Publications

2018

• 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
• 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
• 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
• 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
• Minimization of the eigenvalues of the Dirichlet-LapIacian with a diameter constraint
  
  • Bogosel B
  • Henrot A
  • Lucardesi I
  SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2018, 50 (5), pp.5337-5361. In this paper we look for the domains minimizing the h-th eigenvalue of the Dirichlet-Laplacian λ h with a constraint on the diameter. Existence of an optimal domain is easily obtained, and is attained at a constant width body. In the case of a simple eigenvalue, we provide non standard (i.e., non local) optimality conditions. Then we address the question whether or not the disk is an optimal domain in the plane, and we give the precise list of the 17 eigenvalues for which the disk is a local minimum. We conclude by some numerical simulations showing the 20 first optimal domains in the plane. (10.1137/17M1162147)
  DOI : 10.1137/17M1162147
• 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.
• 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.
• 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.
• Avis en réponse à la saisine HCB - dossier 2017-143. Paris, le 15 mai 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.
• Laser Beam Imaging from the Speckle Pattern of the Off-Axis Scattered Intensity
  
  • Borcea Liliana
  • Garnier Josselin
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2018, 78 (2), pp.677-704. (10.1137/17M1139059)
  DOI : 10.1137/17M1139059
• Global acoustic daylight imaging in a stratified Earth-like model
  
  • Garnier Josselin
  • de Hoop Maarten V.
  • Sølna Knut
  Inverse Problems, IOP Publishing, 2018, 34 (1). (10.1088/1361-6420/aa9ad7)
  DOI : 10.1088/1361-6420/aa9ad7
• 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
• 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
• The derivation of homogenized diffusion kurtosis models for diffusion MRI
  
  • Haddar Houssem
  • Kchaou Marwa
  • Moakher Maher
  Journal of Magnetic Resonance, Elsevier, 2018, 298, pp.48-57.
• Adiabatic ensemble control of a continuum of quantum systems
  
  • Augier Nicolas
  • Boscain Ugo
  • Sigalotti Mario
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2018, 56, pp.4045-4068. In this article we discuss how to control a parameter-dependent family of quantum systems. Our technique is based on adiabatic approximation theory and on the presence of curves of conical eigenvalue intersections of the controlled Hamiltonian. As particular cases, we recover chirped pulses for two-level quantum systems and counter-intuitive solutions for three-level stimulated Raman adiabatic passage (STIRAP). The proposed technique works for systems evolving both in finite-dimensional and infinite-dimensional Hilbert spaces. We show that the assumptions guaranteeing ensemble controllability are structurally stable with respect to perturbations of the parametrized family of systems.
• Parking 3-sphere swimmer I. Energy minimizing strokes
  
  • Alouges François
  • Di Fratta Giovanni
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2018, 23 (4), pp.1797-1817. The paper is about the parking 3-sphere swimmer (sPr$_3$), a low-Reynolds number model swimmer composed of three balls of equal radii. The three balls can move along three horizontal axes (supported in the same plane) that mutually meet at the center of sPr$_3$ with angles of 120°. The governing dynamical system is introduced and the implications of its geometric symmetries revealed. It is then shown that, in the first order range of small strokes, optimal periodic strokes are ellipses embedded in 3d space, i.e., closed curves of the form t ∈ [0,2π ] → (cos t)${u}$ +(sin t)${v}$ for suitable vectors ${u}$ and ${v}$ of $\mathbb{R}^3$. A simple analytic expression for the vectors ${u}$ and ${v}$ is derived (10.3934/dcdsb.2018085)
  DOI : 10.3934/dcdsb.2018085
• Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs
  
  • Czichowsky Christoph
  • Peyre Rémi
  • Schachermayer Walter
  • Yang Junjian
  Finance and Stochastics, Springer Verlag (Germany), 2018, 22 (1), pp.161-180. The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, we are able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market. (10.1007/s00780-017-0351-5)
  DOI : 10.1007/s00780-017-0351-5
• High order moment model for polydisperse evaporating sprays towards interfacial geometry
  
  • Essadki Mohamed
  • de Chaisemartin Stephane
  • Laurent Frédérique
  • Massot Marc
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2018, 78 (4), pp.2003-2027. In this paper we propose a new Eulerian modeling and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model is its capacity to describe some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in interfacial flows. For this purpose, we use fractional size-moments, where the size variable is taken as the droplet surface. In order to evaluate the evaporation of the polydisperse spray, we use a smooth reconstruction which maximizes the Shannon entropy. However, the use of fractional moments introduces some theoretical and numerical difficulties, which need to be tackled. First, relying on a study of the moment space, we extend the Maximum Entropy (ME) reconstruction of the size distribution to the case of fractional moments. Then, we propose a new accurate and realizable algorithm to solve the moment evolution due to evaporation, which preserves the structure of the moment space. This algorithm is based on a mathematical analysis of the kinetic evolution due to evaporation, where it shown that the evolution of some negative order fractional moments have to be properly predicted, a peculiarity related to the use of fractional moments. The present model and numerical schemes yield an accurate and stable evaluation of the moment dynamics with minimal number of variables, as well as a minimal computational cost as with the EMSM model, but with the very interesting additional capacity of coupling with diffuse interface model and transport equation of averaged geometrical interface variables, which are essential in oder to describe atomization. (10.1137/16M1108364)
  DOI : 10.1137/16M1108364
• Optimization of classification and regression analysis of four monoclonal antibodies from Raman spectra using collaborative machine learning approach
  
