Publications

2011

• Le processus de construction de la courbe de von Koch
  
  • Colonna Jean-François
  , 2011. The construction process of the von Koch curve (Le processus de construction de la courbe de von Koch)
• 5-étoile récursive
  
  • Colonna Jean-François
  , 2011. Recursive 5-star (5-étoile récursive)
• Pentagone récursif
  
  • Colonna Jean-François
  , 2011. Recursive pentagon (Pentagone récursif)
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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.
• 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.
• Sampling the Fermi statistics and other conditional product measures
  
  • Gaudilliere Alexandre
  • Reygner Julien
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2011, 47, pp.790-812. Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km(ln k) for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous) products of ultra log-concave measures (like binomial or Poisson laws) with a global constraint. As a consequence of this general result we also obtain a disorder-independent upper bound on the mixing time of a simple exclusion process on the complete graph with site disorder. This general result is based on an elementary coupling argument and extended to (non-homogeneous) products of log-concave measures.
• On the reconstruction of conductivity of bordered two-dimensional surface in R^3 from electrical currents measurements on its boundary
  
  • Henkin Gennadi
  • Novikov Roman
  The Journal of Geometric Analysis, Springer, 2011, 21, pp.543-587. An electrical potential U on bordered surface X (in Euclidien three-dimensional space) with isotropic conductivity function sigma>0 satisfies equation d(sigma d^cU)=0, where d^c is real operator associated with complex (conforme) structure on X induced by Euclidien metric of three-dimensional space. This paper gives exact reconstruction of conductivity function sigma on X from Dirichlet-to-Neumann mapping (for aforementioned conductivity equation) on the boundary of X. This paper extends to the case of the Riemann surfaces the reconstruction schemes of R.Novikov (1988) and of A.Bukhgeim (2008) given for the case of domains in two-dimensional Euclidien space. The paper extends and corrects the statements of Henkin-Michel (2008), where the inverse boundary value problem on the Riemann surfaces was firstly considered.
• Explicit characterization of the support of non-linear inclusions
  
  • Lechleiter Armin
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2011, 5 (3), pp.675--694. (10.3934/ipi.2011.5.675)
  DOI : 10.3934/ipi.2011.5.675
• On the existence of a limit value in some non expansive optimal control problems
  
  • Quincampoix Marc
  • Renault Jérôme
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2011, 49 (5), pp.2118-2132. We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature. (10.1137/090756818)
  DOI : 10.1137/090756818
• A nonasymptotic theorem for unnormalized Feynman-Kac particle models
  
  • Cérou Frédéric
  • del Moral Pierre
  • Guyader Arnaud
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2011, 47 (3), pp.629-649. We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman-Kac models. We provide an original stochastic analysis-based on Feynman-Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the L(2)-relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis. (10.1214/10-AIHP358)
  DOI : 10.1214/10-AIHP358
• Optimal Design of Low-contrast Two-phase Structures For the Wave Equation
  
  • Allaire Grégoire
  • Kelly Alex
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2011, 21 (7), pp.1499--1538. This paper is concerned with the following optimal design problem:¯nd the distribution of two phases in a given domain that minimizes an objective function evaluated through the solution of a wave equation. This type of optimization problem is known to be ill-posed in the sense that it generically does not admit a minimizer among classical admissible designs. Its relaxation could be found, in principle, through homogenization theory but, unfortunately, it is not always explicit, in particular for objective functions depending on the solution gradient. To circumvent this di±culty, we make the simplifying assumption that the two phases have a low constrast. Then, a second-order asymptotic expansion with respect to the small amplitude of the phase coe±cients yields a simpli¯ed optimal design problem which is amenable to relaxation by means of H-measures. We prove a general existence theorem in a larger class of composite materials and propose a numerical algorithm to compute minimizers in this context. As in the case of an elliptic state equation, the optimal composites are shown to be rank-one laminates. However, the proof that relaxation and small-amplitude limit commute is more delicate than in the elliptic case. (10.1142/S0218202511005477)
  DOI : 10.1142/S0218202511005477
• Control of the bilinear Schrödinger equation for fully coupling potentials
  
  • Caponigro Marco
  • Boscain Ugo
  • Chambrion Thomas
  • Sigalotti Mario
  , 2011, pp.to appear. We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximations, lifted in SU(n). The method allows to estimate the L 1 norm of the control laws achieving controllability.
• 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
• 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