes in large dimensions or with
different time scales. Several approximation results have been obtained in these
directions. In [GR09], a system of interacting PDMPs is defined and the typical
behavior of a single component is derived: as for the McKean-Vlasov equations
(see [Szn89]) its dynamic depends on its whole law. In the same spirit, [Tou11a]
and [Tou11b] deal with mean-field interacting neurons via a diffusion model.
In [PTW09] and [CDR09], approximations are established for two-time-scale
processes in connection to neuron models or gene networks. Under suitable
scalings, movements of bacteria that are naturally modeled by PDMPs turn to
look like diffusion processes (see [ODA88], [EO05] and [HV10]). Finally, in
[CPSV09], the authors deal with the long time behavior of particles moving with
constant speed and reflected with random angles at the domain boundary.
Ergodicity and central limit theorems are derived. In [CPSV10] quenched
invariance principles are established for specific billiards.
As usual, the evolution of a PDMP is related to a partial differential equation: this
one looks like an integro-differential transport equation. From the seminal work
[Kac74], many authors investigate these evolution equations. In particuler,
[PR05] and [LP09] use PDEs techniques to study the long time behavior of a
population of divising cells.
Even if PDMPs are extensively studied in many models, statistical issues have
been essentially ignored. In the recent and promising work [DHRR11], the
nonparametric estimation of the division rate of a size-structured population is
under study via kernel methods with automatic bandwidth selection. This work is
inspired by model selection and recent results of Goldenschluger and Lepski.
Several alternative strategies have been proposed to simulate PDMPs. The
accuracy of direct methods which consist in making the deterministic flow
discrete, and the jump mechanism have been studied in [Rie11]: the order of the
numerical scheme for the random process is the same as for the derministic flow.
Besides the studies [dSG10], [BdSD12a] and [BdSD12b] rely on quantization
algorithms, i.e. dividing the state and time spaces in a finite number of cells at
each jump time of the process.
2.4. OBJECTIFS
ET CARACTÈRE AMBITIEUX/NOVATEUR DU PROJET
/ OBJECTIVES,
ORIGINALITY AND
NOVELTY OF THE PROJECT
The essential strong point of this project is to federate researchers with different
backgrounds in order to pool all their expertise. All the members of this project
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PROGRAMME
Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
are experts in their fields and have already brought their contributions to the
theoretical or applied study of PDMPs. Several of them are members of a projectteam INRIA whose lines of research are linked to this study (B. de Saporta at
CQFD, M. Doumic at BANG, F. Malrieu at ASPI, Ph. Robert at RAP).
3. PROGRAMME SCIENTIFIQUE ET TECHNIQUE, ORGANISATION DU PROJET /
SCIENTIFIC AND TECHNICAL PROGRAMME, PROJECT ORGANISATION
3.1. PROGRAMME
SCIENTIFIQUE ET STRUCTURATION DU PROJET
/ SCIENTIFIC
PROGRAMME,
PROJECT STRUCTURE
In this four-year project as proposed, several tasks will be carried out in parallel
in order to achieve a description as accurate as possible of the PDMPs. The first
task will be to develop efficient tools to study the long time and large size
behaviour of models, for example derived from neuronal dynamics or from
exchange procedures in large size networks. More precisely it is about studying
phenomena of metastability and interaction mean field type for PDMPs. Besides,
in order to be able to correctly calibrate models, it is essential to have at disposal
efficient estimation procedures of PDMP parameters (flow, jump rate, jump
measure) from observation of a trajectory on one hand, and of simulation on the
other hand.
3.2. MANAGEMENT
DU PROJET
/ PROJECT
MANAGEMENT
The scientific program of the proposal consists in three tasks. Each of these three
research areas will be managed by a member of the proposal.
Task 1: Limits and scalings
- Head: Zitt
- Main participants: Bardet, Cloez, Doumic, Genadot, Malrieu, Robert, Wainrib.
Task 2: Control and Regularity
- Head: Goréac
- Main participants: de Saporta, Malrieu, Zitt.
Task 3: Simulation and Estimation
- Head: de Saporta
- Main participants: Cloez, Doumic, Krell, Malrieu.
3.3. DESCRIPTION
DES TRAVAUX PAR TÂCHE
/ DESCRIPTION
BY TASK
3.3.1 TÂCHE 1 / TASK 1 : LIMITS AND SCALINGS
If the PDMPs have very simple dynamics, their theoretical study is rather tricky.
General "Meyn-Tweedie" criteria enable to establish ergodicity results. However
the provided estimates appear to be of no practical use for processes from
specific issues. If several studies have already given satisfactory answers on
some instances (see [CFK10], [FGM11]), general criteria are missing such as
existing for diffusion processes or Markov chains (coupling or comparison
methods, functional inequalities). Several members of the proposal (e.g. Malrieu,
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PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
Zitt) have developped applications of functional inequalities (as Poincaré or
logarithmic Sobolev inequalities) to study diffusion processes. It is still an open
question to construct similar tools for the PDMPs that are neither diffusion
processes nor continuous time Markov chains on countable sets. J.-B. Bardet, F.
Malrieu and P.-A. Zitt will tackle this problem.
In several application areas, a large population (of size N) of interacting
individuals is under study. The natural question is to describe the typical behavior
of a small group of particles in the entire population. Typically these few particles
become independent when N goes to infinity and each one evolves with a
nonlinear dynamics that depends on its law. This is the so-called propagation of
chaos property. Many works are devoted to mean field interacting diffusion
processes of McKean-Vlasov type. See for example [Szn89], [Mal01] or [CGM08]
for theoretical results and [TGF11], [Tou11a] and [Tou11b] for an application to
the collective behavior of neurons. However, we have a small understanding of
the behavior of mean field interacting PDMPs. The seminal work [GR09] should
be completed with quantitative estimates of the propagation of chaos and
extended to other fields of applications as interacting neurons by J.-B. Bardet, F.
