Publications

2018

• Avis en réponse à la saisine HCB - dossier 2014-123. Paris, le 27 juin 2018
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2018.
• Pharmacometrics Models with Hidden Markovian Dynamics
  
  • Lavielle Marc
  Journal of Pharmacokinetics and Pharmacodynamics, Springer Verlag, 2018, 45 (1), pp.91--105. The aim of this paper is to provide an overview of pharmacometric models that involve some latent process with Markovian dynamics. Such models include hidden Markov models which may be useful for describing the dynamics of a disease state that jumps from one state to another at discrete times. On the contrary, diffusion models are continuous-time and continuous-state Markov models that are relevant for modelling non observed phenomena that fluctuate continuously and randomly over time. We show that an extension of these models to mixed effects models is straightforward in a population context. We then show how the Forward-Backward algorithm used for inference in hidden Markov models and the extended Kalman filter used for inference in diffusion models can be combined with standard inference algorithms in mixed effects models for estimating the parameters of the model. The use of these models is illustrated with two applications: a hidden Markov model for describing the epileptic activity of a large number of patients and a stochastic differential equation based model for describing the pharmacokinetics of theophyllin. (10.1007/s10928-017-9541-1)
  DOI : 10.1007/s10928-017-9541-1
• Rapid discrimination and quantification analysis of five antineoplastic drugs in aqueous solutions using Raman spectroscopy
  
  • Lê Laetitia Minh Mai
  • Berge Marion
  • Tfayli Ali
  • Zhou Jiangyan
  • Prognon Patrice
  • Baillet-Guffroy Arlette
  • Caudron Eric
  European Journal of Pharmaceutical Sciences, Elsevier, 2018, 111, pp.158-166. (10.1016/j.ejps.2017.09.046)
  DOI : 10.1016/j.ejps.2017.09.046
• Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  Annales de l'Institut Henri Poincaré (A). Physique Theorique, Birkhäuser, 2018, 19 (6). We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of atoms with the rigid body: these collisions, due to the geometry of the rigid body, require developing a new type of trajectory analysis. (10.1007/s00023-018-0674-6)
  DOI : 10.1007/s00023-018-0674-6
• Darboux–Moutard transformations and Poincare–Steklov operators
  
  • Novikov Roman
  • Taimanov Iskander
  Proceedings of the Steklov Institute of Mathematics, MAIK Nauka/Interperiodica, 2018, 302, pp.315–324. Formulas relating Poincare–Steklov operators for Schrödinger equations related by Darboux–Moutard transformations are derived. They can be used for testing algorithms of reconstruction of the potential from measurements at the boundary. (10.1134/S0081543818060160)
  DOI : 10.1134/S0081543818060160
• New interior transmission problem applied to a single Floquet–Bloch mode imaging of local perturbations in periodic media
  
  • Cakoni Fioralba
  • Haddar Houssem
  • Nguyen Thi-Phong
  Inverse Problems, IOP Publishing, 2018, 35 (1), pp.015009.
• An integrate-and-fire model to generate spike trains with long memory
  
  • Richard Alexandre
  • Orio Patricio
  • Tanré Etienne
  Journal of Computational Neuroscience, Springer Verlag, 2018. Long-range dependence (LRD) has been observed in a variety of phenomena in nature, and for several years also in the spiking activity of neurons. Often, this is interpreted as originating from a non-Markovian system. Here we show that a purely Markovian integrate-and-re (IF) model, with a noisy slow adaptation term, can generate data that appears as having LRD with a Hurst exponent (H) greater than 0.5. A proper analysis shows that the asymptotic value of H is 0.5 if a long enough sequence of events is taken into account. For comparison, we also consider a new model of individual IF neuron with fractional noise. The correlations of its spike trains are studied and proved to have long memory, unlike classical IF models. On the other hand, to correctly measure long-range dependence, it is usually necessary to know if the data are stationary. Thus, a methodology to evaluate stationarity of the interspike intervals (ISIs) is presented and applied to the various IF models. In conclusion, the spike trains of our fractional model have the long-range dependence property, while those from classical Markovian models do not. However, Markovian IF models may seem to have it because of apparent non-stationarities. (10.1007/s10827-018-0680-1)
  DOI : 10.1007/s10827-018-0680-1
• FEM and BEM simulations with the Gypsilab framework
  
