Publications

2008

• The value of Repeated Games with an informed controller
  
  • Renault Jérôme
  , 2008. We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform value, generalizing several results of the literature. A preliminary existence result is obtained for a certain class of stochastic games played with pure strategies.
• Localisation et caractérisation de défauts simples dans un cristal photonique 2D de dimension finie
  
  • Groby Jean-Philippe
  • Lesselier Dominique
  , 2008.
• Uniform value in Dynamic Programming
  
  • Renault Jérôme
  , 2008. We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are uniformly continuous and the transition correspondence is non expansive. In the same spirit, we give an existence result for the limit value. We also apply our results to Markov decision processes and obtain a few generalizations of existing results.
• Placement 'harmonieux' de 26 points sur une sphère par recuit simulé
  
  • Colonna Jean-François
  , 2008. Harmonious' arrangement of 26 points on a sphere by means of simulated annealing (Placement 'harmonieux' de 26 points sur une sphère par recuit simulé)
• Placement 'harmonieux' de 26 points sur une sphere par recuit simule
  
  • Colonna Jean-François
  , 2008. Harmonious' arrangement of 26 points on a sphere by means of simulated annealing (Placement 'harmonieux' de 26 points sur une sphere par recuit simule)
• Multi-static response of spherical scatterers and the back-propagation of singular fields
  
  • Iakovleva Ekaterina
  • Lesselier Dominique
  IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers, 2008, 56 (3), pp.825-833. In view of the development of multiple signal clas- sification-type, non-iterative imaging procedures based on the singular value decomposition of the multistatic response (MSR) matrix of a collection of inclusions, the full 3-D electromagnetic case with arbitrary contrasts of permeability and permittivity (including perfectly electric conducting or perfectly magnetic con- ducting limit cases) is studied. The structure of the MSR matrix of a single inclusion (or a set of well-separated ones) is analyzed. Emphasis is on a far-field situation, in which one considers an electric dipole array operated in the transmit/receive mode at a single frequency. Back-propagated electric and magnetic fields associated to the singular vectors of the MSR matrix for a single spherical inclusion (or again for well-separated ones) are given in closed form and their leading-order values are exhibited. Numerical illustrations (cross-sectional maps of back-propagated fields computed from a singular value decomposition of the MSR matrix) are presented, for one and two inclusions, to illustrate this behavior as a function of the geometric and electromagnetic parameters of the configuration in a possibly noisy case. (10.1109/TAP.2008.916913)
  DOI : 10.1109/TAP.2008.916913
• Texture tridimensionnelle
  
  • Colonna Jean-François
  , 2008. texture tridimensionnelle obtenue dans le corps des quaternions avec une arithmétique "non standard
• Proof(s) of the Lamperti representation of Continuous-State Branching Processes
  
  • Caballero Maria-Emilia
  • Lambert Amaury
  • Uribe Bravo Geronimo
  , 2008. The representation of continuous-state branching processes (CSBPs) as time-changed Lévy processes with no negative jumps was discovered by John Lamperti in 1967 but was never proved. The goal of this paper is to provide a proof, and we actually provide two. The first one relies on studying the time-change, using martingales and the Lévy-Itô representation of Lévy processes. It gives insight into a stochastic differential equation satisfied by CSBPs and on its relevance to the branching property. The other method studies the time-change in a discrete model, where an analogous Lamperti representation is evident, and provides functional approximations to Lamperti transforms by introducing a new topology on Skorohod space. Some classical arguments used to study CSBPs are reconsidered and simplified.
• Vibrations 0003
  
  • Colonna Jean-François
  , 2008. Vibrations 0003 (Vibrations 0003)
• Sequential Monte Carlo smoothing with application to parameter estimation in non-linear state space models
  
  • Olsson Jimmy
  • Cappé Olivier
  • Douc Randal
  • Moulines Eric
  Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2008, 14 (1), pp.155-179. This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces degeneracy of the approximation in the path space. However, when performing maximum likelihood estimation via the EM algorithm, all functionals involved are of additive form for a large subclass of models. To cope with the problem in this case, a modification of the standard method (based on a technique proposed by Kitagawa and Sato) is suggested. Our algorithm relies on forgetting properties of the filtering dynamics and the quality of the estimates produced is investigated, both theoretically and via simulations. (10.3150/07-BEJ6150)
  DOI : 10.3150/07-BEJ6150
• Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half space: II. large and infinite number of identical equispaced blocks
  
  • Wirgin Armand
  • Groby Jean-Philippe
  Geophysical Journal International, Oxford University Press (OUP), 2008, 172, pp.725-758. We address the problem of the response to a seismic wave of an urban site consisting of a large and infinite number ($N_{b}$) of identical, equispaced blocks overlying a soft layer underlain by a hard substratum. The results of the theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite element (FE) method. The two methods are shown to give rise to much the same prediction of seismic response for $N_{b}=10$. The MM technique is also applied to the case $N_{b}=\infty$, notably to reveal the structure and natural frequencies of the vibration modes of the urban site. The mechanism of the interaction between blocks and the ground, as well as that of the collective effects of the blocks, are studied. It is shown that the presence of a large number of blocks modifies the seismic disturbance in a manner which evokes, and may partially account for, what was observed during many earthquakes in Mexico City. Disturbances at a much smaller level, induced by a small number of blocks are studied in the companion paper.
• Shoot-1.1 Package - User Guide
  