Malrieu, Ph. Robert and G. Wainrib.
Neuron dynamics sometimes behave in a metastable way: the activation of ion
channels alternates with several regimes. Metastability phenomenom has been
extensively studied in diffusion processes (see the review [Ber11]) and in Markov
chains such as the famous Curie-Weiss model. J.-B. Bardet, F. Malrieu, G. Wainrib
and P.-A. Zitt intend to work on the derivation of precise estimates (large
deviations, spectral gaps) for metastable PDMPs in collaboration with M.
Thieullen.
3.3.2 TÂCHE 2 / TASK 2 : CONTROL AND REGULARITY
Even if considering a PDMP starting from a given point, its law at a finite time of
is not regular (it can be written as a mixture of laws with singular supports), its
invariant measure usually admits a smooth density with respect to the Lebesgue
measure. A challenging problem is to describe precisely how the jump
mechanism produces "regularity". In a work in progress, F. Malrieu and P.-A. Zitt
(in collaboration with M. Benaïm and S. Le Borgne) try to adapt in the framework
of PDMPs the Hörmander approach to study hypoelliptic diffusions. This approach
is closely related to deterministic control theory used by D. Goreac (see [Gor11]
and [GS11]).
3.3.3 TÂCHE 3 / TASK 3 : ESTIMATION AND SIMULATION
This task can be split in two major directions: estimation and simulation.
*Estimation*
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Projet : PIECE
EDITION 2012
The first challenge consists in generalizing the statistical study [DHRR11]
dedicated to cell division to a large scope of models. This study is about the
inference of the macroscopic division rate in a size-structured population of
Escherichia coli. In their study in progress, M. Doumic, M. Hoffmann and N. Krell
adopt a microscopic point of view: their model describes the evolution of the size
of each bacterium. As it appears in the study of random fragmentations, there
exists a "many-to-one formula" reducing the study of the complete process to
the study of a marked particle which is a real PDMP. So, the micro and macro
points of view appear to be consistent. Besides, this new approach improves the
accuracy of the estimators introduced in [DHRR11].
The long time behavior estimates expected in Task 1 should provide rates of
convergence for new estimators in various open fields. In biology, a challenging
problem is to test the independence of individual growth rate within a population.
In communication networks, the congestion control algorithms, such as the TCP
protocol, are known to be rather similar to the models studied in [DHRR11].
Consequently, estimation processes should work rapidly in this framework. As for
neuronal models there are quite different and their statistical study will need new
tools.
*Simulation*
Although there exists an extensive litterature on numerical methods to simulate
diffusion processes and compute expectations, stopping times and other
interesting quantities, the litterature on practical numerical procedures for PDMPs
is surprisingly scarce, despite their high applicative potential in various fields. In
addition numerical procedures for diffusion processes usually cannot be directly
applied to PDMP's because of their specificities. First, PDMPs are in essence
discontinuous at random times. Therefore, one must be careful in dividing time
into discretization grids. In particular, fixed-step time-discretization schemes
appear ill-advised. Second, as PDMPs are non diffusive, there is no quick
regularization, and most expectations or operators related to PDMP's involve
indicator functions that are not regular. Finally, PDMPs are hybrid processes with
interacting continuous and discrete variables, and these closed-loop interactions
may be tricky to deal with numerically.
On the other hand, PDMP's have nice specific properties. For instance, all the
randomness of the process can be described by the discrete time (continuous
state space) Markov chain of the post jump locations and inter-jump times. B. de
Saporta (in collaboration with F. Dufour, H. Zhang and some PhS students K.
Gonzalez and A. Brandejsky) has developped iterative numerical schemes based
on this discrete time Markov chain to solve optimal stopping problems [dSDG10],
impulse control problems [dSD12], approximate distributions of exit times
[BdSD12b] and compute expectations of functionals of PDMP's [BdSD12a].
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PROGRAMME
Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
This task aims at proposing new algorithms for PDMP's and investigating their
convergence properties and practical implementation on the various examples
studied in this ANR. In addition to the random jumps and closed-loop interactions
mentionned above, other practical problems to be tackled include the possible
high dimensionnality of the continuous variable or high cardinality of the discrete
one, long time horizon,...
To begin with, the numerical procedures developped in ANR Fautocoes in the
context of reliability and safety problems could be adapted to the framework of
neuron dynamics. Several informal meetings on this topic have already taken
place between B. de Saporta and M. Thieullen. The team will also investigate
numerical procedures specific to communication networks and populations of
bacteria. First, we will compare these problems to relability models and find out
what their major specificities are, as well as the major figures of interest to be
numerically approximated. Then we will design specific algorithms to solve these
problems and study their convergence properties.
3.4. CALENDRIER
DES TÂCHES, LIVRABLES ET JALONS
/ TASKS
SCHEDULE, DELIVERABLES AND
MILESTONES
For the three tasks, some members of the proposal have already submitted
several papers as for example [FGM11] and [BCGMZ11](task 1), [Gor11] (task
2) or [DHRR11] (task 3).
Even if it is quite optimistic to plan succesfull attempts in mathematics, one can
guess that in the four-year period of the proposal several papers will be
submitted for each task. Let us briefly try to organize the objectives in an
increasing order of difficulty.
