Publications

2006

• Un sous-ensemble du système solaire (Uranus,Neptune,Pluto) avec une planète virtuelle orange supplémentaire -point de vue de la planète virtuelle
  
  • Colonna Jean-François
  , 2006. A subset of the Solar System (Uranus,Neptune,Pluto) with an extra orange virtual planet -virtual planet point of view- (Un sous-ensemble du système solaire (Uranus,Neptune,Pluto) avec une planète virtuelle orange supplémentaire -point de vue de la planète virtuelle-)
• Papillon quaternionique avec arithmetique etendue
  
  • Colonna Jean-François
  , 2006. Quaternionic butterfly with extended arithmetics (Papillon quaternionique avec arithmetique etendue)
• Lion quaternionique avec arithmetique etendue
  
  • Colonna Jean-François
  , 2006. Quaternionic lion with extended arithmetics (Lion quaternionique avec arithmetique etendue)
• Optimal Quantization : Evolutionary Algorithm vs Stochastic Gradient
  
  • Hamida Sana Ben
  • Mrad Moez
  , 2006. We propose a new method based on evolutionary optimization for obtaining an optimal L p-quantizer of a multidimen-sional random variable. First, we remind briefly the main results about quantization. Then, we present the classical gradient-based approach (this approach is well detailed in [2] and [7] for p=2) used up to now to find a "local" optimal L p-quantizer. Then, we give an algorithm that permits to deal with the problem in the evolutionary optimization framework and illustrate a numerical comparison between the proposed method and the stochastic gradient method. Finally, a numerical application to option pricing in finance is provided. (10.2991/jcis.2006.161)
  DOI : 10.2991/jcis.2006.161
• Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
  
  • Lemor Jean-Philippe
  • Gobet Emmanuel
  • Warin Xavier
  Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2006, 12 (5), pp.889-916. This study is focused on the numerical resolution of backward stochastic differential equations, with data dependent on a jump-diffusion process. We propose and analyze a numerical scheme based on iterative regression functions, which are approximated by projections on vector spaces of functions, with coefficients evaluated using Monte Carlo simulations. Regarding the error, we derive explicit bounds with respect to the time step, the number of simulated paths and the number of functions : this allows us to optimally adjust the parameters to achieve a given accuracy. We also present numerical tests related to option pricing with differential interest rates and locally risk-minimizing strategies (Föllmer-Schweizer decomposition) (10.3150/bj/1161614951)
  DOI : 10.3150/bj/1161614951
• Separation of arterial pressure into solitary waves and windkessel flow
  
  • Laleg Taous-Meriem
  • Crépeau Emmanuelle
  • Sorine Michel
  , 2006. A simplified model of arterial blood pressure intended for use in model-based signal processing applications is presented. The main idea is to decompose the pressure into two components: a travelling wave describes the fast propagation phenomena predominating during the systolic phase and a windkessel flow represents the slow phenomena during the diastolic phase. Instead of decomposing the blood pressure pulse into a linear superposition of forward and backward harmonic waves, as in the linear wave theory, a nonlinear superposition of travelling waves matched to a reduced physical model of the pressure, is proposed. Very satisfactory experimental results are obtained by using forward waves, the N- soliton solutions of a Korteweg-de Vries equation in conjunction with a two-element windkessel model. The parameter identifiability in the practically important 3- soliton case is also studied. The proposed approach is briefly compared with the linear one and its possible clinical relevance is discussed.
• Total Variation Minimization and Graph Cuts for Moving Objects Segmentation
  
  • Ranchin Florent
  • Chambolle Antonin
  • Dibos Françoise
  , 2006. In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem involving the shape weighted perimeter and an additional term depending on a parameter. Based on recent works and in particular the one of Darbon and Sigelle, we justify the equivalence of the shape optimization problem and a weighted total variation regularization. For solving this problem, we adapt the projection algorithm proposed recently for solving the basic TV regularization problem. Another solution to the shape optimization investigated here is the graph cut technique. Both methods have the advantage to lead to a global minimum. Since we can distinguish moving objects from static elements of a scene by analyzing norm of the optical flow vectors, we choose the optical flow norm as initial data. In order to have the contour as close as possible to an edge in the image, we use a classical edge detector function as the weight of the weighted total variation. This model has been used in one of our former works. We also apply the same methods to a video segmentation model used by Jehan-Besson, Barlaud and Aubert. In this case, only standard perimeter is incorporated in the shape functional. We also propose another way for finding moving objects by using an a contrario detection of objects on the image obtained by solving the Rudin-Osher-Fatemi Total Variation regularization problem.We can notice the segmentation can be associated to a level set in the former methods.
• Homogénéisation de modèles de transferts thermiques et radiatifs : Application au coeur des réacteurs à caloporteur gaz.
  
  • El Ganaoui Karima
  , 2006. Dans le cadre de l'homogénéisation, nous étudions des problèmes de transfert d'énergie posés dans un domaine solide perforé périodique où coexistent deux échelles d'espace (macroscopique et microscopique). Ces problèmes modélisent le transfert de chaleur par conduction dans le solide et par rayonnement au bord de chaque perforation. La présence du rayonnement implique des conditions aux limites non usuelles (vis à vis de la théorie de l'homogénéisation). Deux types de rayonnement sont considérés: rayonnement en milieu infini (condition non linéaire) et rayonnement en cavité à parois grises diffusantes (condition non linéaire et non locale). L'homogénéisation dans les deux cas conduit à un modèle de conduction posé dans un solide équivalent ayant! une conductivité effective qui prend en compte le rayonnement aux bords. Nous développons donc une méthodologie (homogénéisation et validation) basée sur une justification théorique du processus d'homogénéisation via la méthode de convergence à deux échelles et une validation numérique via des simulations au moyen du code de calcul CAST3M. Cette étude est menée dans le cadre de l'analyse de fonctionnement des réacteurs à caloporteur gaz. Les résultats sont également exploitables pour d'autres domaines perforés impliquant les phénomènes de transferts en question.
• Boundary sensitivities for diffusion processes in time dependent domains
  
