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.
• 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
• 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.
• Singular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity
  
  • Méléard Sylvie
  • Mirrahimi Sepideh
  Communications in Partial Differential Equations, Taylor & Francis, 2015, 40 (5), pp.957-993. We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplacian in determining this speed is at the initial layer where it determines the thickness of the tails of the solutions. Next, we show that such rescaling is also possible for models with non-local reaction terms, as selection-mutation models. However, to obtain a more relevant qualitative behavior for this second case, we introduce, in the second part of the paper, a second rescaling where we assume that the diffusion steps are small. In this way, using a WKB ansatz, we obtain a Hamilton-Jacobi equation in the limit which describes the asymptotic dynamics of the solutions, similarly to the case of selection-mutation models with a classical Laplace term or an integral kernel with thin tails. However, the rescaling introduced here is very different from the latter cases. We extend these results to the multidimensional case. (10.1080/03605302.2014.963606)
  DOI : 10.1080/03605302.2014.963606
• Inverse scattering without phase information
  
  • Novikov Roman
  Séminaire Laurent Schwartz - EDP et applications, Centre de mathématiques Laurent Schwartz, 2015, 2014-2015, pp.Exposé no. 16, 13 pp. We report on nonuniqueness, uniqueness and reconstruction results in quantum mechanical and acoustic inverse scattering without phase information. We are motivated by recent and very essential progress in this domain. This paper is an extended version of the talk given at Séminaire Laurent Schwartz on March 31, 2015. (10.5802/slsedp.74)
  DOI : 10.5802/slsedp.74
• The topological derivative of stress-based cost functionals in anisotropic elasticity
  
  • Delgado Gabriel
  • Bonnet Marc
  Computers & Mathematics with Applications, Elsevier, 2015, 69, pp.1144-1166. The topological derivative of cost functionals J that depend on the stress (through the displacement gradient, assuming a linearly elastic material behavior) is considered in a quite general 3D setting where both the background and the inhomogeneity may have arbitrary anisotropic elastic properties. The topological derivative dJ(z) of J quantifies the asymptotic behavior of J under the nucleation in the background elastic medium of a small anisotropic inhomogeneity of characteristic radius a at a specified location z. The fact that the strain perturbation inside an elastic inhomogeneity remains finite for arbitrarily small a makes the small-inhomogeneity asymptotics of stress-based cost functionals quite different than that of the more usual displacement-based functionals. The asymptotic perturbation of J is shown to be of order O(a^3) for a wide class of stress-based cost functionals having smooth densities. The topological derivative of J, i.e. the coefficient of the O(a^3) perturbation, is established, and computational procedures then discussed. The resulting small-inhomogeneity expansion of J is mathematically justified (i.e. its remainder is proved to be of order o(a^3)). Several 2D and 3D numerical examples are presented, in particular demonstrating the proposed formulation of \dJ on cases involving anisotropic elasticity and non-quadratic cost functionals. (10.1016/j.camwa.2015.03.010)
  DOI : 10.1016/j.camwa.2015.03.010
• Training Schr\"odinger's cat: quantum optimal control
  
  • Glaser Stefffen J.
  • Boscain Ugo
  • Calarco Tommaso
  • Koch Christiane P.
  • Köckenberger Walter
  • Kosloff Ronnie
  • Kuprov Ilya
  • Luy Burkard
  • Schirmer Sophie
  • Schulte-Herbrüggen Thomas
  • Sugny Dominique
  • Wilhelm Frank K.
  , 2015. It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy and resources -- as famously applied in the Apollo programme. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. --- Here state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium uniting expertise in optimal control theory and applications to spectroscopy, imaging, quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap to future developments.
• MatVPC: A User-Friendly MATLAB-Based Tool for the Simulation and Evaluation of Systems Pharmacology Models
  
  • Biliouris Kostas
  • Lavielle Marc
  • Trame Mirjam
  CPT: Pharmacometrics and Systems Pharmacology, American Society for Clinical Pharmacology and Therapeutics ; International Society of Pharmacometrics, 2015. Quantitative systems pharmacology (QSP) models are progressively entering the arena of contemporary pharmacology. The efficient implementation and evaluation of complex QSP models necessitates the development of flexible computational tools that are built into QSP mainstream software. To this end, we present MatVPC, a versatile MATLAB-based tool that accommodates QSP models of any complexity level. MatVPC executes Monte Carlo simulations as well as automatic construction of visual predictive checks (VPCs) and quantified VPCs (QVPCs). VPC is a model diagnostic tool that facilitates the evaluation of both the structural and the stochastic part of a model. It is constructed by superimposing the observations over the model simulations while accounting for both the interindivid-ual variability as well as the residual variability. 1 Once underutilized, 2 the VPC now is recognized as one of the most valuable model diagnostics in pharmacological model evaluation. 3–5 Its superiority over comparable diagnostic tools has been established 6 and reflected by the fact that regulatory agencies recommend it as one of the central model diagnostics. 7 (10.1002/psp4.12011)
  DOI : 10.1002/psp4.12011
• Ensuring robustness of domain decomposition methods by block strategies
  