Task 1:
1- Coupling criterion,
2- Quantitative propagation of chaos estimates,
3- Metastibility of PDMPs,
4- Functional inqualities.
Task 2:
1- Hörmander criterion for the regularity of the distribution of certain PDMPs,
2- General criterion and smoothness estimates.
Task 3:
1- Comparison between existing simulation algorithms,
2- Statistical inference for bacteria populations,
3- Statistical inference for neuron activity.
To fulfill this program, several events will be planned during the four years of the
project as it is described in the table below.
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Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
Event
S1
One-day workshop 1
S2
S3
S4
S5
S6
S7
S8
*
Opening meeting
*
Two-day workshop 1
*
One-day workshop 2
*
Two-day workshop 2
*
One-day workshop 3
*
Two-day workshop 3
*
One-day workshop 4
*
Lectures on applications and theory
*
Two-day workshop 4
*
Closing conference
*
4. STRATÉGIE
RÉSULTATS
DE VALORISATION, DE PROTECTION ET D’EXPLOITATION DES
/ DISSEMINATION
AND EXPLOITATION OF RESULTS.
INTELLECTUAL PROPERTY
The PIECE project gathers mathematicians from various scientific communities
--- probability, statistics, dynamical systems and PDEs --- to study models
coming from different fields --- biology, physics, computer science, etc. As a
consequence, we will organize our communication on three levels.
4.1. COMMUNICATION
TO THE MATHEMATICAL COMMUNITY
Apart from the publication of scientific results in peer-reviewed journals, we
intend to communicate in four specific ways.
1- The members of the project will write a synthesis of the recent advances on
the subject, with the intent of complementing the current references [Dav93]
and [Jac06].
2- Two advanced courses (around 10 hours each) will be organized for graduate
students. The first one will deal with mathematical tools, the second one with
applications. These courses will probably take place in Rennes, and will be open
to students from Rennes and elsewhere.
3- Two large workshops will be organized, with an international audience.
4- Information on the project events and realizations will be presented on a
dedicated website.
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EDITION 2012
4.2. COMMUNICATION
TO THE SCIENTIFIC COMMUNITY AT LARGE
We have at heart to keep a link with researchers in the scientific domains where
the models come from. The book and website mentioned above will naturally be
accessible to anyone. More specifically, as was stated above, one of the advanced
courses will focus on the applications of the theory; moreover, we will invite
members of other scientific communities to the workshops to encourage
collaboration.
4.3. COMMUNICATION
TO THE GENERAL PUBLIC
The members will organize specific interventions in scientific events geared
toward the general public, such as the French science festival "Fête de la
Science".
5. DESCRIPTION
DE L’EQUIPE
/ TEAM
DESCRIPTION
5.1. DESCRIPTION, ADÉQUATION ET COMPLÉMENTARITÉ
DESCRIPTION & RELEVANCE, COMPLEMENTARITY
DES PARTICIPANTS
/ PARTNERS
Even if most members of the proposal are young researchers, all of them are
leaders in the field of PDMPs. Some of them have already taken the opportunity
of working together and, through past prospective sessions, new promising
questions and strategies have already sprung out which should be solved thanks
to the wide spectrum of skills of the members of the team.
5.2. QUALIFICATION
DU COORDINATEUR DU PROJET
/ QUALIFICATION
OF THE PROJECT
COORDINATOR
F. Malrieu is interested in PDMPs for several years and has produced about six
papers (published, submitted or in progress) on this topic. Moreover, he has a
great understanding of functional inequalities and propagation of chaos property.
Besides, he is involved in the animation of science through many events :
- the probability seminar in Rennes,
- several workshops (interacting particle systems, Freidlin-Wentzell theory) of the
probability team in Rennes,
- two workshops on PDMPs (2011 and 2012) in collaboration with D. Chafaï,
- workshop of the ANR EVOL in Rennes (2008),
- the conference "Journées de probabilités 2012",
- four 2-day meetings in Rennes called "Journées Louis Antoine" (twice a year).
5.3. QUALIFICATION,
RÔLE ET IMPLICATION DES PARTICIPANTS
/ QUALIFICATION
AND
CONTRIBUTION OF EACH PARTNER
Nom / Name
Bardet
Prénom /
First name
Emploi actuel / Position
Jean-Baptiste MC (Rouen)
Discipline /
Field of
research
%
Probability
50
Personne.
Rôle/Responsabilité dans la
mois* / proposition de projet/ Contribution
PM
to the proposal
24
Task 1
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PROGRAMME
Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
De Saporta
Benoîte
MC (Bordeaux)
Reliability
60
28.8
Doumic
Marie
Ingénieur Ponts (INRIA Roc.)
Goreac
Dan
Krell
PDE
25
12
MC (Marne-La-Vallée)
Control
40
19.2
Nathalie
MC (Rennes)
Statistics
50
24
Malrieu
Florent
MC (Rennes)
Probability
80
38.4
Coordinator of the proposal
Robert
Philippe
DR INRIA Roc.
Networks
10
4.8
Task 1
Wainrib
Gilles
MC (Paris 13)
Modelling
40
19.2
Tasks 1 and 3
Zitt
Pierre-André MC (Dijon)
Probability
50
24
Leader of Task 1
Cloez
Bertrand
Doctorant (Marne-La-Vallée)
Probability
60
0.6
Tasks 1 and 3
Genadot
Alexandre
Doctorant (Paris 6)
Probability
60
0.6
Task 1
Total
•
Leader of Task 3
Task 3
Leader of Task 2
Task 3
195.6
à renseigner par rapport à la durée totale du projet
J.-B. Bardet is interested in the long time behavior of Markov processes
(invariant measure(s), rate of convergence). In a collaboration with H. Guérin
and F. Malrieu [BGM10a], he studied an Orstein-Uhlenbeck diffusion with Markov
switching. More recently, J.-B. Bardet, A. Christen, A. Guillin, F. Malrieu and P.-A.