  • Alouges François
  • Aussal Matthieu
  SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2018, 4, pp.297-318. (10.5802/smai-jcm.36)
  DOI : 10.5802/smai-jcm.36
• Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures
  
  • Allaire Grégoire
  • Yamada T
  Numerische Mathematik, Springer Verlag, 2018, 140 (2), pp.265-326. We study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion. More precisely, we consider the case of a two-phase composite medium with an 8-fold symmetry assumption of the periodicity cell in two space dimensions. We obtain upper and lower bound for the dispersive properties, along with optimal microgeometries.
• SEME 2017 : identification de véhicules en utilisant le numéro VIN
  
  • Besson Rémi
  • Etchegaray Christèle
  • Ferrari Luca
  • Nordmann Samuel
  , 2018.
• Log-barrier interior point methods are not strongly polynomial
  
  • Allamigeon Xavier
  • Benchimol Pascal
  • Gaubert Stéphane
  • Joswig Michael
  SIAM Journal on Applied Algebra and Geometry, Society for Industrial and Applied Mathematics, 2018, 2 (1), pp.140-178. We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by constructing a family of linear programs with $3r+1$ inequalities in dimension $2r$ for which the number of iterations performed is in $\Omega(2^r)$. The total curvature of the central path of these linear programs is also exponential in $r$, disproving a continuous analogue of the Hirsch conjecture proposed by Deza, Terlaky and Zinchenko. Our method is to tropicalize the central path in linear programming. The tropical central path is the piecewise-linear limit of the central paths of parameterized families of classical linear programs viewed through logarithmic glasses. This allows us to provide combinatorial lower bounds for the number of iterations and the total curvature, in a general setting. (10.1137/17M1142132)
  DOI : 10.1137/17M1142132
• Study of new rare event simulation schemes and their application to extreme scenario generation
  
  • Agarwal Ankush
  • de Marco Stefano
  • Gobet Emmanuel
  • Liu Gang
  Mathematics and Computers in Simulation, Elsevier, 2018, 143, pp.89-98. This is a companion paper based on our previous work [ADGL15] on rare event simulation methods. In this paper, we provide an alternative proof for the ergodicity of shaking transformation in the Gaussian case and propose two variants of the existing methods with comparisons of numerical performance. In numerical tests, we also illustrate the idea of extreme scenario generation based on the convergence of marginal distributions of the underlying Markov chains and show the impact of the discretization of continuous time models on rare event probability estimation. (10.1016/j.matcom.2017.05.004)
  DOI : 10.1016/j.matcom.2017.05.004
• Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
  
  • Walsh Cormac
  Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2018, 68 (5), pp.1831-1877. We study the horofunction boundaries of Hilbert and Thompson geome-tries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the only Hilbert and Thompson geometries that are isometric to Banach spaces are the ones defined on the cone of positive continuous functions on a compact space.
• Optimizing supports for additive manufacturing
  
  • Allaire Grégoire
  • Bogosel Beniamin
  Structural and Multidisciplinary Optimization, Springer Verlag, 2018, 58 (6), pp.2493-2515. In additive manufacturing process support structures are often required to ensure the quality of the final built part. In this article we present mathematical models and their numerical implementations in an optimization loop, which allow us to design optimal support structures. Our models are derived with the requirement that they should be as simple as possible, computationally cheap and yet based on a realistic physical modeling. Supports are optimized with respect to two different physical properties. First, they must support overhanging regions of the structure for improving the stiffness of the supported structure during the building process. Second, supports can help in channeling the heat flux produced by the source term (typically a laser beam) and thus improving the cooling down of the structure during the fabrication process. Of course, more involved constraints or manufacturability conditions could be taken into account, most notably removal of supports. Our work is just a first step, proposing a general framework for support optimization. Our optimization algorithm is based on the level set method and on the computation of shape derivatives by the Hadamard method. In a first approach, only the shape and topology of the supports are optimized, for a given and fixed structure. In second and more elaborated strategy, both the supports and the structure are optimized, which amounts to a specific multiphase optimization problem. Numerical examples are given in 2-d and 3-d.
• Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling
  
