Publications

2014

• Milieu tridimensionnel érodé
  
  • Colonna Jean-François
  , 2014. Tridimensional eroded medium (Milieu tridimensionnel érodé)
• A semi-discrete scheme for the stochastic Landau-Lifshitz equation
  
  • Alouges François
  • de Bouard Anne
  • Hocquet Antoine
  , 2014. We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the scheme up to a subsequence.
• 10.000 chiffres aléatoires -base 10- visualisées comme une marche aléatoire bidimensionnelle 'absolue
  
  • Colonna Jean-François
  , 2014. 10.000 random digits -base 10- displayed as an 'absolute' bidimensional random walk (10.000 chiffres aléatoires -base 10- visualisées comme une marche aléatoire bidimensionnelle 'absolue')
• Découverte et analyse de la biodiversité : les moyens actuels
  
  • Elias Marianne
  • Condamine Fabien
  Mémoires de la SEF, 2014 (9), pp.23-39. – Depuis l’antiquité, la diversité des formes biologiques fascine, et fait l’objet de descriptions, d’analyses et classifications. Alors que pendant des siècles la caractérisation de la biodiversité a reposé sur des critères morphologiques, l’avènement et le développement rapide des techniques moléculaires et des méthodes analytiques associées ont permis de développer des approches complexes et intégratives pour étudier la biodiversité, tout en incorporant les données issues de la morphologie. Ces approches se classent en trois catégories : 1) Les approches microévolutives de type “génétique des populations”, basées sur de nombreux marqueurs moléculaires répartis dans tout le génome, et qui renseignent sur la structure fine de la biodiversité en étudiant les processus de spéciation (formation des espèces). 2) Les approches de type barcoding, qui permettent de caractériser génétiquement un individu et de lui assigner un nom d’espèce sur la base de la variation de la séquence d’ADN d’un ou de plusieurs gènes. Éventuellement, cette approche permet de définir les limites d’espèces. Combiné à la morphologie, le barcoding moléculaire a conduit à la taxonomie intégrative. 3) Les approches macroévolutives de type “phylogénies” (établies sur des données moléculaires et/ou morphologiques), qui reconstruisent les relations de parenté entre espèces et sont donc non seulement informatives sur la systématique du groupe étudié, mais également sur les processus évolutifs qui en ont structuré la biodiversité (biogéographie historique, rôle de caractères particuliers dans la diversification du groupe, variation des taux de diversification dans le temps ou entre lignées...). Ces trois approches, qui peuvent être combinées entre elles ainsi qu’aux approches morphologiques, ont contribué à mieux caractériser et comprendre les facteurs à l’origine de la biodiversité, par exemple en mettant en évidence des espèces cryptiques (des espèces qui se ressemblent tellement qu’elles étaient considérées comme une seule et même espèce), notamment chez les Insectes; en bouleversant les classifications traditionnelles; ou en remettant en cause le paradigme de l’isolement géographique dans la formation des espèces. Bien que la contribution de ces approches modernes soit notable, elles restent cependant très complexes et perfectibles. Plus important encore, il est essentiel aujourd’hui d’intégrer des experts de divers domaines pour appréhender sous divers angles et mieux comprendre cette biodiversité.
• Weak approximation of averaged diffusion processes
  
  • Gobet Emmanuel
  • Miri Mohammed
  Stochastic Processes and their Applications, Elsevier, 2014, 124, pp.475--504. We derive expansion results in order to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approximation is based on the use of proxys with normal distribution or log-normal distribution, so that the expansion terms are explicit. We provide non asymptotic error bounds, which justifies the expansion accuracy as the time or the diffusion coefficients are small in a suitable sense.
• Variational Curvature Flows
  
  • Chambolle Antonin
  • Morini Massimiliano
  • Ponsiglione Marcello
  , 2014. Variational Curvature Flows
• Policy iteration for stochastic zero-sum games
  
  • Akian Marianne
  , 2014. Recent results of Ye and Hansen, Miltersen and Zwick show that policy iteration for one or two player (perfect information) zero-sum stochastic games, restricted to instances with a fixed discount rate, is strongly polynomial. We show that policy iteration for mean-payoff zero-sum stochastic games is also strongly polynomial when restricted to instances with bounded first mean return time to a given state. The proof is based on methods of nonlinear Perron-Frobenius theory, allowing us to reduce the mean-payoff problem to a discounted problem with state dependent discount rate. Our analysis also shows that policy iteration remains strongly polynomial for discounted problems in which the discount rate can be state dependent (and even negative) at certain states, provided that the spectral radii of the nonnegative matrices associated to all strategies are bounded from above by a fixed constant strictly less than 1.
• The horofunction boundary and isometry group of the Hilbert geometry
  
