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)
• Les outils stochastiques des marchés financiers
  
  • El Karoui Nicole
  • Gobet Emmanuel
  , 2011, pp.238. Depuis 40 ans, les outils mathématiques probabilistes ont montré leur rôle central dans le développement d’outils d’aide à la décision pour les marchés financiers. Ils offrent un cadre méthodologique robuste de modélisation et calcul des risques associés aux produits dérivés, ces fameux instruments financiers qui dépendent de manière plus ou moins complexe d’autres produits financiers plus simples (actions, indices, taux de change, taux d’intérêt, matières premières ...). Cet ouvrage se veut être une introduction aux outils stochastiques de la finance de marché, et à leurs utilisations dans la gestion dynamique des produits dérivés. Pour le développement des outils probabilistes du calcul stochastique, nous suivons une approche élémentaire à la Föllmer, qui permettra à un lecteur ayant juste des bases de probabilité de rentrer plus facilement dans le sujet. Pour autant, cette grande simplification permet de traiter de manière complète des applications aux options (simples ou exotiques) sur actions, à la modélisation des taux d’intérêt ou du risque de crédit. À travers l’expérience de la crise financière actuelle, nous expliquons l’importance des hypothèses sous-tendant l’utilisation de ces outils en salle de marché.
• The singular values and vectors of low rank perturbations of large rectangular random matrices
  
  • Benaych-Georges Florent
  • Rao Nadakuditi Raj
  , 2011. In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate projections of the corresponding singular vectors of the perturbed matrix. As in the prequel, where we considered the eigenvalue aspect of the problem, the non-random limiting value is shown to depend explicitly on the limiting singular value distribution of the unperturbed matrix via an integral transforms that linearizes rectangular additive convolution in free probability theory. The large matrix limit of the extreme singular values of the perturbed matrix differs from that of the original matrix if and only if the singular values of the perturbing matrix are above a certain critical threshold which depends on this same aforementioned integral transform. We examine the consequence of this singular value phase transition on the associated left and right singular eigenvectors and discuss the finite $n$ fluctuations above these non-random limits.
• Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains
  
  • Abboud Toufic
  • Joly Patrick
  • Rodríguez Jerónimo
  • Terrasse Isabelle
  Journal of Computational Physics, Elsevier, 2011, 230 (15), pp.5877-5907. This work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. The coupling formula enforces a discrete energy identity ensuring the stability under the usual CFL condition in the interior. Moreover, the scheme allows to use a smaller time step in the interior domain yielding to quasi-optimal discretization parameters for both methods. The aliasing phenomena introduced by the local time stepping are reduced by a post-processing by averaging in time obtaining a stable and second order consistent (in time) coupling algorithm. We compute the numerical rate of convergence of the method for an academic problem. The numerical results show the feasibility of the whole discretization procedure. © 2011 Elsevier Inc. (10.1016/j.jcp.2011.03.062)
  DOI : 10.1016/j.jcp.2011.03.062
• New global stability estimates for the Gel'fand-Calderon inverse problem
  
  • Novikov Roman
  Inverse Problems, IOP Publishing, 2011, 27 (1), pp.015001 (21pp). We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172]. (10.1088/0266-5611/27/1/015001)
  DOI : 10.1088/0266-5611/27/1/015001
• Large time asymptotics for the Grinevich-Zakharov potentials
  
  • Kazeykina Anna
  • Novikov Roman
  Bulletin des Sciences Mathématiques, Elsevier, 2011, 135 (4), pp.374-382. In this article we show that the large time asymptotics for the Grinevich-Zakharov rational solutions of the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) is given by a finite sum of localized travel waves (solitons). (10.1016/j.bulsci.2011.02.003)
  DOI : 10.1016/j.bulsci.2011.02.003
• Absence of exponentially localized solitons for the Novikov--Veselov equation at negative energy
  
  • Kazeykina Anna
  • Novikov Roman
  Nonlinearity, IOP Publishing, 2011, 24, pp.1821-1830. We show that Novikov--Veselov equation (an analog of KdV in dimension 2 + 1) does not have exponentially localized solitons at negative energy. (10.1088/0951-7715/24/6/007)
  DOI : 10.1088/0951-7715/24/6/007
• An adaptive high-gain observer for wastewater treatment systems
  
  • Lafont Frédéric
  • Busvelle Eric
  • Gauthier Jean-Paul
  Journal of Process Control, Elsevier, 2011, 21, pp.893-900.
• Direct and inverse medium scattering in a three-dimensional homogeneous planar waveguide
  
  • Arens Tilo
  • Gintides Drossos
  • Lechleiter Armin
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2011, 71 (3), pp.753--772. (10.1137/100806333)
  DOI : 10.1137/100806333
• 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
• 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
• 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
• 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.
• 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
• 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
• 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
• 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.
• 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.
• 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
• 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
• 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).