Publications

2015

• Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models
  
  • Haddar Houssem
  • Jiang Zixian
  Inverse Problems, IOP Publishing, 2015. Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and are therefore important to be identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layer's small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. Standard iterative inversion algorithm is then applied to the asymptotic models in order to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and benefit of the inversion procedure are provided.
• Boundary Integral Equations for the Transmission Eigenvalue Problem for Maxwell’s Equations
  
  • Cakoni Fioralba
  • Haddar Houssem
  • Meng Shixu
  Journal of Integral Equations and Applications, Rocky Mountain Mathematics Consortium, 2015, pp.26. In this paper we consider the transmission eigenvalue problem for Maxwell’s equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission eigenvalue problem as an equivalent homogeneous system of boundary integral equa- tion, and assuming that the contrast is constant near the boundary of the support of the inhomogeneity, we prove that the operator associated with this system is Fredholm of index zero and depends analytically on the wave number. Then we show the existence of wave numbers that are not transmission eigenvalues which by an application of the analytic Fredholm theory implies that the set of transmission eigenvalues is discrete with positive infinity as the only accumulation point.
• Avis en réponse à la saisine 150519 - dossier C-NL-13-02. Paris, le 7 septembre 2015
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie Anne M. A.
  • Bellivier Florence
  • Berny Philippe
  • Bertheau Yves
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Coléno François
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Eychenne Nathalie
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Jestin André
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie V.
  • Lemaire Olivier O.
  • Lereclus Didier
  • Maximilien Rémi
  • Meurs Eliane
  • Moreau de Bellaing Cédric
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Parzy Daniel
  • Regnault-Roger Catherine
  • Renard Michel
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2015, pp.21 p.. Le Haut Conseil des biotechnologies (HCB) a été saisi le 20 mai 2015 par les autorités compétentes françaises (le ministère de l’Agriculture, de l’Agroalimentaire et de la Forêt) d’une demande d’avis relative au dossier C/NL/13/02 de demande de mise sur le marché de la lignée d’oeillets génétiquement modifiés FLO-40685-1 à des fins d’importation et de commercialisation de fleurs coupées. Ce dossier a été déposé par la société Suntory Holdings Limited auprès des autorités compétentes néerlandaises dans le cadre de la directive 2001/18/CE. Conformément à cette directive, la Commission européenne a adressé le rapport d’évaluation des Pays-Bas ainsi que le dossier du pétitionnaire à l’ensemble des Etats membres. Par cette saisine, les autorités compétentes françaises consultent le HCB au stade ultime de la préparation au vote des Etats membres à la Commission européenne. Le Comité scientifique (CS)2 du HCB a examiné le dossier en séance du 25 juin 2015 sous la présidence de Jean-Christophe Pagès. Le présent avis a été adopté par voie électronique le 7 septembre 2015 et publié le 10 septembre 2015.
• Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion
  
  • Belaouar Radoin
  • de Bouard Anne
  • Debussche Arnaud
  Stochastics and Partial Differential Equations: Analysis and Computations, Springer US, 2015, 3 (1), pp.103-132. This article is devoted to the numerical study of a nonlinear Schrödinger equation in which the coefficient in front of the group velocity dispersion is multiplied by a real valued Gaussian white noise. We first perform the numerical analysis of a semi-discrete Crank-Nicolson scheme in the case when the continuous equation possesses a unique global solution. We prove that the strong order of convergence in probability is equal to one in this case. In a second step, we numerically investigate, in space dimension one, the behavior of the solutions of the equation for different power nonlinearities, corresponding to subcritical, critical or supercritical nonlinearities in the deterministic case. Numerical evidence of a change in the critical power due to the presence of the noise is pointed out. (10.1007/s40072-015-0044-z)
  DOI : 10.1007/s40072-015-0044-z
• On the scaling limits of Galton–Watson processes in varying environments
  