  • Walsh Cormac
  , 2014, 22. The horofunction boundary is a means of compactifying metric spaces that was introduced by Gromov in the 1970s. We describe explicitly the horofunction boundary of the Hilbert geometry, and sketch how it may be used to study the isometry group of this space.
• Characterization of Glioma Microcirculation and Tissue Features Using Intravoxel Incoherent Motion Magnetic Resonance Imaging in a Rat Brain Model
  
  • Iima M.
  • Reynaud O.
  • Tsurugizawa T.
  • Ciobanu Luisa
  • Li Jing-Rebecca
  • Geffroy F.
  • Djemai B.
  • Umehana M.
  • Le Bihan Denis
  Investigative Radiology, Lippincott, Williams & Wilkins, 2014, pp.485–490. (10.1097/RLI.0000000000000040)
  DOI : 10.1097/RLI.0000000000000040
• On certain hyperelliptic signals that are natural controls for nonholonomic motion planning
  
  • Gauthier Jean-Paul
  • Monroy-Perez Felipe
  , 2014. In this paper we address the general problem of approximating, in a certain optimal way, non admissible motions of a kinematic system with nonholonomic constraints. Since this kind of problems falls into the general subriemannian geometric setting, it is natural to consider optimality in the sense of approximating by means of subriemannian geodesics. We consider sys-tems modeled by a subriemannian Goursat structure, a particular case being the well known system of a car with trailers, along with the associated parallel parking problem. Several authors approximate the successive Lie brackets by using trigonometric functions. By contrast, we show that the more natural op-timal motions are related with closed hyperelliptic plane curves with a certain number of loops.
• Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations
  
  • Rao Zhiping
  • Siconolfi Antonio
  • Zidani Hasnaa
  Journal of Differential Equations, Elsevier, 2014, 257 (11), pp.3978--4014. We establish a comparison principle for a Hamilton-Jacobi-Bellman equation, more appropriately a system, related to an infinite horizon problem in presence of an interface. Namely a low dimensional subset of the state variable space where discontinuities in controlled dynamics and costs take place. Since corresponding Hamiltonians, at least for the subsolution part, do not enjoy any semicontinuity property, the comparison argument is rather based on a separation principle of the controlled dynamics across the interface. For this, we essentially use the notion of "-partition and minimal "-partition for intervals of definition of an integral trajectory. (10.1016/j.jde.2014.07.015)
  DOI : 10.1016/j.jde.2014.07.015
• Beyond first-order finite element schemes in micromagnetics
  
  • Kritsikis E.
  • Vaysset A.
  • Buda-Prejbeanu L.D.
  • Alouges F.
  • Toussaint Jean-Christophe
  Journal of Computational Physics, Elsevier, 2014, 256, pp.357. (10.1016/j.jcp.2013.08.035)
  DOI : 10.1016/j.jcp.2013.08.035
• Two-dimensional von Neumann--Wigner potentials with a multiple positive eigenvalue
  
  • Novikov Roman
  • Taimanov Iskander
  • Tsarev Sergey
  Functional Analysis and Its Applications, Springer Verlag, 2014, 48 (4), pp.295-297. By the Moutard transformation method we construct two-dimensional Schrodinger operators with real smooth potential decaying at infinity and with a multiple positive eigenvalue. These potentials are rational functions of spatial variables and their sines and cosines.
• The $\Gamma$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension
  
  • Bellettini Giovanni
  • Chambolle Antonin
  • Goldman Michael
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014. In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functionals with discontinuities penalized with a ''cohesive'' energy, that is, whose cost depends on the actual opening of the discontinuity.
• Weighted Radon transforms and first order differential systems on the plane
  
  • Novikov Roman
  Moscow Mathematical Journal, Independent University of Moscow, 2014, 14 (4), pp.807–823. We consider weighted Radon transforms on the plane, where weights are given as finite Fourier series in angle variable. By means of additive Riemann-Hilbert problem techniques, we reduce inversion of these transforms to solving first order differential systems on $\R^2=\C$ with a decay condition at infinity. As a corollary, we obtain new injectivity and inversion results for weighted Radon transforms on the plane.
• Quick reachability and proper extension for problems with unbounded controls
  
