Publications

2011

• Visualisation tridimensionnelle de l'ensemble de Mandelbrot avec 'mapping' des arguments
  
  • Colonna Jean-François
  , 2011. Tridimensional visualization of the Mandelbrot set with mapping of the arguments (Visualisation tridimensionnelle de l'ensemble de Mandelbrot avec 'mapping' des arguments)
• 5-étoile récursive
  
  • Colonna Jean-François
  , 2011. Recursive 5-star (5-étoile récursive)
• Pentagone récursif
  
  • Colonna Jean-François
  , 2011. Recursive pentagon (Pentagone récursif)
• Application of convex lexicographical optimization to the balance of GRTgaz gas grid
  
  • Bonnans Joseph Frederic
  • Paraisy Ruben
  • Veyrat Sébastien
  • Adam Soizic
  Journal of Global Optimization, Springer Verlag, 2011, 49 (3), pp.415--423.
• On a heated incompressible magnetic fluid model
  
  • Amirat Youcef
  • Hamdache Kamel
  Communications on Pure and Applied Mathematics, Wiley, 2011, 11 (2), pp.675 - 696. In this paper we study the equations describing the dynamics of heat transfer in an incompressible magnetic fluid under the action of an applied magnetic field. The system consists of the Navier-Stokes equations, the magnetostatic equations and the temperature equation. We prove global-in-time existence of weak solutions to the system posed in a bounded domain of R-3 and equipped with initial and boundary conditions. The main difficulty comes from the singularity of the term representing the Kelvin force due to magnetization. (10.3934/cpaa.2012.11.675)
  DOI : 10.3934/cpaa.2012.11.675
• Sensor fault reconstruction and observability for unknown inputs, with an application to wastewater treatment plants
  
  • Methnani Salowa
  • Gauthier Jean-Paul
  • Lafont Frédéric
  International Journal of Control, Taylor & Francis, 2011, 84, pp.822-833.
• Homogenization of the linearized ionic transport equations in rigid periodic porous media
  
  • Allaire Grégoire
  • Mikelic Andro
  • Piatnitski Andrey
  Journal of Mathematical Physics, American Institute of Physics (AIP), 2011, 52 (6), pp.063701. (10.1063/1.3521555)
  DOI : 10.1063/1.3521555
• Reconstruction of the electromagnetic field in layered media using the concept of approximate transmission conditions
  
  • Ozdemir Ozgur
  • Haddar Houssem
  • Yaka Ali
  IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers, 2011, 59 (8), pp.2964 - 2972. (10.1109/TAP.2011.2158967)
  DOI : 10.1109/TAP.2011.2158967
• An introduction to direct and inverse scattering theory
  
  • Dorfler Willy
  • Lechleiter Armin
  • Plum Michael
  • Schneider Guido
  • Wieners Christian
  , 2011, 42, pp.79-126. (10.1007/978-3-0348-0113-3_4)
  DOI : 10.1007/978-3-0348-0113-3_4
• Bandlet Image Estimation with Model Selection
  
  • Dossal Charles H
  • Le Pennec Erwan
  • Mallat Stéphane
  Signal Processing, Elsevier, 2011, 91 (12), pp.2743-2753. To estimate geometrically regular images in the white noise model and obtain an adaptive near asymptotic minimaxity result, we consider a model selection based bandlet estimator. This bandlet estimator combines the best basis selection behaviour of the model selection and the approximation properties of the bandlet dictionary. We derive its near asymptotic minimaxity for geometrically regular images as an example of model selection with general dictionary of orthogonal bases. This paper is thus also a self contained tutorial on model selection with orthogonal bases dictionary. (10.1016/j.sigpro.2011.01.013)
  DOI : 10.1016/j.sigpro.2011.01.013
• Minimal Time Problems with Moving Targets and Obstacles
  
  • Bokanowski Olivier
  • Zidani Hasnaa
  , 2011, 18, Part 1, pp.2589-2593. We consider minimal time problems governed by nonlinear systems under general time dependant state constraints and in the two-player games setting. In general, it is known that the characterization of the minimal time function, as well as the study of its regularity properties, is a difficult task in particular when no controlability assumption is made. In addition to these difficulties, we are interested here to the case when the target, the state constraints and the dynamics are allowed to be time-dependent. We introduce a particular "reachability" control problem, which has a supremum cost function but is free of state constraints. This auxiliary control problem allows to characterize easily the backward reachable sets, and then, the minimal time function, without assuming any controllability assumption. These techniques are linked to the well known level-set approachs. Partial results of the study have been published recently by the authors in SICON. Here, we generalize the method to more complex problems of moving target and obstacle problems. Our results can be used to deal with motion planning problems with obstacle avoidance. (10.3182/20110828-6-IT-1002.02261)
  DOI : 10.3182/20110828-6-IT-1002.02261
• Weak Dynamic Programming Principle for Viscosity Solutions
  