  • Bansaye Vincent
  • Simatos Florian
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2015, 20 (75), pp.1-36. We establish a general sufficient condition for a sequence of Galton–Watson branching processes in varying environments to converge weakly. This condition extends previ- ous results by allowing offspring distributions to have infinite variance. Our assumptions are stated in terms of pointwise convergence of a triplet of two real- valued functions and a measure. The limiting process is characterized by a backwards integro-differential equation satisfied by its Laplace exponent, which generalizes the branching equation satisfied by continuous state branching processes. Several examples are discussed, namely branching processes in random environment, Feller diffusion in varying environments and branching processes with catastrophes. (10.1214/EJP.v20-3812)
  DOI : 10.1214/EJP.v20-3812
• Converse Lyapunov-Krasovskii theorems for uncertain retarded differential equations
  
  • Haidar Ihab
  • Mason Paolo
  • Sigalotti Mario
  Automatica, Elsevier, 2015, 62, pp.263-273. In this article we give a collection of converse Lyapunov–Krasovskii theorems for uncertain retarded differential equations. We show that the existence of a weakly-degenerate Lyapunov–Krasovskii functional is a necessary and sufficient condition for the global exponential stability of linear retarded functional differential equations. This is carried out using a switched system representation approach. (10.1016/j.automatica.2015.09.034)
  DOI : 10.1016/j.automatica.2015.09.034
• A remark on accelerated block coordinate descent for computing the proximity operators of a sum of convex functions.
  
  • Chambolle Antonin
  • Pock Thomas
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2015, 1, pp.29 - 54. We analyze alternating descent algorithms for minimizing the sum of a quadratic function and block separable non-smooth functions. In case the quadratic interactions between the blocks are pairwise, we show that the schemes can be accelerated, leading to improved convergence rates with respect to related accelerated parallel proximal descent. As an application we obtain very fast algorithms for computing the proximity operator of the 2D and 3D total variation. (10.5802/smai-jcm.3)
  DOI : 10.5802/smai-jcm.3
• Unveiling the Diversification Dynamics of Australasian Predaceous Diving Beetles in the Cenozoic
  
  • Toussaint Emmanuel F.A.
  • Condamine Fabien L.
  • Hawlitschek Oliver
  • Watts Chris H.
  • Porch Nick
  • Hendrich Lars
  • Balke Michael
  Systematic Biology, Oxford University Press (OUP), 2015, 64 (1), pp.3-24. During the Cenozoic, Australia experienced major climatic shifts that have had dramatic ecological consequences for the modern biota. Mesic tropical ecosystems were progressively restricted to the coasts and replaced by arid-adapted floral and faunal communities. Whilst the role of aridification has been investigated in a wide range of terrestrial lineages, the response of freshwater clades remains poorly investigated. To gain insights into the diversification processes underlying a freshwater radiation, we studied the evolutionary history of the Australasian predaceous diving beetles of the tribe Hydroporini (147 described species). We used an integrative approach including the latest methods in phylogenetics, divergence time estimation, ancestral character state reconstruction, and likelihood-based methods of diversification rate estimation. Phylogenies and dating analyses were reconstructed with molecular data from seven genes (mitochondrial and nuclear) for 117 species (plus 12 outgroups). Robust and well-resolved phylogenies indicate a late Oligocene origin of Australasian Hydroporini. Biogeographic analyses suggest an origin in the East Coast region of Australia, and a dynamic biogeographic scenario implying dispersal events. The group successfully colonized the tropical coastal regions carved by a rampant desertification, and also colonized groundwater ecosystems in Central Australia. Diversification rate analyses suggest that the ongoing aridification of Australia initiated in the Miocene contributed to a major wave of extinctions since the late Pliocene probably attributable to an increasing aridity, range contractions and seasonally disruptions resulting from Quaternary climatic changes. When comparing subterranean and epigean genera, our results show that contrasting mechanisms drove their diversification and therefore current diversity pattern. The Australasian Hydroporini radiation reflects a combination of processes that promoted both diversification, resulting from new ecological opportunities driven by initial aridification, and a subsequent loss of mesic adapted diversity due to increasing aridity. (10.1093/sysbio/syu067)
  DOI : 10.1093/sysbio/syu067
• New high order sufficient conditions for configuration tracking
  
  • Barbero-Liñán M.
  • Sigalotti M.
  Automatica, Elsevier, 2015, 62, pp.222-226. In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature. The new results are proved by a combination of averaging procedures by highly oscillating controls with the notion of kinematic reduction. (10.1016/j.automatica.2015.09.032)
  DOI : 10.1016/j.automatica.2015.09.032
• Control of a Quantum Model for Two Trapped Ions
  