Zitt [BCGMZ11], studied the rate of convergence of the so called TCP window
size process which is a very important PDMP that appears in many fields of
applications (communication networks, biology). Estimates in total variation
distance are provided improving the classical methodology due to Meyn-Tweedie
[MT93]. Moreover J.-B. Bardet studied interacting dynamical systems. In
particular, [BKZ09] describes a metastable behavior for a mean field model. This
work should be adapted to describe the metastability of neurons activation.
M. Doumic is an expert in the fields of PDEs and simulation and N. Krell has a
deep knowledge in stochastic processes and estimation procedures. These
complemetary skills added to the contributions of F. Malrieu and P.-A. Zitt on
functional inequalities are precious assets to investigate the fine properties of
estimators to solve an inverse problem presented in [DPZ09].
F. Malrieu has studied several examples of PDMPs (see [CKM10], [FGM11] for
example). Moreover, its works on interacting particles systems (as [Mal01])
should be useful to provide quantitative estimates for the propagation of chaos
studied in [GR09].
Ph. Robert is an expert in the fields of stochastic processes and theirs
applications to algorithms for communication networks. In this area, PDMPs play
a important role.
12/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
G. Wainrib has already deeply studied the applications of PDMPs to
neurosciences. He developped several promising theoretical results (fluid limit,
averaging) in connection with applications.
P.-A. Zitt have been interested in finding ways to control the convergence of
stochastic processes to their equilibrium. In particular, the study of stochastic
algorithms (Robbins-Monro, simulated annealing) often requires tools to quantify
this convergence. The usual framework was the case of elliptic or hypo-elliptic
diffusion processes, where strong regularity results are available, and many tools
are well developed (functional inequalities, spectral approaches). These tools are
not (yet) available for PDMPs.
Finally, B. Cloez and A. Genadot are two promising PHD students. They began
their thesis in 2010 on PDMPs and applications.
6. JUSTIFICATION
SCIENTIFIQUE DES MOYENS DEMANDÉS
/ SCIENTIFIC
JUSTIFICATION OF REQUESTED RESSOURCES
One of the major targets of the proposal is to enable young French researchers
to meet and work efficiently together on a 48 month period. Therefore, the major
financial needs are travel expenses and organisation costs of several workshops
and conferences.
1. Équipement / Equipment
- 7 laptops: 7*1500 euros,
- 3 individual licences for Matlab: about 3*500 euros
Total charge of the paragraph: 12000 euros.
2. Personnel / Staff
No staff costs are charged.
3. Prestation de service externe / Subcontracting
No subcontracting costs are charged.
4. Missions / Travel
Missions and invitations can be divided in two parts, according to whether they
are directly related to the events organized in the frame of the proposal or not.
1- Missions/Invitations directly related to the frame of the proposal:
13/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
An opening meeting, a closing conference and eight (four one-day and four twoday) workshops will be organized.
For the opening meeting and the closing conference, we expect an average
audience of 50 people. We would like to encourage young researchers (PhD and
Post-Doc) to attend them. We need to cover the expenses of 10 of them and of 4
foreign invited speakers. Besides, about 9 people will attend each of the eight
workshops.
For the opening meeting, the two-day workshops and the closing conference, the
costs have been approximately estimated as follows:
– Accomodation and meals: 100 euros/day.
– Travel: 200 euros (for French people), 500 euros (for foreign people).
For the one-day workshops, the costs cover the travel inside France (200
euros) and a meal and extra fees (35 euros).
For the opening meeting and the closing conference:
-Number of days: 5;
-Number of members of the proposal: 9;
-Number of French external experts (including PhD): 11;
-Number of foreign external experts: 4;
Charge: 2*(100*5*24+200*(9+11)+500*4)=36000 euros
For the four two-day workshops
Charge: 4*(200*9+100*2*9)=14400 euros
For the four one-day workshops
Charge: 4*(200*9+35*9)=8460 euros
Total charge of the paragraph: 58860 euros.
2- Missions not directly related to the workshops:
An average amount of 4000 euros/4years will be attributed to each
permanent participant to attend conferences related to the proposal (as
a complement to other fundings, for instance from University
Departments, other research projects etc.).
Total charge of the paragraph: 9*4000=36000 euros
Total charge of the missions 94860 euros.
14/25
PROGRAMME
Projet : PIECE
JEUNES CHERCHEURS
EDITION 2012
5. Dépenses justifiées sur une procédure de facturation interne /
Costs justified by internal procedures of invoicing
No costs are charged in this section.
6. Autres dépenses de fonctionnement / Other expenses
1- Two advanced courses (around 10 hours each) will be organized for
graduate students.
Cost of the remunerations and expenses of the speakers: 2*1000=2000 euros.
2- Documentation (purchase of research books)
Cost: 2000 euros.
3- four "semestres de délégation" for the "young" researchers of the
proposal.
Cost: 4*10000=40000 euros.
Total charge: 44000 euros.
7. RÉFÉRENCES
BIBLIOGRAPHIQUES
/ REFERENCES
[AGTE10] Azaïs, R., Gégout-Petit, A. Touzet, M. Elegbede. Estimation, simulation
et prévision d'un modèle de propagation de fissures par des processus
markoviens déterministes par morceaux, C. Lambda-Mu 17, 2010,
La Rochelle.