  • Aronna Maria Soledad
  • Motta Monica
  • Rampazzo Franco
  , 2014. For a CONTROL SYSTEM of the form _ x = f (x; u; v) + Σm =1 g (x)u_ ; on [0;T]; (x; u)(0) = ( x; u); with x : [0;T] ! IRn; u : [0;T] ! U IRm; v : [0;T] ! V IRl ; we rely on the notion of LIMIT SOLUTION, and we investigate whether minimum problems with L1controls are PROPER EXTENSIONS of regular problems with more regular controls (AC or BV). Motivation: optimality conditions, numerical methods, etc.
• Geometric Control Theory and sub-Riemannian Geometry
  
  • Stefani Gianna
  • Boscain Ugo
  • Gauthier Jean-Paul
  • Sarychev Andrey
  • Sigalotti Mario
  , 2014, pp.372. This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
• A generalized formulation of the Linear Sampling Method with exact characterization of targets in terms of farfield measurements
  
  • Audibert Lorenzo
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2014, 30 (035011). We propose and analyze a new formulation of the Linear Sampling Method that uses an exact characterization of the targets shape in terms of the so-called farfield operator (at a fixed frequency). This characterization is based on constructing nearby solutions of the farfield equation using minimizing sequences of a least squares cost functional with an appropriate penalty term. We first provide a general framework for the theoretical foundation of the method in the case of noise-free and noisy measurements operator. We then explicit applications for the case of inhomogeneous inclusions and indicate possible straightforward generalizations. We finally validate the method through some numerical tests and compare the performances with classical LSM and the factorization methods. (10.1088/0266-5611/30/3/035011)
  DOI : 10.1088/0266-5611/30/3/035011
• A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging
  
  • Bonnard Bernard
  • Claeys Mathieu
  • Cots Olivier
  • Jacquemard Alain
  • Martinon Pierre
  , 2014. In this article, the contrast imaging problem by saturation in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal solution of the Maximum Principle and analyzed with the recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on shooting and continuation methods implemented in the HamPath software. The results are compared with a direct approach to the optimization problem and implemented within the Bocop toolbox. In complement lmi techniques are used to estimate a global optimum. It is completed with the analysis of the saturation problem of an ensemble of spin particles to deal with magnetic fields inhomogeneities.
• Integrative taxonomy of New Caledonian beetles: species delimitation and definition of the [i]Uloma isoceroides[/i] species group (Coleoptera, Tenebrionidae, Ulomini), with the description of four new species
  
  • Soldati Laurent
  • Kergoat Gael
  • Clamens Anne Laure
  • Jourdan Hervé
  • Jabbour-Zahab Roula
  • Condamine Fabien L.
  Zookeys, Pensoft, 2014, 415, pp.133-167. New Caledonia is an important biodiversity hotspot with much undocumented biodiversity, especially in many insect groups. Here we used an integrative approach to explore species diversity in the tenebrionid genus Uloma (Coleoptera, Tenebrionidae, Ulomini), which encompasses about 150 species, of which 22 are known from New Caledonia. To do so, we focused on a morphologically homogeneous group by comparing museum specimens with material collected during several recent field trips. We also conducted molecular phylogenetic analyses based on a concatenated matrix of four mitochondrial and three nuclear genes for 46 specimens. The morphological study allowed us to discover and describe four new species that belong to the group of interest, the Uloma isoceroides group. Molecular analyses confirmed the species boundaries of several of the previously described species and established the validity of the four new species. The phylogenetic analyses also provided additional information on the evolutionary history of the group, highlighting that a species that was thought to be unrelated to the group was in fact a member of the same evolutionary lineage. Molecular species delimitation confirmed the status of the sampled species of the group and also suggested some hidden (cryptic) biodiversity for at least two species of the group. Altogether this integrative taxonomic approach has allowed us to better define the boundaries of the Uloma isoceroides species group, which comprises at least 10 species: Uloma isoceroides (Fauvel, 1904), Uloma opacipennis (Fauvel, 1904), Uloma caledonica Kaszab, 1982, Uloma paniei Kaszab, 1982, Uloma monteithi Kaszab, 1986, Uloma robusta Kaszab, 1986, Uloma clamensae sp. n., Uloma condaminei sp. n., Uloma jourdani sp. n., and Uloma kergoati sp. n. We advocate more studies on other New Caledonian groups, as we expect that much undocumented biodiversity can be unveiled through the use of similar approaches (10.3897/zookeys.415.6623)
  DOI : 10.3897/zookeys.415.6623
• Higher level molecular phylogeny of darkling beetles (Coleoptera: Tenebrionidae)
  