  • Costantini Cristina
  • Gobet Emmanuel
  • El Karoui Nicole
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2006, 54 (2), pp.159-187. We study the sensitivity, with respect to a time dependent domain Ds, of expectations of functionals of a diffusion process stopped at the exit from Ds or normally reflected at the boundary of Ds. We establish a differentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pricing of American options, to singular stochastic control and others are discussed. (10.1007/s00245-006-0863-4)
  DOI : 10.1007/s00245-006-0863-4
• Optimal control of ordinary differential equations
  
  • Bonnans Frédéric J.
  , 2006, pp.81.
• Nœud '5-trefle' torique sur son tore
  
  • Colonna Jean-François
  , 2006. 5-foil torus knot on its torus (Noeud '5-trefle' torique sur son tore)
• Noeud '7-trefle' torique sur son tore
  
  • Colonna Jean-François
  , 2006. 7-foil torus knot on its torus (Noeud '7-trefle' torique sur son tore)
• Noeud '7-trefle' torique sur son tore
  
  • Colonna Jean-François
  , 2006. 7-foil torus knot on its torus (Noeud '7-trefle' torique sur son tore)
• Noeud '3-trefle' torique sur son tore
  
  • Colonna Jean-François
  , 2006. 3-foil torus knot on its torus (Noeud '3-trefle' torique sur son tore)
• Noeud '3-trefle
  
  • Colonna Jean-François
  , 2006. 3-foil knot (Noeud '3-trefle')
• Noeud '3-trefle
  
  • Colonna Jean-François
  , 2006. 3-foil knot (Noeud '3-trefle')
• Characterization of the optimal plans for the Monge-Kantorovich transport problem
  
  • Léonard Christian
  , 2006. We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without constraint qualification. As an example of application, the Monge-Kantorovich optimal transport problem is solved in great detail. In particular, the optimal transport plans are characterized without restriction. This characterization improves the already existing literature on the subject.
• Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact
  
  • Hauret Patrice
  • Le Tallec Patrick
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2006, 195 (37-40), pp.4890-4916. It is now well established that discrete energy conservation/dissipation plays a key-role for the unconditional stability of time integration schemes in nonlinear elastody-namics. In this paper, from a rigorous conservation analysis of the Hilber-Hughes-Taylor time integration scheme [1], we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like [2–5]. Moreover, we extend the technique proposed in [3] to provide energy-controlling time integration schemes for frictionless contact problems enforcing the standard Kuhn-Tucker conditions at time discretization points. We also extend this technique to viscoelastic models. Numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis. (10.1016/j.cma.2005.11.005)
  DOI : 10.1016/j.cma.2005.11.005
• Coquillage quaternionique
  
  • Colonna Jean-François
  , 2006. Quaternionic shell (Coquillage quaternionique)
• Coquillage quaternionique
  
  • Colonna Jean-François
  , 2006. Quaternionic shell (Coquillage quaternionique)
• Traitement géométrique des images par bandelettes
  
  • Peyré Gabriel
  • Mallat Stéphane
  , 2006, pp.36-69. Comprendre comment représenter les structures géométriques complexes est nécessaire pour améliorer l'état de l'art du traitement d'images mais a aussi une portée scientifique beaucoup plus large. Cet enjeu apparaît dans des problèmes de physique, de mathématiques et de physiologie de la perception. Un regard naif sur les images peut laisser penser que la géométrie se réduit aux contours d'objets distincts comme dans le monde de la bande-dessinée. De tels contours existent mais constituent une faible partie des "structures géométriques" des images. Dans une image réelle, les textures ont souvent une géométrie beaucoup plus complexe. Le saut en complexité est analogue à la différence de complexité entre un écoulement fluide laminaire et un champ turbulent, qui s'apparente à une texture.
• Learning near-optimal policies with Bellman-residual minimization based fitted policy iteration and a single sample path
  
  • Antos Andras
  • Szepesvari Csaba
  • Munos Rémi
  , 2006. We consider batch reinforcement learning problems in continuous space, expected total discounted-reward Markovian Decision Problems. As opposed to previous theoretical work, we consider the case when the training data consists of a single sample path (trajectory) of some behaviour policy. In particular, we do not assume access to a generative model of the environment. The algorithm studied is policy iteration where in successive iterations the Q-functions of the intermediate policies are obtained by means of minimizing a novel Bellman-residual type error. PACstyle polynomial bounds are derived on the number of samples needed to guarantee near-optimal performance where the bound depends on the mixing rate of the trajectory, the smoothness properties of the underlying Markovian Decision Problem, the approximation power and capacity of the function set used.
• Chat quaternionique
  
  • Colonna Jean-François
  , 2006. Quaternionic cat (Chat quaternionique)
• Lion quaternionique
  
  • Colonna Jean-François
  , 2006. Quaternionic lion (Lion quaternionique)
• Improved Interface conditions for 2D domain decomposition with corners: Numerical applications
  
  • Chniti Chokri
  • Nataf Frédéric
  • Nier Francis
  , 2006. This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. After explaining the main results of the theoreticalanalysis carried out in a former artilce, the numerical experiments presented in this article confirm the optimality properties of the new interface conditions. A MODIFIED VERSION OF THIS PREPRINT HAS BEEN PUBLISHED IN JOURNAL OF SCIENTIFIC COMPUTING (10.1007/s10915-008-9234-4)
  DOI : 10.1007/s10915-008-9234-4