[AGT10] R. Azaïs, A. Gégout-Petit, M. Touzet. Modélisation de propagation de
fissure par un processus markovien déterministe par morceaux Journées MAS
2010, Bordeaux.
[BCGMZ11] J.-B. Bardet, A. Christen, A. Guillin, F. Malrieu and P.-A. Zitt. Total
variation estimates for the TCP process, preprint (2011).
[Ber11] N. Berglund. Kramers' law: Validity, derivations and generalisations,
preprint (2011).
[BdSDE11] A. Brandejsky, B. de Saporta, F. Dufour, C. Elegbede. Numerical
method for the distribution of a service time, ESREL 2011, Troyes, France.
15/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
[BdSD12a] A. Brandejsky, B. de Saporta, and F. Dufour. Numerical method for
expectations of PDMPs, to appear in CAMCoS, 2012.
[BdSD12b] A. Brandejsky, B. de Saporta and F. Dufour. Numerical methods for
the exit time of a PDMP, to appear in Advances in Applied Probability 44(1),
2012
[BdSG09] B. Bercu, B. de Saporta, A. Gégout-Petit, Asymptotic analysis for
bifurcating autoregressive processes via a martingale approach, Electronic
Journal of Probability 14(87), 2009, pp 2492-2526.
[BF11] J.-B. Bardet and B. Fernandez. Extensive escape rate in lattices
of weakly coupled expanding maps. Discrete and Continuous Dynamical
Systems, Series A, 31 (3), 669-684 (2011).
[BGK07] J.-B. Bardet, S. Gouëzel and G. Keller. Limit theorems for
coupled interval maps, Stochastics and Dynamics, 7 (1), 17-36 (2007).
[BGM10a] J.-B. Bardet, H. Guérin and F. Malrieu. Long time behavior of
diffusions with Markov switching. ALEA Latin American Journal of
Probability and Mathematical Statistics (2010) Vol. 7, 151-170
[BGM10b] F. Bolley, A. Guillin and F. Malrieu. Trend to equilibrium and
particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck
Equation. ESAIM Mathematical Modelling and Numerical Analysis (2010)
Vol. 44, no. 5, 867-884
[BGQ11] R. Buckdahn, D. Goreac and M. Quincampoix, Stochastic Optimal
Control and Linear Programming Approach, Appl. Math. Optim., vol. 63 (2011),
no. 2, pp. 257-276.
[BKZ09] J.-B. Bardet, G. Keller and R. Zweimüller. Stochastically stable
globally coupled maps with bistable thermodynamic limit, Communications
in Mathematical Physics, 292 (1), 237-270 (2009).
[CCZ11] H. Cardot, P. Cénac, et P.-A. Zitt, Efficient and fast
estimation of the geometric median in Hilbert spaces with an averaged
stochastic gradient algorithm., accepté pour publication dans Bernoulli.
[CD08] O. L. Costa and F. Dufour, Stability and ergodicity of PDMPs, SIAM J.
Control Optim. 47 (2008), no. 2, 1053-1077.
[CD10a] O. Costa and F. Dufour. The policy iteration algorithm for average
continuous control of PDMPs, Applied Mathematics and Optimization. Vol. 62,
No. 2, pp. 185-204, 2010.
16/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
[CD10b] O. Costa and F. Dufour. Average control of PDMPs, SIAM Journal of
Control and Optimization. Vol. 48, No. 7, pp. 4262-4291, 2010.
[CD11] O. Costa and F. Dufour, Singular Perturbation for the discounted
continuous contol of PDMPs, Applied Mathematics and Optimization Vol. 63, No.
3, pp. 357-384, 2011.
[CDG11] V. Calvez, M. Doumic, P. Gabriel, Self-similarity in a General
Aggregation-Fragmentation Problem ; Application to Fitness Analysis ,
2011, J. de Math. Pur. et Appl., accepté.
[CDR09] A. Crudu, A. Debussche and O. Radulescu. Hybrid stochastic
simplifications for multiscale gene networks, BMC Systems Biology, 3:89 (2009).
[CFK10] D. Chafaï, F. Malrieu and K. Paroux, On the long time behavior of the
TCP window size process, Stoch. Process. Appl. 120 (2010), no. 8, 1518–1534.
[CGZ11] P. Cattiaux, A. Guillin, et P.-A. Zitt, Poincaré inequalities
and hitting times, accepté pour publication aux Annales de l’IHP (B).
[CMP10] D. Chafaï, K. Paroux and F. Malrieu. On the long time behavior
of the TCP window size process. Stochastic Processes and their
Applications (2010) Vol. 120, no. 8, 1518-1534
[CM10] D. Chafaï and F. Malrieu. On fine properties of mixtures with
respect to concentration of measure and Sobolev type inequalities.
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
(2010) Vol. 46, no. 1, 72-96
[CGM08] P. Cattiaux, A. Guillin and F. Malrieu. Probabilistic approach
for granular media equations in the non uniformly convex case.
Probability Theory and Related Fields (2008) Vol. 140, no.1-2, 19-40
[Cos90] O. Costa. Stationary distributions for PDMPs, J. Appl. Probab. 27 (1990),
no. 1, 60–73.
[CPSV09] F. Comets, S. Popov, G. Schütz and M. Vachkovskaia, Billiards in a
general domain with random reflections. Arch. Ration. Mech. Anal. 191 (2009),
no. 3, 497–537.