  • Le Laetitia Minh Maï
  • Kégl Balázs
  • Gramfort Alexandre
  • Marini Camille
  • Nguyen David
  • Cherti Mehdi
  • Tfaili Sana
  • Tfayli Ali
  • Baillet-Guffroy Arlette
  • Prognon Patrice
  • Chaminade Pierre
  • Caudron Eric
  Talanta, Elsevier, 2018, 184, pp.260-265. The use of monoclonal antibodies (mAbs) constitutes one of the most important strategies to treat patients suffering from cancers such as hematological malignancies and solid tumors. These antibodies are prescribed by the physician and prepared by hospital pharmacists. An analytical control enables the quality of the preparations to be ensured. The aim of this study was to explore the development of a rapid analytical method for quality control. The method used four mAbs (Infliximab, Bevacizumab, Rituximab and Ramucirumab) at various concentrations and was based on recording Raman data and coupling them to a traditional chemometric and machine learning approach for data analysis. Compared to conventional linear approach, prediction errors are reduced with a data-driven approach using statistical machine learning methods. In the latter, preprocessing and predictive models are jointly optimized. An additional original aspect of the work involved on submitting the problem to a collaborative data challenge platform called Rapid Analytics and Model Prototyping (RAMP). This allowed using solutions from about 300 data scientists in collaborative work. Using machine learning, the prediction of the four mAbs samples was considerably improved. The best predictive model showed a combined error of 2.4% versus 14.6% using linear approach. The concentration and classification errors were 5.8% and 0.7%, only three spectra were misclassified over the 429 spectra of the test set. This large improvement obtained with machine learning techniques was uniform for all molecules but maximal for Bevacizumab with an 88.3% reduction on combined errors (2.1% versus 17.9%). (10.1016/j.talanta.2018.02.109)
  DOI : 10.1016/j.talanta.2018.02.109
• Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding
  
  • Gautier Eric
  • Le Pennec Erwan
  Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (1), pp.277-320. (10.1214/17-EJS1383)
  DOI : 10.1214/17-EJS1383
• Transport et diffusion
  
  • Allaire Grégoire
  • Blanc Xavier
  • Després Bruno
  • Golse François
  , 2018, pp.328. Ce livre est issu d'un cours enseigné par les auteurs en troisième année de l'Ecole Polytechnique, ce qui correspond à un niveau de première année de Master. Le sujet en est l'étude mathématique et numérique de modèles d'équations aux dérivées partielles, dits de transport et diffusion. Ces équations modélisent l'évolution d'une densité de particules ou d'individus en interaction avec leur milieu. L'origine de ces modèles est très variée. Ils proviennent classiquement de la physique et servent à décrire des particules neutres comme les neutrons et les photons. Dans le premier cas on parle aussi de neutronique alors que le dernier cas est appelé transfert radiatif. La biologie fait aussi appel aux équations de transport pour modéliser la dynamique de populations structurées. Citons aussi pour mémoire la dynamique des gaz raréfiés, le transport d'électrons dans les semi-conducteurs ou encore la physique des plasmas qui sont des phénomènes modélisés par des équations où l'opérateur de transport est une brique de base essentielle.
• Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation
  
  • Hu Ying
  • Lin Yiqing
  • Soumana-Hima Abdoulaye
  Stochastic Processes and their Applications, Elsevier, 2018, 128 (11), pp.3724-3750. In this paper, we consider backward stochastic differential equations driven by $G$-Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the $G$-framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces. (10.1016/j.spa.2017.12.004)
  DOI : 10.1016/j.spa.2017.12.004
• The Asymptotic of Transmission Eigenvalues for a Domain with a Thin Coating
  
  • Boujlida Hanen
  • Haddar Houssem
  • Khenissi Moez
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2018, 78 (5), pp.2348-2369. We consider the transmission eigenvalue problem for a medium surrounded by a thin layer of inhomogeneous material with different refractive index. We derive explicit asymptotic expansion for the transmission eigenvalues with respect to the thickness of the thin layer. We prove error estimate for the asymptotic expansion up to order 1 for simple eigenvalues. This expansion can be used to obtain explicit expressions for constant index of refraction.
• Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau.
  
  • Durmus Alain
  • Moulines Éric
  • Pereyra Marcelo
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2018, 11 (1). In this paper, two new algorithms to sample from possibly non-smooth log-concave probability measures are introduced. These algorithms use Moreau-Yosida envelope combined with the Euler-Maruyama discretization of Langevin diffusions. They are applied to a de-convolution problem in image processing, which shows that they can be practically used in a high dimensional setting. Finally, non-asymptotic bounds for one of the proposed methods are derived. These bounds follow from non-asymptotic results for ULA applied to probability measures with a convex continuously differentiable log-density with respect to the Lebesgue measure. (10.1137/16M110834)
  DOI : 10.1137/16M110834
• Maximal lower bounds in the Löwner order
  
  • Stott Nikolas
  Proceedings of the American Mathematical Society, American Mathematical Society, 2018. We show that the set of maximal lower bounds of two symmetric matrices with respect to the L\"owner order can be identified to the quotient set O(p,q)/(O(p)×O(q)). Here, (p,q) denotes the inertia of the difference of the two matrices, O(p) is the p-th orthogonal group, and O(p,q) is the indefinite orthogonal group arising from a quadratic form with inertia (p,q). We also show that a similar result holds for positive semidefinite maximal lower bounds with maximal rank of two positive semidefinite matrices. We exhibit a correspondence between the maximal lower bounds C of two matrices A,B and certain pairs of subspaces, describing the directions on which the quadratic form associated with C is tangent to the one associated with A or B. The present results refines a theorem from Kadison that characterizes the existence of the infimum of two symmetric matrices and a theorem from Moreland, Gudder and Ando on the existence of the positive semidefinite infimum of two positive semidefinite matrices. (10.1090/proc/13785)
  DOI : 10.1090/proc/13785