Publications

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
• Solving generic nonarchimedean semidefinite programs using stochastic game algorithms
  
  • Allamigeon Xavier
  • Gaubert Stephane
  • Skomra Mateusz
  Journal of Symbolic Computation, Elsevier, 2018, 85, pp.25-54. A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algorithmic game theory. This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances. (10.1016/j.jsc.2017.07.002)
  DOI : 10.1016/j.jsc.2017.07.002
• Variational methods for tomographic reconstruction with few views
  
  • Bergounioux Maïtine
  • Abraham Isabelle
  • Abraham Romain
  • Carlier Guillaume
  • Le Pennec Erwan
  • Trélat Emmanuel
  Milan Journal of Mathematics, Springer Verlag, 2018, 86 (2), pp.157--200. We deal with a severe ill posed problem, namely the reconstruction process of an image during tomography acquisition with (very) few views. We present different methods that we have been investigated during the past decade. They are based on variational analysis. This is a survey paper and we refer to the quoted papers for more details. Mathematics Subject Classification (2010). 49K40, 45Q05,65M32.
• 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.
• Relaxation Limit and Initial-Layers for a Class of Hyperbolic-Parabolic Systems
  
  • Giovangigli Vincent
  • Yang Zai-Bao
  • Yong Wen-An
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018. We consider a class of hyperbolic-parabolic systems with small diffusion terms and stiff sources. Existence of solutions to the Cauchy problem with ill prepared initial data is established by using composite expansions including initial-layer correctors and a convergence-stability lemma. New multitime expansions are introduced and lead to second-order error estimates between the composite expansions and the solution. Reduced equilibrium systems of second-order accuracy are also investigated as well as initial-layers of Chapman-Enskog expansions. (10.1137/18M1170091)
  DOI : 10.1137/18M1170091
• Dynamic programming approach to principal-agent problems
  
  • Cvitanić Jakša
  • Possamaï Dylan
  • Touzi Nizar
  Finance and Stochastics, Springer Verlag (Germany), 2018, 22, pp.1-37. We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following: we first find the contract that is optimal among those for which the agent's value process allows a dynamic programming representation, for which the agent's optimal effort is straightforward to find. We then show that the optimization over the restricted family of contracts represents no loss of generality. As a consequence, we have reduced this non-zero sum stochastic differential game to a stochastic control problem which may be addressed by the standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case. (10.1007/s00780-017-0344-4)
  DOI : 10.1007/s00780-017-0344-4
• 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
• 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
• Elasto-plastic shape optimization using the level set method
  
  • Maury Aymeric
  • Allaire Grégoire
  • Jouve François
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2018, 56 (1), pp.556-581. This article focused on shape optimization of static perfect plasticity problems in the framework of the Von Mises criterion, thanks to the level set method. We circumvent the ill-posedness of the model, by using two regularized versions of the mechanical problem. The rst one is the classical Perzyna formulation which we regularize, the second one is a new regularized formulation derived for the Von Mises criterion. Shape gradients are calculated thanks to the adjoint method. To illustrate the validity of the method, 2D examples are performed.
• 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
• 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
• Full Likelihood Inference from the Site Frequency Spectrum based on the Optimal Tree Resolution
  
  • Sainudiin Raazesh
  • Véber Amandine
  Theoretical Population Biology, Elsevier, 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.
• Solutions for models of chemically reacting mixtures
  
  • Giovangigli Vincent
  , 2018. The mathematical modeling of chemically reacting mixtures is investigated. The governing equations, that may be split between conservation equations, thermochemistry and transport fluxes, are presented as well as typical simplifications often encountered in the literature. The hyperbolic-parabolic structure of the resulting system of partial differential equations is analyzed using symmetrizing variables. The Cauchy problem is discussed for the full system derived from the kinetic theory of gases as well as relaxation towards chemical equilibrium fluids in the fast chemistry limit. The situations of traveling waves and reaction-diffusion systems is also addressed. (10.1007/978-3-319-10151-4_73-1)
  DOI : 10.1007/978-3-319-10151-4_73-1
• One-sided convergence in the Boltzmann-Grad limit
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  • Simonella Sergio
  Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc, 2018, 27 (5). We review various contributions on the fundamental work of Lanford deriving the Boltzmann equation from hard-sphere dynamics in the low density limit. We focus especially on the assumptions made on the initial data and on how they encode irreversibility. The impossibility to reverse time in the Boltzmann equation (expressed for instance by Boltzmann's H-theorem) is related to the lack of convergence of higher order marginals on some singular sets. Explicit counterexamples single out the microscopic sets where the initial data should converge in order to produce the Boltzmann dynamics. (10.5802/afst.1589)
  DOI : 10.5802/afst.1589
• Where does the droplet size distribution come from?
  