  • Kergoat Gael G.
  • Soldati Laurent L.
  • Clamens Anne Laure
  • Jourdan Hervé
  • Jabbour-Zahab Roula
  • Genson Guénaëlle
  • Bouchard Patrice
  • Condamine Fabien
  Systematic Entomology, Wiley-Blackwell, 2014, 39 (3), pp.486-499. Insect diversity represents about 60% of the estimated million-and-a-half described eukaryotic species worldwide, yet comprehensive and well-resolved intra-ordinal phylogenies are still lacking for the majority of insect groups. This is the case especially for the most species-rich insect group, the beetles (Coleoptera), a group for which less than 4% of the known species have had their DNA sequenced. In this study, we reconstruct the first higher level phylogeny based on DNA sequence data for the species-rich darkling beetles, a family comprising at least 20000 species. Although amongst all families of beetles Tenebrionidae ranks seventh in terms of species diversity, the lack of knowledge on the phylogeny and systematics of the group is such that its monophyly has been questioned (not to mention those of the subfamilies and tribes contained within it). We investigate the evolutionary history of Tenebrionidae using multiple phylogenetic inference methods (Bayesian inference, maximum likelihood and parsimony) to analyse a dataset consisting of eight gene fragments across 404 taxa (including 250 tenebrionid species). Although the resulting phylogenetic framework only encompasses a fraction of the known tenebrionid diversity, it provides important information on their systematics and evolution. Whatever the methods used, our results provide strong support for the monophyly of the family, and highlight the likely paraphyletic or polyphyletic nature of several important tenebrionid subfamilies and tribes, notably the polyphyletic subfamilies Diaperinae and Tenebrioninae that clearly require substantial revision in the future. Some interesting associations in several groups are also revealed by the phylogenetic analyses, such as the pairing of Aphtora Bates with Phrenapatinae. Furthermore this study advances our knowledge of the evolution of the group, providing novel insights into much-debated theories, such as the apparent relict distribution of the tribe Elenophorini. (10.1111/syen.12065)
  DOI : 10.1111/syen.12065
• Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media
  
  • Cakoni Fioralba
  • Haddar Houssem
  • Chaulet Nicolas
  IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2014, pp.36. We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max–Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order 3. (10.1093/imamat/hxu045)
  DOI : 10.1093/imamat/hxu045
• Stochastic Approximation Finite Element method: analytical formulas for multidimensional diffusion process
  
  • Bompis Romain
  • Gobet Emmanuel
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2014, 52 (6), pp.3140-3164. We derive an analytical weak approximation of a multidimensional diffusion process as coefficients or time are small. Our methodology combines the use of Gaussian proxys to approximate the law of the diffusion and a Finite Element interpolation of the terminal function applied to the diffusion. We call this method Stochastic Approximation Finite Element (SAFE for short) method. We provide error bounds of our global approximation depending on the diffusion process coefficients, the time horizon and the regularity of the terminal function. Then we give estimates of the computational cost of our algorithm. This shows an improved efficiency compared to Monte-Carlo methods in small and medium dimensions (up to 10), which is confirmed by numerical experiments. (10.1137/130928431)
  DOI : 10.1137/130928431
• The Factorization Method for a Cavity in an Inhomogeneous Medium
  
  • Meng Shixu
  • Haddar Houssem
  • Cakoni Fioralba
  Inverse Problems, IOP Publishing, 2014, 30 (045008). We consider the inverse scattering problem for a cavity that is bounded by a penetrable anisotropic inhomogeneous medium of compact support and seek to determine the shape of the cavity from internal measurements on a curve or surface inside the cavity. We derive a factorization method which provides a rigorous characterization of the support of the cavity in terms of the range of an operator which is computable from the measured data. The support of the cavity is determined without a-priori knowledge of the constitutive parameters of the surrounding anisotropic medium provided they satisfy appropriate physical as well as mathematical assumptions imposed by our analysis. Numerical examples are given showing the viability of our method. (10.1088/0266-5611/30/4/045008)
  DOI : 10.1088/0266-5611/30/4/045008
• A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging
  
  • Nguyen Dang Van
  • Li Jing-Rebecca
  • Grebenkov Denis S
  • Le Bihan Denis
  Journal of Computational Physics, Elsevier, 2014, pp.283–302. The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explict Runge-Kutta-Chebychev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI. (10.1016/j.jcp.2014.01.009)
  DOI : 10.1016/j.jcp.2014.01.009