  • Paduro Esteban
  • Sigalotti Mario
  , 2015.
• Approximate Controllability of the Two Trapped Ions System
  
  • Paduro Esteban
  • Sigalotti Mario
  Quantum Information Processing, Springer Verlag, 2015, 14, pp.2397-2418. We prove the approximate controllability of a bilinear Schr\"odinger equation modelling a two trapped ions system. A new spectral decoupling technique is introduced, which allows to analyze the controllability of the infinite-dimensional system through finite-dimensional considerations.
• Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations
  
  • Kröner Axel
  • Rodrigues Sergio S.
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1020–1055. The feedback stabilization of the Burgers system to a nonstationary solution using finite-dimensional internal controls is considered. Estimates for the dimension of the controller are derived. In the particular case of no constraint on the support of the controla better estimate is derived and the possibility of getting an analogous estimate for the general case is discussed; some numerical examplesare presented illustrating the stabilizing effect of the feedback control, and suggesting that the existence of an estimatein the general case analogous to that in the particular one is plausible.
• Finite element approximation of level set motion by powers of the mean curvature
  
  • Kröner Axel
  • Kröner Eva
  • Kröner Heiko
  , 2015. In this paper we study the level set formulations of certain geometric evolution equations from a numerical point of view. Specifically, we consider the flow by powers greater than one of the mean curvature and the inverse mean curvature flow. Since the corresponding equations in level set form are quasilinear, degenerate and especially possibly singular a regularization method is used in the literature to approximate these equations to overcome the singularities of the equations. Motivated by the paper [29] which studies the finite element approximation of inverse mean curvature flow we prove error estimates for the finite element approximation of the regularized equations for the flow by powers of the mean curvature. We validate the rates with numerical examples. Additionally, the regularization error in the rotational symmetric case for both flows is analyzed numerically. All calculations are performed in the 2D case.
• Mathematical justification of macroscopic models for diffusion MRI through the periodic unfolding method
  
  • Coatléven Julien
  Asymptotic Analysis, IOS Press, 2015, 93 (3), pp.219-258. Diffusion Magnetic Resonance Imaging (dMRI) is a promising tool to obtain useful information on cellular structure when applied to biological tissues. A coupled macroscopic model has been introduced recently through formal homogenization to model dMRI's signal attenuation. This model was based on a particular scaling of the permeability condition modeling cellular membranes. In this article, we explore all the possible scalings and mathematically justify the corresponding limit models, using the periodic unfolding method. We also illustrate through numerical simulations the respective behavior of the limit models when compared to dMRI measurements. (10.3233/ASY-151294)
  DOI : 10.3233/ASY-151294
• Second order BSDEs with jumps: formulation and uniqueness
  
  • Kazi-Tani Mohamed Nabil
  • Possamaï Dylan
  • Zhou Chao
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2015, 25 (5), pp.2867-2908. (10.1214/14-AAP1063)
  DOI : 10.1214/14-AAP1063
• Sparse and spurious: dictionary learning with noise and outliers
  
  • Gribonval Rémi
  • Jenatton Rodolphe
  • Bach Francis
  IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2015, 61 (11), pp.6298-6319. A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio processing, there have only been a few theoretical arguments supporting these evidences. In particular, sparse coding, or sparse dictionary learning, relies on a non-convex procedure whose local minima have not been fully analyzed yet. In this paper, we consider a probabilistic model of sparse signals, and show that, with high probability, sparse coding admits a local minimum around the reference dictionary generating the signals. Our study takes into account the case of over-complete dictionaries, noisy signals, and possible outliers, thus extending previous work limited to noiseless settings and/or under-complete dictionaries. The analysis we conduct is non-asymptotic and makes it possible to understand how the key quantities of the problem, such as the coherence or the level of noise, can scale with respect to the dimension of the signals, the number of atoms, the sparsity and the number of observations. (10.1109/TIT.2015.2472522)
  DOI : 10.1109/TIT.2015.2472522
• Dobrushin ergodicity coefficient for Markov operators on cones
  