  • Bouchard Bruno
  • Touzi Nizar
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (3), pp.948-962. We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In the Markov case, our result is tailor-maid for the derivation of the dynamic programming equation in the sense of viscosity solutions.
• Energy contracts management by stochastic programming techniques
  
  • Cen Zhihao
  • Bonnans J. Frederic
  • Christel Thibault
  Annals of Operations Research, Springer Verlag, 2011, 200 (1), pp.199-222. We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertainty on prices only. After building a finite state Markov chain by using vectorial quantization tree method, we rely on the stochastic dual dynamic programming (SDDP) method to solve the continuous relaxation of this stochastic optimization problem. An heuristic for computing sub optimal solutions to the integer optimization problem, based on the Bellman values of the continuous relaxation, is provided. Combining the previous techniques, we are able to deal with high-dimension state variables problems. Numerical tests applied to realistic energy markets problems have been performed. (10.1007/s10479-011-0973-5)
  DOI : 10.1007/s10479-011-0973-5
• Optimal structure of gas transmission trunklines
  
  • Bonnans J. Frederic
  • André Jean
  Optimization and Engineering, Springer Verlag, 2011, 12 (1), pp.175-198. In this paper, we consider the optimal design of a straight pipeline system. Suppose a gas pipeline is to be designed to transport a specified flowrate from the entry point to the gas demand point. Physical and contractual requirements at supply and delivery nodes are known as well as the costs to buy and lay a pipeline or build a compressor station. In order to minimize the overall cost of creation of this mainline, the following design variables need to be determined: the number of compressor stations, the lengths of pipeline segments between compressor stations, the diameters of the pipeline segments, the suction and discharge pressures at each compressor station. To facilitate the calculation of the design of a pipeline, gas engineers proposed, in several handbooks, to base their cost-assessments on some optimal properties from previous experiences and usual engineering practices: the distance between compressors is constant, all diameters are equal, and all inlet (resp. outlet) pressures are equal. The goals of this paper are (1) to state on which assumptions we can consider that the optimal properties are valid and (2) to propose a rigorous proof of the optimal properties (based on nonlinear programming optimality conditions) within a more general framework than before.
• Convergence of multi-class systems of fixed possibly infinite sizes
  
  • Graham Carl
  Statistics and Probability Letters, Elsevier, 2011, 81 (1), pp.31-35. Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of its finite classes and directing measures of its infinite ones (given by the de Finetti Theorem), corresponds to sampling independently from each class, without replacement from the finite classes and i.i.d. from the directing measure for the infinite ones. The equivalence between the convergence of multi-exchangeable systems with fixed class sizes and the convergence of the corresponding vectors of measures is then established. (10.1016/j.spl.2010.09.015)
  DOI : 10.1016/j.spl.2010.09.015
• A frictionless contact algorithm for deformable bodies
  
  • Pantz Olivier
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 2011, 45 (2), pp.235--254. (10.1051/m2an/2010041)
  DOI : 10.1051/m2an/2010041
• PecS is an important player in the regulatory network governing the coordinated expression of virulence genes during the interaction between [i]Dickeya dadantii[/i] 3937 and plants
  
  • Mhedbi-Hajri Nadia
  • Malfatti Pierrette
  • Pedron Jacques
  • Gaubert Stephane
  • Reverchon Sylvie
  • van Gijsegem Frederique
  Environmental Microbiology, Society for Applied Microbiology and Wiley-Blackwell, 2011, 13 (11), pp.2901 - 2914. Successful infection of a pathogen relies on the coordinated expression of numerous virulence factor-encoding genes. In plantbacteria interactions, this control is very often achieved through the integration of several regulatory circuits controlling cellcell communication or sensing environmental conditions. Dickeya dadantii (formerly Erwinia chrysanthemi), the causal agent of soft rot on many crops and ornamentals, provokes maceration of infected plants mainly by producing and secreting a battery of plant cell wall-degrading enzymes. However, several other virulence factors have also been characterized. During Arabidopsis infection, most D. dadantii virulence gene transcripts accumulated in a coordinated manner during infection. This activation requires a functional GacAGacS two-component regulatory system but the Gac system is not involved in the growth phase dependence of virulence gene expression. Here we show that, contrary to Pectobacterium, the AHL-mediated ExpIR quorum-sensing system does not play a major role in the growth phase-dependent control of D. dadantii virulence genes. On the other hand, the global regulator PecS participates in this coordinated expression since, in a pecS mutant, an early activation of virulence genes is observed both in vitro and in planta. This correlated with the known hypervirulence phenotype of the pecS mutant. Analysis of the relationship between the regulatory circuits governed by the PecS and GacA global regulators indicates that these two regulators act independently. PecS prevents a premature expression of virulence genes in the first stages of colonization whereas GacA, presumably in conjunction with other regulators, is required for the activation of virulence genes at the onset of symptom occurrence. (10.1111/j.1462-2920.2011.02566.x)
  DOI : 10.1111/j.1462-2920.2011.02566.x
• Differential games and Zubov's method
  
