Publications

2011

• 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
• 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
• 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
• 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.
• 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
• 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
• 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.
• 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
• 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
• 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.
• Exponential instability in the Gel'fand inverse problem on the energy intervals
  
  • Isaev Mikhail
  Journal of Inverse and Ill-posed Problems, De Gruyter, 2011, 19 (3), pp.453-473. We consider the Gel'fand inverse problem and continue studies of [Mandache,2001]. We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann map given on the energy intervals. These instability results show, in particular, that the logarithmic stability estimates of [Alessandrini,1988], [Novikov,Santacesaria,2010] and especially of [Novikov,2010] are optimal (up to the value of the exponent).
• Asymptotic behaviour of the number of the Eulerian circuits
  
  • Isaev Mikhail
  The Electronic Journal of Combinatorics, Open Journal Systems, 2011, 18 (1), pp.219. We determine the asymptotic behaviour of the number of the Eulerian circuits in undirected simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). We also prove some new properties of the Laplacian matrix.
• Polymorphic evolution sequence and evolutionary branching
  
  • Champagnat Nicolas
  • Méléard Sylvie
  Probability Theory and Related Fields, Springer Verlag, 2011, 151 (1-2), pp.45-94. We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence, is called polymorphic evolution sequence. Then we introduce a scaling of the size of mutations and we study the polymorphic evolution sequence in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. To this end we finely analyze the asymptotic behavior of 3-dimensional competitive Lotka-Volterra systems. (10.1007/s00440-010-0292-9)
  DOI : 10.1007/s00440-010-0292-9
• A continuous semigroup of notions of independence between the classical and the free one
  
  • Benaych-Georges Florent
  • Lévy Thierry
  The Annals of Probability, Institute of Mathematical Statistics, 2011, 39 (3), pp.904-938. In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These notions are related to the liberation process introduced by D. Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence. (10.1214/10-AOP573)
  DOI : 10.1214/10-AOP573
• Generalized impedance boundary conditions for thin dielectric coatings with variable thickness
  
  • Aslanyurek Birol
  • Haddar Houssem
  • Shahinturk Hulya
  Wave Motion, Elsevier, 2011, 48 (7), pp.681-700. (10.1016/j.wavemoti.2011.06.002)
  DOI : 10.1016/j.wavemoti.2011.06.002
• The role of electrode direction during axonal bipolar electrical stimulation : a bidomain computational model study
  
  • Pantz Olivier
  • Mandonnet Emmanuel
  Acta Neurochirurgica, Springer Verlag, 2011.
• Damage and fracture evolution in brittle materials by shape optimization methods
  
  • Allaire Grégoire
  • Jouve François
  • van Goethem Nicolas
  Journal of Computational Physics, Elsevier, 2011, 230 (12), pp.5010--5044. This paper is devoted to a numerical implementation of the Francfort-Marigo model of damage evolution in brittle materials. This quasi-static model is based, at each time step, on the minimization of a total energy which is the sum of an elastic energy and a Griffith-type dissipated energy. Such a minimization is carried over all geometric mixtures of the two, healthy and damaged, elastic phases, respecting an irreversibility constraint. Numerically, we consider a situation where two well-separated phases coexist, and model their interface by a level set function that is transported according to the shape derivative of the minimized total energy. In the context of interface variations (Hadamard method) and using a steepest descent algorithm, we compute local minimizers of this quasi-static damage model. Initially, the damaged zone is nucleated by using the so-called topological derivative. We show that, when the damaged phase is very weak, our numerical method is able to predict crack propagation , including kinking and branching. Several numerical examples in 2d and 3d are discussed.
• Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W±, II
  
  • Aschbacher Walter H.
  • Barbaroux Jean-Marie
  • Faupin Jérémy
  • Guillot Jean-Claude
  Annales Henri Poincaré, Springer Verlag, 2011, 12 (8), pp.1539-1570. We do the spectral analysis of the Hamiltonian for the weak leptonic decay of the gauge bosons W+/-. Using Mourre theory, it is shown that the spectrum between the unique ground state and the first threshold is purely absolutely continuous. Neither sharp neutrino high energy cutoff nor infrared regularization are assumed. (10.1007/s00023-011-0114-3)
  DOI : 10.1007/s00023-011-0114-3
• Optimal Control of the Atmospheric Reentry of a Space Shuttle by an Homotopy Method
  
  • Hermant Audrey
  Optimal Control Applications and Methods, Wiley, 2011, 32 (6), pp.627-646. This paper deals with the optimal control problem of the atmospheric reentry of a space shuttle with a second-order state constraint on the thermal flux. We solve the problem using the shooting algorithm combined with an homotopy method which automatically determines the structure of the optimal trajectory (composed of one boundary arc and one touch point). (10.1002/oca.961)
  DOI : 10.1002/oca.961
• Lévy flights in evolutionary ecology
  
  • Jourdain Benjamin
  • Méléard Sylvie
  • Woyczynski Wojbor
  Journal of Mathematical Biology, Springer, 2011, pp.31 p.. We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled 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 random mutation causes the offspring to take an instantaneous mutation step at birth to new trait values. In the case we are interested in, the probability distribution of mutations has a heavy tail and belongs to the domain of attraction of a stable law. We investigate the large-population limit with allometric demographies: larger populations made up of smaller individuals which reproduce and die faster, as is typical for micro-organisms. We show that depending on the allometry coefficient the limit behavior of the population process can be approximated by nonlinear Lévy flights of different nature: either deterministic, in the form of nonlocal fractional reaction-diffusion equations, or stochastic, as nonlinear super-processes with the underlying reaction and a fractional diffusion operator. These approximation results demonstrate the existence of such nontrivial fractional objects; their uniqueness is also proved. (10.1007/s00285-011-0478-5)
  DOI : 10.1007/s00285-011-0478-5