  • Gaubert Stéphane
  • Qu Zheng
  Integral Equations and Operator Theory, Springer Verlag, 2015, 1 (81), pp.127-150. Doeblin and Dobrushin characterized the contraction rate of Markov operators with respect the total variation norm. We generalize their results by giving an explicit formula for the contraction rate of a Markov operator over a cone in terms of pairs of extreme points with disjoint support in a set of abstract probability measures. By duality, we derive a characterization of the contraction rate of consensus dynamics over a cone with respect to Hopf’s oscillation seminorm (the infinitesimal seminorm associated with Hilbert’s projective metric). We apply these results to Kraus maps (noncommutative Markov chains, representing quantum channels), and characterize the ultimate contraction of the map in terms of the existence of a rank one matrix in a certain subspace. (10.1007/s00020-014-2193-2)
  DOI : 10.1007/s00020-014-2193-2
• Origin and diversification of living cycads: a cautionary tale on the impact of the branching process prior in Bayesian molecular dating
  
  • Condamine Fabien L.
  • Nagalingum Nathalie S.
  • Marshall Charles R
  • Morlon Hélène
  BMC Evolutionary Biology, BioMed Central, 2015, 15 (1). Background: Bayesian relaxed-clock dating has significantly influenced our understanding of the timeline of biotic evolution. This approach requires the use of priors on the branching process, yet little is known about their impact on divergence time estimates. We investigated the effect of branching priors using the iconic cycads. We conducted phylogenetic estimations for 237 cycad species using three genes and two calibration strategies incorporating up to six fossil constraints to (i) test the impact of two different branching process priors on age estimates, (ii) assess which branching prior better fits the data, (iii) investigate branching prior impacts on diversification analyses, and (iv) provide insights into the diversification history of cycads. Results: Using Bayes factors, we compared divergence time estimates and the inferred dynamics of diversification when using Yule versus birth-death priors. Bayes factors were calculated with marginal likelihood estimated with stepping-stone sampling. We found striking differences in age estimates and diversification dynamics depending on prior choice. Dating with the Yule prior suggested that extant cycad genera diversified in the Paleogene and with two diversification rate shifts. In contrast, dating with the birth-death prior yielded Neogene diversifications, and four rate shifts, one for each of the four richest genera. Nonetheless, dating with the two priors provided similar age estimates for the divergence of cycads from Ginkgo (Carboniferous) and their crown age (Permian). Of these, Bayes factors clearly supported the birth-death prior. Conclusions: These results suggest the choice of the branching process prior can have a drastic influence on our understanding of evolutionary radiations. Therefore, all dating analyses must involve a model selection process using Bayes factors to select between a Yule or birth-death prior, in particular on ancient clades with a potential pattern of high extinction. We also provide new insights into the history of cycad diversification because we found (i) periods of extinction along the long branches of the genera consistent with fossil data, and (ii) high diversification rates within the Miocene genus radiations. (10.1186/s12862-015-0347-8)
  DOI : 10.1186/s12862-015-0347-8
• A highly anisotropic nonlinear elasticity model for vesicles I. Eulerian formulation, rigidity estimates and vanishing energy limit
  
  • Merlet Benoit
  Archive for Rational Mechanics and Analysis, Springer Verlag, 2015, 217 (2), pp.651--680. We propose a nonlinear elasticity model for vesicle membranes which is an Eulerian version of a model introduced by Pantz and Trabelsi.We describe the limit behavior of sequences of configurations whose energy goes to 0 in a fixed domain. The material is highly anisotropic and the analysis is based on some rigidity estimates adapted to this anisotropy. The main part of the paper is devoted to these estimates and to some of their consequences. The strongest form of these estimates are used in a second article to derive the thin-shell limit bending theory of the model. (10.1007/s00205-014-0839-5)
  DOI : 10.1007/s00205-014-0839-5
• Analytical approximations of BSDEs with non-smooth driver
  