[CPSV10] F. Comets, S. Popov, G. Schütz and M. Vachkovskaia, Quenched
invariance principle for the Knudsen stochastic billiard in a random tube. Ann.
Probab. 38 (2010), no. 3, 1019–1061.
17/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
[Dav84] M. H. A. Davis, Piecewise-deterministic Markov processes: a general
class of nondiffusion stochastic models, J. Roy. Statist. Soc. Ser. B 46 (1984), no.
3, 353–388.
[Dav93] M. H. A. Davis, Markov models and optimization, Monographs on
Statistics and Applied Probability, vol 49, Chapman & Hall, London, 1993.
[DC99] F. Dufour and O. Costa, Stability of piecewise-deterministic Markov
processes, SIAM J. Control Optim. 37 (1999), no. 5, 1483–1502.
[DDGS09] M. Doumic, F. Duboc, F. Golse, R. Sentis, Simulation of Laser
Beam Propagation With a Paraxial Model in a Tilted Frame, Journal of
Computational Physics, vol.228, Issue 3 (2009), 861--880.
[DG10] M. Doumic, P. Gabriel, Eigenelements of a General
Aggregation-Fragmentation Model, , Math. Models Methods Appl. Sci.,
20(5):757-783 (2010).
[DGR02] V. Dumas, F. Guillemin and Ph. Robert, A Markovian analysis of
additive-increase multiplicative-decrease algorithms, Adv. in Appl. Probab. 34
(2002), no.1, 85-111.
[DHRR11] M. Doumic, M. Hoffmann, P. Reynaud-Bouret and V. Rivoirard,
Nonparametric estimation of the division rate of a size-structured population,
preprint 2011.
[DMP11] M. Doumic, A. Marciniak, B. Perthame, J.P. Zubelli, A Structured
Population Model of Cell Differentiation , 2011, SIAM J. of Appl. Math.,
accepté.
[DPZ09] M. Doumic, B. Perthame, J. Zubelli, Numerical Solution of an
Inverse Problem in Size-Structured Population Dynamics, Inverse
Problems, vol. 25, Issue 4 (2009).
[dSD12] Numerical method for impulse control of Piecewise Deterministic Markov
Processes, B. de Saporta, F. Dufour, to appear in Automatica, 2012.
[dSDG10] B. de Saporta, F. Dufour and K. Gonzalez. Numerical method for
optimal stopping of PDMPs, Ann. Appl. Probab. 20 (2010), no. 5, 1607–1637.
[dSDZ11] B. de Saporta, F. Dufour, H. Zhang. Approximation of the value
function of an impulse control problem of PDMP, IFAC 18th world congress,
Milano, Italy.
18/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
[dSDZE12] B. de Saporta, F. Dufour, H. Zhang and C. Elegbede. Optimal stopping
for the predictive maintenance of a structure subject to corrosion, to appear in
Journal of Risk and Reliability, 2012.
[dSGL11] B. de Saporta, A. Gégout-Petit, L. Marsalle, Parameters estimation for
asymmetric bifurcating autoregressive processes with missing data, Electronic
Journal of Statistics 5, 2011, pp1313-1353.
[EO05] R. Erban and H. G. Othmer, From individual to collective behavior in
bacterial chemotaxis, SIAM J. Appl. Math. 65 (2004/05), no. 2, 361-391.
[FGM11] J. Fontbona, H. Guérin and F. Malrieu, Quantitative estimates for the
long time behavior of a PDMP describing the movement of bacteria, preprint
2011.
[FK10] J. Fontbona, N. Krell and S. Martinez. Energy efficiency of consecutive
fragmentation processes. J. Appl. Probab. 47, no. 2, 543-561, 2010.
[Gor11a] D. Goreac, D., Viability, invariance and rechability for controlled
piecewise deterministic Markov processes associated to gene networks. To
appear in ESAIM: Control, Optimisation and Calculus of Variations (2011).
[Gor11b] Goreac, D., Viability of Stochastic Semilinear Control Systems via the
Quasi-Tangency Condition, IMA Journal of Mathematical Control and Information
(2011), 28: 391-415.
[GS10] D. Goreac and O.-S. Serea, Discontinuous control problems for nonconvex dynamics and near viability for singularly perturbed control systems,
Nonlinear Anal. 73 (2010), no. 8, pp. 2699-2713.
[GS11a] D. Goreac and O.-S. Serea. Mayer and optimal stopping stochastic
control problems with discontinuous cost, Journal of Mathematical Analysis and
Applications, vol. 380 (1) (2011), pp. 327-342.
[GS11b] D. Goreac and O.S. Serea, Linearization techniques for controlled
piecewise deterministic Markov processes; application to Zubov's method,
preprint 2011.
[GR09] C. Graham and Ph. Robert, Interacting multi-class transmissions
in large stochastic networks, Ann. Appl. Probab. 19 (2009), no. 6, 2334–2361.
[GRZ04] V. Guillemin, Ph. Robert and B. Zwart, AIMD algorithms and exponential
functionals, Ann. Appl. Probab. 14 (2004), no. 1, 90-117.
[HK11] M. Hoffmann and N. Krell, Statistical analysis of self-similar conservative
fragmentation chains, Bernoulli. 17, no. 1, 395-423, 2011.
19/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
[HV10] S. Herrmann and P. Vallois, From persistent random walk to telegraph
noise, Stoch. Dyn. 10 (2010), no. 2, 161-196.
[Kre08] N. Krell, Multifractal spectra and precise rates of decay inhomogeneous
fragmentations, Stochastic Process. Appl. 118, no. 6, 897-916, 2008.