  • Martinon Pierre
  • Gergaud Joseph
  , 2008, pp.41. This package implements a shooting method for solving boundary value problems, for instance resulting of the application of Pontryagin's Minimum Principle to an optimal control problem. The software is mostly Fortran90, with some third party Fortran77 codes for the numerical integration and non-linear equations system. Its features include the handling of right hand side discontinuities (such as caused by a bang-bang control) for the integration of the trajectory and the computation of Jacobians for the shooting method. The particular case of singular arcs for optimal control problems is also addressed.
• Numerical study of optimal trajectories with singular arcs for space launcher problems
  
  • Martinon Pierre
  • Bonnans Frédéric J.
  • Laurent-Varin Julien
  • Trélat Emmanuel
  , 2008, pp.26. The subject of this paper is the study of singular arcs (i.e. with a non maximal thrust) for a space launcher problem. We consider a flight to the GTO orbit for a heavy multi-stage launcher (Ariane 5 class), and use a realistic physical model for the drag force and rocket thrust. As a preliminary result, we first solve the complete flight with stage separations, at full thrust. Then we focus on the first atmospheric climbing phase, to investigate the possible existence of optimal trajectories with singular arcs. We primarily use an indirect shooting method (based on Pontryagin's Minimum Principle), coupled to a continuation (homotopy) approach. Some additional experiments are made with a basic direct method, and confirm the solutions obtained by the shooting. We study two slightly different launcher models, and observe that modifying parameters such as the aerodynamic reference area and specific impulsion can indeed lead to optimal trajectories with either full thrust or singular arcs.
• Identification of generalized impedance boundary conditions in inverse scattering problems
  
  • Bourgeois Laurent
  • Haddar Houssem
  , 2008, pp.27. In the context of scattering problems in the harmonic regime, we consider the problem of identification of some Generalized Impedance Boundary Conditions (GIBC) at the boundary of an object (which is supposed to be known) from far field measurements associated with a single incident plane wave at a fixed frequency. The GIBCs can be seen as approximate models for thin coatings, corrugated surfaces or highly absorbing media. After pointing out that uniqueness does not hold in the general case, we propose some additional assumptions for which uniqueness can be restored. We also consider the question of stability when uniqueness holds. We prove in particular Lipschitz stability when the impedance parameters belong to a compact set. We also extend local stability results to the case of back-scattering data.
• Singular arcs in the generalized Goddard's Problem
  
  • Bonnans J. Frederic
  • Martinon Pierre
  • Trélat Emmanuel
  Journal of Optimization Theory and Applications, Springer Verlag, 2008, 139 (2), pp.439--461. We investigate variants of Goddard's problems for nonvertical tra- jectories. The control is the thrust force, and the ob jective is to max imize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal tra jectories may involve singular arcs (along which the norm of the thrust is neither zero nor maximal), that are computed and characterized. Numerical simulations are carried out, both with direct and indirect methods, demonstrating the relevance of taking into account singular arcs in the control strategy. The indirect method we use is based on our previous theoretical analysis and consists in combining a shooting method with an homotopic method. The homotopic approach leads to a quadratic regularization of the problem and is a way to tackle with the problem of nonsmoothness of the optimal control.
• Probabilistic approach for granular media equations in the non uniformly convex case.
  
  • Cattiaux Patrick
  • Guillin Arnaud
  • Malrieu Florent
  Probability Theory and Related Fields, Springer Verlag, 2008, 140 (1-2), pp.19-40. We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. Proof is straightforward, simplifying deeply proofs of Carrillo-McCann-Villani \cite{CMV,CMV2} and completing results of Malrieu \cite{malrieu03} in the uniformly convex case. It relies on an uniform propagation of chaos property and a direct control in Wasserstein distance of solutions starting with different initial measures. The deviation inequality is obtained via a $T_1$ transportation cost inequality replacing the logarithmic Sobolev inequality which is no more clearly dimension free.
• The GacA global regulator is required for the appropriate expression of Erwinia chrysanthemi 3937 pathogenicity genes during plant infection
  
  • Lebeau Aurore
  • Reverchon Sylvie
  • Gaubert S.
  • Kraepiel Y.
  • Simond-Cote E.
  • Nasser William
  • van Gijsegem F.
  Environmental Microbiology, Society for Applied Microbiology and Wiley-Blackwell, 2008, 10 (3), pp.545-59.
• Infinitely many-armed bandits
  