  • Agrachev Andrei
  • Boscain Ugo
  • Neel Robert
  • Rizzi Luca
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2018, 24 (3), pp.1075–1105. We relate some basic constructions of stochastic analysis to differential geometry , via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either geodesics or integral curves associated to orthonormal frames, and we give particular attention to walks where the choice of step is influenced by a volume on the manifold. A primary motivation is to explore how one can pass, in the parabolic scaling limit, from geodesics, orthonormal frames, and/or volumes to diffusions, and hence their infinitesimal generators , on sub-Riemannian manifolds, which is interesting in light of the fact that there is no completely canonical notion of sub-Laplacian on a general sub-Riemannian mani-fold. However, even in the Riemannian case, this random walk approach illuminates the geometric significance of Ito and Stratonovich stochastic differential equations as well as the role played by the volume. (10.1051/cocv/2017037)
  DOI : 10.1051/cocv/2017037
• Random planar maps and growth-fragmentations
  
  • Bertoin Jean
  • Curien Nicolas
  • Kortchemski Igor
  The Annals of Probability, Institute of Mathematical Statistics, 2018, 46 (1), pp.207-260. (10.1214/17-AOP1183)
  DOI : 10.1214/17-AOP1183
• Infinite Horizon Stochastic Optimal Control Problems with Running Maximum Cost
  
  • Kröner Axel
  • Picarelli Athena
  • Zidani Hasnaa
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2018, 56 (5), pp.3296-3319. An infinite horizon stochastic optimal control problem with running maximum cost is considered. The value function is characterized as the viscosity solution of a second-order Hamilton-Jacobi-Bellman (HJB) equation with mixed boundary condition. A general numerical scheme is proposed and convergence is established under the assumptions of consistency, monotonicity and stability of the scheme. These properties are verified for a specific semi-Lagrangian scheme. (10.1137/17M115253X)
  DOI : 10.1137/17M115253X
• Avis en réponse à la saisine HCB - dossier EFSA-GMO-RX009. Paris, le 4 juin 2018
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2018.
• Fluctuations and Temperature Effects in Bose-Einstein Condensation
  
  • de Bouard Anne
  • Debussche Arnaud
  • Fukuizumi Reika
  • Poncet Romain
  ESAIM: Proceedings and Surveys, EDP Sciences, 2018, 61, pp.55-67. The modeling of cold atoms systems has known an increasing interest in the theoretical physics community, after the first experimental realizations of Bose Einstein condensates, some twenty years ago. We here review some analytical and numerical results concerning the influence of fluctuations , either arising from fluctuations of the confining parameters, or due to temperature effects, in the models describing the dynamics of such condensates. (10.1051/proc/201861055)
  DOI : 10.1051/proc/201861055
• Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots
  
  • Agostinelli Daniele
  • Alouges François
  • Desimone Antonio
  Frontiers in Robotics and AI, Frontiers Media S.A., 2018, 5, pp.99. Peristalsis, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed. (10.3389/frobt.2018.00099)
  DOI : 10.3389/frobt.2018.00099
• Principal-Agent Problem with Common Agency Without Communication
  
  • Mastrolia Thibaut
  • Ren Zhenjie
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2018, 9 (2), pp.775-799. In this paper, we consider a problem of contract theory in which several Principals hire a common Agent and we study the model in the continuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we reduce the optimization problem of the Principals to a system of coupled Hamilton--Jacobi--Bellman (HJB) equations. We provide conditions ensuring that for risk-neutral Principals, the system of coupled HJB equations admits a solution. Further, we apply our study in a more specific linear-quadratic model where two interacting Principals hire one common Agent. In this continuous time model, we extend the result of [B. D. Bernheim and M. D. Whinston, Econometrica, 54 (1986), pp. 923--942] in which the authors compare the optimal effort of the Agent in a noncooperative Principals model and that in the aggregate model, by showing that these two optimizations coincide only in the first best case. We also study the sensibility of the optimal effort and the optimal remunerations with respect to appetence parameters and the correlation between the projects. (10.1137/17M1133609)
  DOI : 10.1137/17M1133609
• Modal basis approaches in shape and topology optimization of frequency response problems
  