  • Gobet Emmanuel
  • Pagliarani Stefano
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2015, 6 (1), pp.919-958. We provide and analyse analytical approximations of BSDEs in the limit of small non-linearity {and short time}, in the case of non-smooth drivers. We identify the first and the second order approximations within this asymptotics and consider two topical financial applications: the two interest rates problem and the Funding Value Adjustment. In high dimensional diffusion setting, we show how to compute explicitly the first order formula by taking advantage of recent proxy techniques. Numerical tests up to dimension 10 illustrate the efficiency of the numerical schemes. (10.1137/14100021X)
  DOI : 10.1137/14100021X
• Phase retrieval for the Cauchy wavelet transform
  
  • Waldspurger Irène
  • Mallat Stéphane
  Journal of Fourier Analysis and Applications, Springer Verlag, 2015. We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuous but not uniformly continuous. We describe how to construct pairs of functions which are far away in L 2-norm but whose wavelet transforms are very close, in modulus. The principle is to modulate the wavelet transform of a fixed initial function by a phase which varies slowly in both time and frequency. This construction seems to cover all the instabilities that we observe in practice; we give a partial formal justification to this fact. Finally, we describe an exact reconstruction algorithm and use it to numerically confirm our analysis of the stability question.
• Time-Optimal Synthesis for Three Relevant Problems: The Brockett Integrator, the Grushin Plane and the Martinet Distribution
  
  • Barilari Davide
  • Boscain Ugo
  • Le Donne Enrico
  • Sigalotti Mario
  , 2015.
• Derivation of nonlinear shell models combining shear and flexure: application to biological membranes
  
  • Pantz Olivier
  • Trabelsi Karim
  Mathematics and Mechanics of Complex Systems, International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS),University of L’Aquila in Italy, 2015, 3 (2), pp.101--138. Biological membranes are often idealized as incompressible elastic surfaces whose strain energy only depends on their mean curvature and pos-sibly on their shear. We show that this type of model can be derived using a formal asymptotic method by considering biological membranes to be thin, strongly anisotropic, elastic, locally homogeneous bodies.
• Sample Complexity of Dictionary Learning and other Matrix Factorizations
  
  • Gribonval Rémi
  • Jenatton Rodolphe
  • Bach Francis
  • Kleinsteuber Martin
  • Seibert Matthias
  IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2015, 61 (6), pp.3469-3486. Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. While the idealized task would be to optimize the expected quality of the factors over the underlying distribution of training vectors, it is achieved in practice by minimizing an empirical average over the considered collection. The focus of this paper is to provide sample complexity estimates to uniformly control how much the empirical average deviates from the expected cost function. Standard arguments imply that the performance of the empirical predictor also exhibit such guarantees. The level of genericity of the approach encompasses several possible constraints on the factors (tensor product structure, shift-invariance, sparsity \ldots), thus providing a unified perspective on the sample complexity of several widely used matrix factorization schemes. The derived generalization bounds behave proportional to $\sqrt{\log(n)/n}$ w.r.t.\ the number of samples $n$ for the considered matrix factorization techniques. (10.1109/TIT.2015.2424238)
  DOI : 10.1109/TIT.2015.2424238
• Convergent stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation
  
  • Allassonnière Stéphanie
  • Kuhn Estelle
  Computational Statistics and Data Analysis, Elsevier, 2015, 91, pp.4-19. Estimation in the deformable template model is a big challenge in image analysis. The issue is to estimate an atlas of a population. This atlas contains a template and the corresponding geometrical variability of the observed shapes. The goal is to propose an accurate estimation algorithm with low computational cost and with theoretical guaranties of relevance. This becomes very demanding when dealing with high dimensional data, which is particularly the case of medical images. The use of an optimized Monte Carlo Markov Chain method for a stochastic Expectation Maximization algorithm, is proposed to estimate the model parameters by maximizing the likelihood. A new Anisotropic Metropolis Adjusted Langevin Algorithm is used as transition in the MCMC method. First it is proven that this new sampler leads to a geometrically uniformly ergodic Markov chain. Furthermore, it is proven also that under mild conditions, the estimated parameters converge almost surely and are asymptotically Gaussian distributed. The methodology developed is then tested on handwritten digits and some 2D and 3D medical images for the deformable model estimation. More widely, the proposed algorithm can be used for a large range of models in many fields of applications such as pharmacology or genetic. The technical proofs are detailed in an appendix. (10.1016/j.csda.2015.04.011)
  DOI : 10.1016/j.csda.2015.04.011