  • Gosselet Pierre
  • Rixen Daniel
  • Spillane Nicole
  • Roux François-Xavier
  , 2015. no abstract
• Lyapunov and Minimum-Time Path Planning for Drones
  
  • Maillot Thibault
  • Boscain Ugo
  • Gauthier Jean-Paul
  • Serres Ulysse
  Journal of Dynamical and Control Systems, Springer Verlag, 2015, 21 (1), pp.1-34. (10.1007/s10883-014-9222-y)
  DOI : 10.1007/s10883-014-9222-y
• Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multi-dimensional and multi-component laws
  
  • Boutin Benjamin
  • Coquel Frédéric
  • LeFloch Philippe G.
  Mathematics of Computation, American Mathematical Society, 2015, 84 (294), pp.1663-1702. This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of partial differential equations. In an earlier work, this strategy allowed us to develop a regularization method based on a thick interface model in one space variable for coupling scalar equations. In the present paper, we significantly extend this framework and, in addition, encompass equations in several space variables. This new formulation includes the coupling of several distinct scalar conservation laws and allows for a possible covering in space. Our main contributions are, on one hand, the design and analysis of a well–balanced finite volume method on general triangulations and, on the other hand, a proof of convergence of this method toward entropy solutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to a single conservation law without coupling). The core of our analysis is, first, the derivation of entropy inequalities as well as a discrete entropy dissipation estimate and, second, a proof of convergence toward the entropy solution of the coupling problem. (10.1090/S0025-5718-2015-02933-0)
  DOI : 10.1090/S0025-5718-2015-02933-0
• Artificial boundary conditions for axisymmetric eddy current probe problems
  
  • Haddar Houssem
  • Jiang Zixian
  • Lechleiter Armin
  Computers & Mathematics with Applications, Elsevier, 2015, 68 (12, Part A,), pp.1844–1870. We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as the truncation parameter tends to infinity. Under stronger assumptions on the physical parameters of the eddy current problem, convergence rates are shown. We further validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes. (10.1016/j.camwa.2014.10.008)
  DOI : 10.1016/j.camwa.2014.10.008
• Developmental Partial Differential Equations
  
  • Pouradier Duteil Nastassia
  • Rossi Francesco
  • Boscain Ugo
  • Piccoli Benedetto
  , 2015. In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold’s evolution. In other words, the manifold’s evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold’s geometry. DPDE is used to study a diffusion equation with source on a growing surface whose growth depends on the intensity of the diffused quantity. The surface may, for instance, represent the membrane of an egg chamber and the diffused quantity a protein activating a signaling pathway leading to growth. Our main objective is to show controllability of the surface shape using a fixed source with variable intensity for the diffusion. More specifically, we look for a control driving a symmetric manifold shape to any other symmetric shape in a given time interval. For the diffusion we take directly the Laplace-Beltrami operator of the surface, while the surface growth is assumed to be equal to the value of the diffused quantity. We introduce a theoretical framework, provide approximate controllability and show numerical results. Future applications include a specific model for the oogenesis of Drosophila melanogaster.
• Phaseless inverse scattering in the one-dimensional case
  
  • Novikov Roman
  Eurasian Journal of Mathematical and Computer Applications, Eurasian National University, Kazakhstan (Nur-Sultan), 2015, 3 (1), pp.64-70. We consider the one-dimensional Schrödinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line x ≥ 0. For this equation at fixed positive energy we give explicit formulas for finding the full complex valued reflection coefficient to the left from appropriate phaseless scattering data measured on the left, i.e. for x < 0. Using these formulas and known inverse scattering results we obtain global uniqueness and reconstruction results for phaseless inverse scattering in dimension d = 1.
• Energy release rate for non smooth cracks in planar elasticity
  
  • Babadjian Jean-François
  • Chambolle Antonin
  • Lemenant Antoine
  Journal de l'École polytechnique — Mathématiques, École polytechnique, 2015, 2, pp.117-152. This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density $1/2$ at the tip. First, the blow-up limit of the displacement is analyzed, and the convergence to the corresponding positively $1/2$-homogenous function in the cracked plane is established. Then, the energy release rate is obtained as the derivative of the elastic energy with respect to an infinitesimal additional crack increment.
• On the control of spin-boson systems
  
  • Boscain Ugo
  • Mason Paolo
  • Panati Gianluca
  • Sigalotti Mario
  Journal of Mathematical Physics, American Institute of Physics (AIP), 2015, 56 (9). In this paper, we study the so-called spin-boson system, namely, a two-level system in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes-Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter. (C) 2015 AIP Publishing LLC. (10.1063/1.4929543)
  DOI : 10.1063/1.4929543
• Identification of magnetic deposits in 2-D axisymmetric eddy current models via shape optimization
  