  • Wang Yizao
  • Audibert Jean-Yves
  • Munos Rémi
  , 2008. We consider multi-armed bandit problems where the number of arms is larger than the possible number of experiments. We make a stochastic assumption on the mean-reward of a new selected arm which characterizes its probability of being a near-optimal arm. Our assumption is weaker than in previous works. We describe algorithms based on upper-confidence-bounds applied to a restricted set of randomly selected arms and provide upper-bounds on the resulting expected regret. We also derive a lower-bound which matches (up to a logarithmic factor) the upper-bound in some cases.
• From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution
  
  • Champagnat Nicolas
  • Ferrière Régis
  • Méléard Sylvie
  Stochastic Models, Taylor & Francis, 2008, 24 (S1), pp.2-44. We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each individual's trait values, and interactions between individuals. An offspring usually inherits the trait values of her progenitor, except when a mutation causes the offspring to take an instantaneous mutation step at birth to new trait values. We look for tractable large population approximations. By combining various scalings on population size, birth and death rates, mutation rate, mutation step, or time, a single microscopic model is shown to lead to contrasting macroscopic limits, of different nature: deterministic, in the form of ordinary, integro-, or partial differential equations, or probabilistic, like stochastic partial differential equations or superprocesses. In the limit of rare mutations, we show that a possible approximation is a jump process, justifying rigorously the so-called trait substitution sequence. We thus unify different points of view concerning mutation-selection evolutionary models. (10.1080/15326340802437710)
  DOI : 10.1080/15326340802437710
• Playing off-line games with bounded rationality
  
  • Scarsini Marco
  • Tomala Tristan
  • Renault Jérôme
  Mathematical Social Sciences, Elsevier, 2008, 56 (2), pp.2078-223. We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payoff is the average of a one-shot payoff over the joint sequence. We consider the maxmin value of the game played in pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we define the complexity of a sequence by its smallest period (a non-periodic sequence being of infinite complexity) and study the maxmin of the game where player~1 is restricted to strategies with complexity at most $n$ and player~2 is restricted to strategies with complexity at most $m$. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall. (10.1016/j.mathsocsci.2008.01.005)
  DOI : 10.1016/j.mathsocsci.2008.01.005
• Continuous cascade models for asset returns
  
  • Bacry Emmanuel
  • Kozhemyak Alexey
  • Muzy J.-F.
  Journal of Economic Dynamics and Control, Elsevier, 2008, pp.156-199. In this paper, we make a short overview of continuous cascade models recently introduced to model asset return fluctuations. We show that these models account in a very parcimonious manner for most of 'stylized facts' of financial time-series. We review in more details the simplest continuous cascade namely the log-normal multifractal random walk (MRW). It can simply be considered as a stochastic volatility model where the (log-) volatility memory has a peculiar 'logarithmic' shape. This model possesses some appealing stability properties with respect to time aggregation. We describe how one can estimate it using a GMM method and we present some applications to volatility and (VaR) Value at Risk forecasting. (10.1016/j.jedc.2007.01.024)
  DOI : 10.1016/j.jedc.2007.01.024
• Non-iterative MUSIC-type algorithm for reconstructing two-dimensional thin dielectric inclusions
  
  • Park Won-Kwang
  • Ammari Habib
  • Lesselier Dominique
  , 2008, 135 (2), pp.297-305. We consider a non-iterative MUSIC-type imaging algorithm for reconstructing thin, curve-like penetrable inclusions in a two-dimensional homogeneous space. It is based on an appropriate asymptotic formula of the scattering amplitude. Operating at fixed nonzero frequency, it yields the shape of the inclusion from scattered fields in addition to estimates of the length of the supporting curve. Numerical implementation shows that it is a fast and efficient algorithm.
• Localization and characterization of simple defects in finite-size photonic crystals
  
  • Groby Jean-Philippe
  • Lesselier Dominique
  Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2008, 25 (1), pp.146-152. Structured materials like photonic crystals require for optimal use a high degree of precision with respect to both position and optical characteristics of their components. Here we present a simple tomographic algorithm, based on a specific Green's function together with a first-order Born approximation, which enables us to localize and characterize identical defects in finite-sized photonic crystals. This algorithm is proposed as a first step to the monitoring of such materials. Illustrative numerical results show in particular the possibility of focalization beyond the Rayleigh criterion. (10.1364/JOSAA.25.000146)
  DOI : 10.1364/JOSAA.25.000146
• Discounted and finitely repeated minority games with public signals
  
  • Scarsini Marco
  • Scarlatti Sergio
  • Renault Jérôme
  Mathematical Social Sciences, Elsevier, 2008, 56 (1), pp.44-74. We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payos Hausdor-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria. (10.1016/j.mathsocsci.2007.12.004)
  DOI : 10.1016/j.mathsocsci.2007.12.004
• Adaptive Importance Sampling in General Mixture Classes
  
  • Cappé Olivier
  • Douc Randal
  • Guillin Arnaud
  • Marin Jean-Michel
  • Robert Christian P.
  Statistics and Computing, Springer Verlag (Germany), 2008, 18 (4), pp.447-459. In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the importance sampling performances, as measured by an entropy criterion. The method is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performances of the proposed scheme are studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme. (10.1007/s11222-008-9059-x)
  DOI : 10.1007/s11222-008-9059-x