[Kre09] N. Krell, Self-similar branching Markov chains. Séminaire de Probabilités
XLII, 261-280, Lecture Notes in Math. 979, Springer, Berlin, 2009.
[KR11] N. Krell and A. Rouault. Martingales and rates of presence in
homogeneous fragmentation, Stochastic Process. Appl. 121, 135-154, 2011.
[Jac06] M. Jacobsen, Point process theory and applications, Probability and its
Applications, Birkhäuser Boston Inc., Boston, MA, 2006.
[Kac74] M. Kac, A stochastic model related to the telegrapher's equation, Rocky
Mountain J. Math. 4 (1974), 497-509.
[Las04] G. Last, Ergodicity properties of stress release, reparaible system and
workload models, Adv. in Appl. Probab. 36 (2004), no. 2, 471-498.
[LP09] Ph. Laurençot and B.Perthame, Exponential decay for the growthfragmentation/cell-division equation. Commun. Math. Sci. 7 (2009), no. 2, 503–
510.
[Mal01] F. Malrieu, Logarithmic Sobolev Inequalities for some nonlinear PDE's,
Stochastic Process. Appl. 95 (2001), no. 1, 109-132.
[MT93] S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability,
Communications and Control Engineering Series, Springer-Verlag London Ltd.,
London, 1993.
[ODA88] H. G. Othmer, S. R. Dunbar and W. Alt, Models of dispersal in biological
systems, J. Math. Biol. 26 (1988), no. 3, 263-298.
[PTW10a] M. Thieullen, K. Pakdaman and G. Wainrib, Diffusion approximation of
birth-death processes : comparison in terms of large deviations and exit point,
Statistics and Probability Letters (2010).
[PTW10b] K. Pakdaman, M. Thieullen and G. Wainrib, Fluid limit theorems for
stochastic hybrid systems with application to neuron models, Adv. In Appl.
Probab. 42 (2010), no.3, 761-794.
[PR05] B. Perthame, and L. Ryzhik, Exponential decay for the fragmentation or
cell-division equation, J. Differential Equations 210 (2005), no. 1, 155–177.
20/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
[Rie11] M. Riedler, Almost sure convergence of numerical approximations for
Piecewise Deterministic Markov Processes. Preprint 2011.
[Szn91] Saint-Flour Summer School on Probability Theory XIX—1989, Papers
from the school held in Saint-Flour, August 16–September 2, 1989. Lecture Notes
in Mathematics, 1464. Springer-Verlag, Berlin, 1991.
[TGF11] J. Touboul, G. Hermann and O. Faugeras. Noise-induced behaviors in
neural mean field dynamics. SIAM Journal on Applied Dynamical Systems (2011).
[Tou11a] J. Touboul. The propagation of chaos in neural fields, preprint
2011.
[Tou11b] J. Touboul. On the dynamics of mean-field equations for stochastic
neural fields with delays, preprint 2011.
[Wai11] Noise-controlled dynamics through the averaging principle for stochastic
slow-fast systems, Physical Review E84, 051113 (2011).
[WTP10] G. Wainrib, M. Thieullen and K. Pakdaman. Intrinsic variability of
latency to first-spike. Biol. Cybernet. 103 (2010), no. 1, 43–56.
[WTP11] G. Wainrib, M. Thieullen and K. Pakdaman, Reduction of stochastic
conductance-based neuron models with time-scales separation, Journal of
Computational Neurosciences (2011).
[Zit08] Annealing diffusions in a potential with a slow growth, Stochastic
Processes and their Applications 118 (2008), no. 1, 76–119,
[Zit08] Functional inequalities and uniqueness of the Gibbs measure — from logSobolev to Poincaré, ESAIM P&S 12 (2008), 258–272.
[Zit10] Super Poincaré inequalities, Orlicz norms and essential spectrum,
Potential Analysis (2010).
8. FICHES
INDIVIDUELLES
8.1. FLORENT MALRIEU
37 ans (né le 18 novembre 1974)
Maître de conférences à l'université de Rennes 1, section 26,
habilité à diriger des recherches
http://perso.univ-rennes1.fr/florent.malrieu/
Cursus
2011-aujourd'hui: Membre extérieur de l'équipe-projet ASPI de l'INRIA
2001-aujourd'hui: Maître de conférences de l'université de Rennes 1
21/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
11/2010 : Habilitation à diriger des recherches, Rennes 1.
1998-2001 : Thèse de doctorat à Toulouse 3 sous la direction de D. Bakry.
5 publications récentes : [BGM10a], [BGM10b], [CMP10], [CM10], [CGM08].
Nombre total de publications dans des revues avec comité de lecture : 13
Membre de l'ANR EVOL (2009-2012) à 50%
8.2. JEAN-BAPTISTE BARDET
36 ans (né le 31 mars 1975)
Maître de conférences à l'université de Rouen, section 26
http://www.univ-rouen.fr/LMRS/Persopage/Bardet/
Cursus
2010-11 : visite d'un an au CMM (Santiago du Chili) dans le cadre d'une
délégation CNRS
2007-aujourd'hui : maître de conférences à l'université de Rouen
2003-2007 : maître de conférences à l'université Rennes 1
2002 : thèse de doctorat sous la direction de Gérard Ben Arous, EPF Lausanne
Publications récentes : [BGK07], [BKZ09], [BGM10], [BF11].
Implication dans d'autres projets :
2012-15 : Membre (à 25%) du projet blanc ANR PRESAGE, "Méthodes
probabilistes pour l'efficacité des structures et algorithmes
géométriques" (coordinateur : Xavier Goaoc).