  • Grüne Lars
  • Serea Oana
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (9), pp.2349-2377. In this paper we provide generalizations of Zubov's equation to differential games without Isaacs' condition. We show that both generalizations of Zubov's equation (which we call min-max and max-min Zubov equation, respectively) possess unique viscosity solutions which characterize the respective controllability domains. As a consequence, we show that under the usual Isaacs condition the respective controllability domains as well as the local controllability assumptions coincide. (10.1137/100787829)
  DOI : 10.1137/100787829
• Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energy
  
  • Novikov Roman
  Physics Letters A, Elsevier, 2011, 375, pp.1233-1235. In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense).
• Deterministic state constrained optimal control problems without controllability assumptions
  
  • Bokanowski Olivier
  • Forcadel Nicolas
  • Zidani Hasnaa
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2011, 17 (4), pp.pp. 995-1015. In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position $x$. In the constrained case, when no controllability assumption is made, the HJB equation may have several solutions. Our first result aims to give the precise information that should be added to the HJB equation in order to obtain a characterization of the value function. This result is very general and holds even when the dynamics is not continuous and the state constraints set is not smooth. On the other hand we study also some stability results for relaxed or penalized control problems. (10.1051/cocv/2010030)
  DOI : 10.1051/cocv/2010030
• Branching Feller diffusion for cell division with parasite infection
  
  • Bansaye Vincent
  • Tran Viet Chi
  ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....], 2011, 8, pp.95-127. We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells).
• Adaptive High-Gain observers with an application to wastewater treatment plants
  
  • Methnani Salowa
  • Damak Tarak
  • Toumi Ahmed
  • Lafont Frédéric
  • Gauthier Jean-Paul
  , 2011. no abstract
• Weighted Radon transforms for which the Chang approximate inversion formula is precise
  
  • Novikov Roman
  Uspekhi Mat. Nauk, 2011, 66 (2), pp.237-238. We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given.
• Electromagnetic Wave Scattering from Rough Penetrable Layers
  
  • Haddar Houssem
  • Lechleiter Armin
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43, pp.2418-2443. We consider scattering of time-harmonic electromagnetic waves from an unbounded penetrable dielectric layer mounted on a perfectly conducting infinite plate. This model describes for instance propagation of monochromatic light through dielectric photonic assemblies mounted on a metal plate. We give a variational formulation for the electromagnetic scattering problem in a suitable Sobolev space of functions defined in an unbounded domain containing the dielectric structure. Further, we derive a Rellich identity for a solution to the variational formulation. For simple material configurations and under suitable non-trapping and smoothness conditions, this integral identity allows to prove an a-priori estimate for such a solution. A-priori estimates for solutions to more complicated material configurations are then shown using a perturbation approach. While the estimates derived from the Rellich identity show that the electromagnetic rough surface scattering problem has at most one solution, a limiting absorption argument finally implies existence of a solution to the problem. (10.1137/100783613)
  DOI : 10.1137/100783613
• On adaptive stratification
  
  • Etoré Pierre
  • Fort Gersende
  • Jourdain Benjamin
  • Moulines Éric
  Annals of Operations Research, Springer Verlag, 2011, 189 (1), pp.127-154. This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the strata, which should be ideally fitted to thesubsets where the functions to integrate is nearly constant, and on the allocation of the number of samples within each strata. When the dimension is large and the function to integrate is complex, finding such partitions and allocating the sample is a highly non-trivial problem. In this work, we investigate a novel method to improve the efficiency of the estimator "on the fly", by jointly sampling and adapting the strata and the allocation within the strata. The accuracy of estimators when this method is used is examined in detail, in the so-called asymptotic regime (\ie\ when both the number of samples and the number of strata are large). We illustrate the use of the method for the computation of the price of path-dependent options in models with both constant and stochastic volatility. The use of this adaptive technique yields variance reduction by factors sometimes larger than 1000 compared to classical Monte Carlo estimators. (10.1007/s10479-009-0638-9)
  DOI : 10.1007/s10479-009-0638-9