  • Canu Romain
  • Puggelli Stefano
  • Essadki Mohammed
  • Duret Benjamin
  • Menard Thibaut
  • Massot Marc
  • Reveillon Julien
  • Demoulin F.X.
  International Journal of Multiphase Flow, Elsevier, 2018, 107, pp.230-245. This study employs DNS of two-phase flows to enhance primary atomization understanding and modeling to be used in numerical simulation in RANS or LES framework. In particular, the work has been aimed at improving the information on the liquid-gas interface evolution for modeling approaches, such as the Eulerian-Lagrangian Spray Atomization (ELSA) framework. Even though this approach has been already successfully employed to describe the complete liquid atomization process from the primary region to the dilute spray, improvements are still expected on the derivation of the drop size distribution (DSD). The main aim of the present work is the introduction of a new framework to achieve a continuous description of the DSD formation during the atomization process. The attention is here focused on the extraction from DNS data of the behavior of geometrical variable of the liquid-gas interface, such as the mean (H) and Gauss (G) surface curvatures. The use of a Surface Curvature Distribution is also proposed and studied. A Rayleigh-Plateau instability along a column of liquid and a droplet collision case are first of all considered to analyze and to verify the capabilities of the code to correctly predicting the curvature distributions. A statistical analysis based on the curvatures data, in terms of probability density function, is presented in order to determine the physical parameters that control the curvatures on this test case. Then, the same formulation is applied in the analysis of the two phase Homogeneous Isotropic Turbulence (HIT) configuration to study how the curvatures evolve all along the atomization process. Joint PDFs are used to illustrate the topological changes of the interface when increasing the liquid volume fraction. (10.1016/j.ijmultiphaseflow.2018.06.010)
  DOI : 10.1016/j.ijmultiphaseflow.2018.06.010
• Impact of the interruption of a large heart failure regional disease management program on hospital admission rate: a population-based study
  
  • Alla François
  • Agrinier Nelly
  • Lavielle Marc
  • Rossignol Patrick
  • Gonthier Damien
  • Boivin Jean-Marc
  • Zannad Faiez
  European Journal of Heart Failure, European Society of Cardiology (Wiley), 2018, 20 (6), pp.1066-1068. (10.1002/ejhf.1193)
  DOI : 10.1002/ejhf.1193
• Characteristic and Universal Tensor Product Kernels
  
  • Szabó Zoltán
  • Sriperumbudur Bharath K
  Journal of Machine Learning Research, Microtome Publishing, 2018, 18, pp.233. Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. Thanks to their kernel-based foundations, MMD and HSIC are applicable on a wide variety of domains. Despite their tremendous success, quite little is known about when HSIC characterizes independence and when MMD with tensor product kernel can discriminate probability distributions. In this paper, we answer these questions by studying various notions of characteristic property of the tensor product kernel.
• A NON-INTRUSIVE STRATIFIED RESAMPLER FOR REGRESSION MONTE CARLO: APPLICATION TO SOLVING NON-LINEAR EQUATIONS
  
  • Gobet Emmanuel
  • Liu Gang
  • Zubelli Jorge
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2018, 56 (1), pp.50-77. Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that the model for X is not known in full detail and only a root sample X1, . . . , XM of such process is available. By a stratification of the space and a suitable choice of a probability measure ν, we design a new resampling scheme that allows to compute local regressions (on basis functions) in each stratum. The combination of the stratification and the resampling allows to compute the solution to the dynamic programming equation (possibly in large dimensions) using only a relatively small set of root paths. To assess the accuracy of the algorithm, we establish non-asymptotic error estimates in L2(ν). Our numerical experiments illustrate the good performance, even with M = 20 − 40 root paths. (10.1137/16M1066865)
  DOI : 10.1137/16M1066865
• Inverse scattering for the Bethe-Peierls model
  
  • Novikov Roman
  Eurasian Journal of Mathematical and Computer Applications, Eurasian National University, Kazakhstan (Nur-Sultan), 2018, 6 (1), pp.52-55. We consider the phased and phaseless inverse scattering problems for the Bethe-Peierls model. We give complete solutions of these problems including questions of uniqueness, nonuniqueness, reconstruction and characterization.
• Long time behavior of Gross-Pitaevskii equation at positive temperature
  
  • de Bouard Anne
  • Debussche Arnaud
  • Fukuizumi Reika
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018, 50 (6), pp.5887–5920. The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise. Two important questions for this system are the global existence of solutions in the support of the Gibbs measure, and the convergence of those solutions to the equilibrium for large time. In this paper, we give a proof of these two results in one space dimension. In order to prove the convergence to equilibrium, we use the associated purely dissipative equation as an auxiliary equation, for which the convergence may be obtained using standard techniques. (10.1137/17M1149195)
  DOI : 10.1137/17M1149195
• Avis en réponse à la saisine HCB - dossier C/NL/06/01_001. Paris, le 17 octobre 2018
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie Anne M. A.
  • Bellivier Florence
  • Berny Philippe
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Coléno François
  • Couvet Denis
  • Dassa Elie
  • 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
  • de Verneuil Hubert
  • Vilotte Jean-Luc
  , 2018, pp.25 p.. Le Haut Conseil des biotechnologies (HCB) a été saisi le 14 août 2018 par les autorités compétentes françaises (le ministère de l’Agriculture et de l’Alimentation) d’une demande d’avis relative au dossier C/NL/06/01_001 de demande de renouvellement d’autorisation de mise sur le marché de la lignée d’oeillets génétiquement modifiés 123.8.12 (identificateur unique FLO- 40689-6) à des fins d’importation et de commercialisation de fleurs coupées. Ce dossier a été déposé par la société Suntory Flowers Limited auprès des autorités compétentes néerlandaises sur le fondement 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, qui disposent de 60 jours pour faire des commentaires, demander des informations complémentaires ou émettre des objections à la mise sur le marché. Par cette saisine, les autorités compétentes françaises consultent le HCB dans cette perspective, en amont du vote des Etats membres à la Commission européenne. Le Comité scientifique (CS)2 du HCB a examiné le dossier en séance du 17 octobre 2018 sous la présidence de Jean-Christophe Pagès. Le présent avis a été adopté en séance et publié le 23 octobre 2018.