2009-11 : Membre (à 50%) du projet ANR Jeunes Chercheurs RANDYMECA,
"Marches aléatoires, systèmes dynamiques et mécanique statistique
mathématique" (porteur : Arnaud Le Ny).
8.3. BENOÎTE DE SAPORTA
34 ans (née le 31 juillet 1977)
Maître de conférences à l'université Bordeaux IV, section 26
http://www.math.u-bordeaux1.fr/~saporta/
Cursus
2007-aujourd'hui : Membre de l’équipe projet INRIA CQFD.
2006-aujourd'hui : Maître de conférences, univ. Montesquieu Bordeaux IV
2005-2006 : Post Doc, INRIA Sophia Antipolis, équipe OMEGA
2004-2005 : ATER à l'université de Nantes
2001-2004 : thèse de doctorat sous la direction de J.-F. Yao, Univ. Rennes 1
22/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
5 publications récentes : [dSD12], [BdSD12b], [dSGL11], [dSDG10], [BdSG09].
ANR Fautocoes (2009-2013) Fault tolerant control for embedded systems
(coordinator : François Dufour).
Contrat Astrium (2008-2009) Modélisation de la propagation de fissures
par de PDMP.
Contrat EDF (oct 2010-march 2012, dans le cadre du GIS 3SGS)
Implémentation d'un simulateur du circuit secondaire d'une centrale
nucléaire à l'aide de PDMP.
8.4. MARIE DOUMIC
35 and (née le 18 juin 1976)
Ingénieur des Ponts et Chaussées en détachement
Chercheuse dans l'équipe-projet BANG, INRIA Paris Rocquencourt
http://www-roc.inria.fr/bang/MDJ/index.html
Cursus
2007-aujourd'hui: chercheuse dans l'équipe-projet BANG
2003-2007: chef du service Techniques de la voie d'eau, Service
Navigation de la Seine (encadrement d'une équipe de 35 personnes,
programmation et travaux sur les ouvrages de navigation - 40 MEuros par an)
mai 2005: soutenance de thèse "Etude asymptotique et simulation
numérique de la propagation laser dans un milieu inhomogène",
directeurs: F. Golse et R. Sentis
2000-2003: études aux Ponts et Chaussées
1996-2000: études à l'Ecole Normale Supérieure (Ulm)
5 publications récentes : [CDG11], [DMP11], [DG10], [DDGS09], [DPZ09].
Nombre total de publications dans des revues à comité de lecture: 14
ANR TOPPAZ se terminant fin août 2012 (60%) - pas de recouvrement temporel
ANR CALIBRATION 2011-2014 25%
8.5. DAN GOREAC
29 ans (né le 26 mars 1982)
Maître de conférences à l’Université Paris-Est Marne-la-Vallée (section 26)
http://www.goreac.net/
Cursus
2008-aujourd'hui : Maître de conférences à l’Université Paris-Est Marne-la-Vallée
2005-2008 : thèse de doctorat sous la direction de R. Buckdahn et M.
Quincampoix à Brest.
23/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
5 publications récentes : [BGQ11], [Gor11a], [Gor11b], [GS10], [GS11a]
8.6. NATHALIE KRELL
31 ans (né le 26 septembre 1980)
Maître de conférences à l'université de Rennes 1 (section 26).
http://perso.univ-rennes1.fr/nathalie.krell/
Cursus
2009-aujourd'hui : Maître de conférences de l'université de Rennes 1
2004-2008 : thèse de doctorat sous la direction de J. Bertoin et M. Hoffmann.
5 publications récentes : [Kre08], [Kre09], [FK10], [HK11], [KR11].
Prix, distinctions: 2010 L'allocation d'installation scientifique de Rennes Métropole
Membre de l'ANR auto-similarité à 20% (2010-2013).
8.7. GILLES WAINRIB
28 ans (né le 18 août 1983)
Maître de conférences à l'Université Paris 13, section 26
http://sites.google.com/site/gwainrib/
Cursus :
2011-aujourd'hui : Maître de conférences à l'Université Paris 13 (LAGA)
2010-2011 : Post-doc à Stanford University
2007-2010 : Thèse de mathématiques appliquées (école doctorale de l'X)
2006-2007 : M2 Probabilités Paris 6,
2003-2006 : Ecole Polytechnique.
Publications récentes : [PTW10a], [PTW10b], [WTP10], [Wai11], [WTP11].
Implication dans d'autres projets:
- ANR MANDy (2009/2012)
- Labex Inflammex
8.8. PIERRE-ANDRÉ ZITT
31 ans (né le 21 janvier 1980)
Maître de conférences à l'université de Bourgogne, section 26
http://math.u-bourgogne.fr/IMB/zitt/
24/25
PROGRAMME
JEUNES CHERCHEURS
Projet : PIECE
EDITION 2012
Cursus :
2003–2006 Thèse de mathématiques appliquées sous la direction P. Cattiaux,
université de Nanterre.
2002–2003 DEA « Modélisation stochastique et statistique » à
l’université Paris XI (Orsay). Mémoire de DEA : « Diffusions
auto-interactives », sous dir. O. Raimond (Paris XI).
2002–2003 Agrégation de mathématiques (rang : 34).
2000–2002 Licence et Maîtrise de mathématiques (ENS & Paris XI).
2000 Admis à l’Ecole normale supérieure (rang : 22).
5 publications récentes : [CCZ11], [CGZ11], [Zit10], [Zit08], [Zit08].
Membre des projets ANR EVOL (2009-2012) et ProbaGeo (2009-2013, 33%).
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projet ANR PIECE

Transcription

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