  • Jiang Zixian
  • Haddar Houssem
  • Lechleiter Armin
  • El-Guedri Mabrouka
  Inverse Problems in Science and Engineering, Taylor & Francis, 2015. The non-destructive control of steam generators is an essential task for the safe and failure-free operation of nuclear power plants. Due to magnetite particles in the cooling water of the plants, a frequent source for failures are magnetic deposits in the cooling loop of steam generators. From eddy current signals measured inside a U-tube in the steam generator, we propose and analyze a regularized shape optimization algorithm to identify magnetic deposits outside the U-tube with either known or unknown physical properties. Motivated by the cylindrical geometry of the U-tubes we assume an axisymmetric problem setting, reducing Maxwell's equations to a 2-D elliptic eddy current problem. The feasibility of the proposed algorithms is illustrated via numerical examples demonstrating in particular the stability of the method with respect to noise.
• A Convergent Data Completion Algorithm Using Surface Integral Equations
  
  • Boukari Yosra
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2015, pp.21. We propose and analyze a data completion algorithm based on the representation of the solution in terms of surface integral operators to solve the Cauchy problem for the Helmholtz or the Laplace equations. The proposed method is non iterative and intrinsically handle the case of noisy and incompatible data. In order to cope with the ill-posedness of the problem, our formulation is compatible with standard regularization methods associated with linear ill posed inverse problems and leads to convergent scheme. We numerically validate our method with different synthetic examples using a Tikhonov regularization.
• Analysis of Some Qualitative Methods for Inverse Electromagnetic Scattering Problems
  
  • Haddar Houssem
  , 2015, pp.51. This chapter provides a comprehensive presentation of some qualitative methods associated with inverse 3D electromagnetic scattering problem from inhomogeneous and anisotropic media. We first discuss the problem in the framework of so-called Born approximation, that leads to a linearisation of the inverse problem. We second present and analyze the application of the Linear Sampling Method to the full non linear problem using multistatic data at a given frequency. We especially focus on a generalization of this method based on an exact characterization of the inclusion shape in terms of the available data. We then discuss the closely related interior transmission problem and associated transmission eigenvalues. We complement each chapter with some open challenging questions as well as references for further readings. (10.1007/978-3-319-19306-9)
  DOI : 10.1007/978-3-319-19306-9
• Rare event simulation using reversible shaking transformations
  
  • Gobet Emmanuel
  • Liu Gang
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2015, 37 (5), pp.A2295-A2316. We introduce random transformations called reversible shaking transformations which we use to design two schemes for estimating rare event probability. One is based on interacting particle systems (IPS) and the other on time-average on a single path (POP) using ergodic theorem. We discuss their convergence rates and provide numerical experiments including continuous stochastic processes and jump processes. Our examples cover rather important situations related to insurance, queueing system and random graph for instance. Both schemes have good performance, with a seemingly better one for POP. (10.1137/14098418X)
  DOI : 10.1137/14098418X
• A deterministic approximation method in shape optimization under random uncertainties
  
  • Allaire Grégoire
  • Dapogny Charles
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2015, 1, pp.83-143. This paper is concerned with the treatment of uncertainties in shape optimization. We consider uncertainties in the loadings, the material properties, the geometry and the vibration frequency, both in the parametric and geometric optimization setting. We minimize objective functions which are mean values, variances or failure probabilities of standard cost functions under random uncertainties. By assuming that the uncertainties are small and generated by a finite number N of random variables, and using first-or second-order Taylor expansions, we propose a deterministic approach to optimize approximate objective functions. The computational cost is similar to that of a multiple load problems where the number of loads is N. We demonstrate the effectiveness of our approach on various parametric and geometric optimization problems in two space dimensions. (10.5802/smai-jcm.5)
  DOI : 10.5802/smai-jcm.5
• Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
  
  • Bokanowski Olivier
  • Picarelli Athena
  • Zidani Hasnaa
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2015, 71 (1), pp.125--163. This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton- Jacobi-Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach. (10.1007/s00245-014-9255-3)
  DOI : 10.1007/s00245-014-9255-3
• Mean field games systems of first order
  
  • Cardaliaguet Pierre
  • Graber Philip Jameson
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2015, 21 (3), pp.690–722. We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
• Influence of a spatial structure on the long time behavior of a competitive Lotka-Volterra type system
  
  • Leman Hélène
  • Meleard Sylvie
  • Mirrahimi Sepideh
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2015, 20 (2), pp.469-493. To describe population dynamics, it is crucial to take into account jointly evolution mechanisms and spatial motion. However, the models which include these both aspects, are not still well-understood. Can we extend the existing results on type structured populations, to models of populations structured by type and space, considering diffusion and nonlocal competition between individuals? We study a nonlocal competitive Lotka-Volterra type system, describing a spatially structured population which can be either monomorphic or dimorphic. Considering spatial diffusion, intrinsic death and birth rates, together with death rates due to intraspecific and interspecific competition between the individuals, leading to some integral terms, we analyze the long time behavior of the solutions. We first prove existence of steady states and next determine the long time limits, depending on the competition rates and the principal eigenvalues of some operators, corresponding somehow to the strength of traits. Numerical computations illustrate that the introduction of a new mutant population can lead to the long time evolution of the spatial niche.
• Avis en réponse à la saisine 150519 - dossier C-NL-13-01. Paris, le 7 septembre 2015
  
  • 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.27 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/13/01 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.