  • Allaire Grégoire
  • Michailidis Georgios
  International Journal for Numerical Methods in Engineering, Wiley, 2018, 113 (8), pp.1258-1299. The optimal design of mechanical structures subject to periodic excitations within a large frequency interval is quite challenging. In order to avoid bad performances for non-discretized frequencies, it is necessary to finely discretize the frequency interval, leading to a very large number of state equations. Then, if a standard adjoint-based approach is used for optimization, the computational cost (both in terms of CPU and memory storage) may be prohibitive for large problems, especially in three space dimensions. The goal of the present work is to introduce two new non-adjoint approaches for dealing with frequency response problems in shape and topology optimization. In both cases, we rely on a classical modal basis approach to compute the states, solutions of the direct problems. In the first method, we do not use any adjoint but rather directly compute the shape derivatives of the eigenmodes in the modal basis. In the second method, we compute the adjoints of the standard approach by using again the modal basis. The numerical cost of these two new strategies are much smaller than the usual ones if the number of modes in the modal basis is much smaller than the number of discretized excitation frequencies. We present numerical examples for the minimization of the dynamic compliance in two and three space dimensions. (10.1002/nme.5504)
  DOI : 10.1002/nme.5504
• Quadratic BSDEs with mean reflection
  
  • Hibon Hélène
  • Hu Ying
  • Lin Yiqing
  • Luo Peng
  • Wang Falei
  Mathematical Control and Related Fields, AIMS, 2018, 8 (3 & 4), pp.721-738. The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the $z$ argument. This work is the sequel of Briand et al. [BSDEs with mean reflection, arXiv:1605.06301] in which a notion of BSDEs with mean reflection is developed to tackle the super-hedging problem under running risk management constraints. By the contraction mapping argument, we first prove that the quadratic BSDE with mean reflection admits a unique deterministic flat local solution on a small time interval whenever the terminal value is bounded. Moreover, we build the global solution on the whole time interval by stitching local solutions when the generator is uniformly bounded with respect to the $y$ argument. (10.3934/mcrf.2018031)
  DOI : 10.3934/mcrf.2018031
• Generic uniqueness of the bias vector of finite stochastic games with perfect information
  
  • Akian Marianne
  • Gaubert Stéphane
  • Hochart Antoine
  Journal of Mathematical Analysis and Applications, Elsevier, 2018, 457, pp.1038-1064. Mean-payoff zero-sum stochastic games can be studied by means of a nonlinear spectral problem. When the state space is finite, the latter consists in finding an eigenpair (u,λ) solution of T(u)=λe+u, where T:Rn→Rn is the Shapley (or dynamic programming) operator, λ is a scalar, e is the unit vector, and u∈Rn. The scalar λ yields the mean payoff per time unit, and the vector u, called the bias, allows one to determine optimal stationary strategies. The existence of the eigenpair (u,λ) is generally related to ergodicity conditions. A basic issue is to understand for which classes of games the bias vector is unique (up to an additive constant). In this paper, we consider perfect-information zero-sum stochastic games with finite state and action spaces, thinking of the transition payments as variable parameters, transition probabilities being fixed. We show that the bias vector, thought of as a function of the transition payments, is generically unique (up to an additive constant). The proof uses techniques of max-plus (or tropical) algebra and nonlinear Perron-Frobenius theory. As an application of our results, we obtain a perturbation scheme allowing one to solve degenerate instances of stochastic games by policy iteration. (10.1016/j.jmaa.2017.07.017)
  DOI : 10.1016/j.jmaa.2017.07.017
• Uncovering Causality from Multivariate Hawkes Integrated Cumulants
  
  • Achab Massil
  • Bacry Emmanuel
  • Gaïffas Stéphane
  • Mastromatteo Iacopo
  • Muzy Jean-François
  Journal of Machine Learning Research, Microtome Publishing, 2018, 18, pp.192. We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. As a consequence, it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows us to prove that this new estimation technique is consistent. Moreover, we show, on numerical experiments, that our approach is indeed very robust with respect to the shape of the kernels and gives appealing results on the MemeTracker database and on financial order book data.