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
• 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.
• 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
• 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
• 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
• 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
• 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.
• 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.
• 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
• 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
• 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
• 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
• 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.
• 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
• 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.
• 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
• 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
• 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
• 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.
• 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