Publications

2018

• Principal-Agent Problem with Common Agency without Communication
  
  • Mastrolia Thibaut
  • Ren Zhenjie
  , 2018. 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 optimisation 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 Bernheim and Whinston (1986) in which the authors compare the optimal effort of the Agent in a non-cooperative Principals model and that in the aggregate model, by showing that these two optimisations 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
• Development and performance of npde for the evaluation of time-to-event models
  
  • Cerou Marc
  • Lavielle Marc
  • Brendel Karl
  • Chenel Marylore
  • Comets Emmanuelle
  Pharmaceutical Research, American Association of Pharmaceutical Scientists, 2018, 35 (2), pp.30. Purpose - Normalised prediction distribution errors (npde) are used to graphically and statistically evaluate mixed-effect models for continuous responses. In this study, our aim was to extend npde to time-to-event (TTE) models and evaluate their performance. Methods - Let V denote a dataset with censored TTE observations. The null hypothesis (H) is that observations in V can be described by model M. We extended npde to TTE models using imputations to take into account censoring. We then evaluated their performance in terms of type I error and power to detect model misspecifications for TTE data by means of a simulation study with different sample sizes. Results - Type I error was found to be close to the expected 5% significance level for all sample sizes tested. The npde were able to detect misspecifications in the baseline hazard as well as in the link between the longitudinal variable and the survival function. The ability to detect model misspecifications increased as the difference in the shape of the survival function became more apparent. As expected, the power also increased as the sample size increased. Imputing the censored events tended to decrease the percentage of rejections. Conclusions - We have shown that npde can be readily extended to TTE data and that they perform well with an adequate type I error. (10.1007/s11095-017-2291-3)
  DOI : 10.1007/s11095-017-2291-3
• Quantitative estimates for the flux of TASEP with dilute site disorder
  
  • Bahadoran Christophe
  • Bodineau Thierry
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23. We prove that the flux function of the totally asymmetric simple exclusion process (TASEP) with site disorder exhibits a flat segment for sufficiently dilute disorder. For high dilution, we obtain an accurate description of the flux. The result is established under a decay assumption of the maximum current in finite boxes, which is implied in particular by a sufficiently slow power tail assumption on the disorder distribution near its minimum. To circumvent the absence of explicit invariant measures, we use an original renormalization procedure and some ideas inspired by homogenization. (10.1214/18-EJP137)
  DOI : 10.1214/18-EJP137
• Sufficient optimality conditions for bilinear optimal control of the linear damped wave equation
  
  • Bethke Franz
  • Kröner Axel
  , 2018. In this paper we discuss sufficient optimality conditions for an optimal control problem for the linear damped wave equation with the damping parameter as the control. We address the case that the control enters quadratic in the cost function as well as the singular case that the control enters affine. For the non-singular case we consider strong and weak local minima , in the singular case we derive sufficient optimality conditions for weak local minima. Thereby, we take advantage of the Goh transformation applying techniques recently established in Aronna, Bonnans, and Kröner [Math. Program. 168(1):717–757, 2018] and [INRIA research report, 2017]. Moreover, a numerical example for the singular case is presented.
• Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations
  
  • Aronna Maria Soledad
  • Bonnans Joseph Fréderic
  • Kröner Axel
  Mathematical Programming, Springer Verlag, 2018, 168 (1-2), pp.717-757. In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linearly in the cost function. We derive first and second order optimality conditions, taking advantage of the Goh transform. We then apply the results to the heat and wave equations.
• Avis en réponse à la saisine HCB - dossier 2018-150. Paris, le 24 octobre 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.
• Linearized Navier-Stokes Equations for Aeroacoustics using Stabilized Finite Elements: Boundary Conditions and Industrial Application to Aft-Fan Noise Propagation
  
  • Bissuel Aloïs
  • Allaire Grégoire
  • Daumas Laurent
  • Barré Sébastien
  • Rey Floriane
  Computers and Fluids, Elsevier, 2018. In this paper, a numerical method for solving the linearized Navier-Stokes equations is presented for aeroacoustic sound propagation problem. The Navier-Stokes equations are linearized in the frequency domain. The fan noise of jet engine is emitted nearly selectively at certain frequencies, which depend on the rotation velocity of the fan. A frequency domain approach is highly suitable for this kind of problem, instead of a costly time-dependent simulation which can handle a large range of frequencies depending on the time step and the mesh. The calculations presented here were all made using Aether, a Navier-Stokes code which uses finite elements stabilized with SUPG (Streamline Upwind Galerkin). Automatic code differentiation was used to linearize this code. Entropy variables bring interesting mathematical properties to the numerical scheme, but also prevent the easy implementation of boundary conditions. For instance, the pressure is a non-linear combination of the entropy variables. Imposing a pressure variation needs a linearization of this relation which is detailed herein. The performance of different types of boundary conditions used to impose the acoustic pressure variation inside the engine is studied in detail. Finally, a very surprising effect of the SUPG scheme was to transform a homogeneous Dirichlet boundary condition on all variables to a transparent one which is able to let only outgoing waves pass * Dassault Aviation 78, quai Marcel 1 through with no incoming wave. A one-dimensional toy model is given to explain how SUPG brings about this transformation. The last part of the article is dedicated to an industrial test case. The geometry of a model turbine from the Clean Sky European project was used for sound propagation of the fan exhaust noise of a jet engine. Computations on several modes with increasing complexities were done and the results compared to a boundary element method which served as a reference when no mean flow is present. Results of a computation with a mean flow are shown.
• Gauge-reversing maps on cones, and Hilbert and Thompson isometries
  
  • Walsh Cormac
  Geometry and Topology, Mathematical Sciences Publishers, 2018, 22 (1), pp.55-104. We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the Hilbert geometry is the projective space of a non-Lorentzian symmetric cone, in which case the collineation group is of index two in the isometry group. We also determine the isometry group of the Thompson geometry on a cone. (10.2140/gt.2018.22.55)
  DOI : 10.2140/gt.2018.22.55
• Continuous Optimal Control Approaches to Microgrid Energy Management
  
  • Heymann Benjamin
  • Bonnans J. Frederic
  • Martinon Pierre
  • Silva Francisco
  • Lanas Fernando
  • Jimenez Guillermo
  Energy Systems, Springer, 2018, 9 (1), pp.59-77. —We propose a novel method for the microgrid energy management problem by introducing a continuous-time, rolling horizon formulation. The energy management problem is formulated as a deterministic optimal control problem (OCP). We solve (OCP) with two classical approaches: the direct method [1], and Bellman's Dynamic Programming Principle (DPP) [2]. In both cases we use the optimal control toolbox BOCOP [3] for the numerical simulations. For the DPP approach we implement a semi-Lagrangian scheme [4] adapted to handle the optimization of switching times for the on/off modes of the diesel generator. The DPP approach allows for an accurate modeling and is computationally cheap. It finds the global optimum in less than 3 seconds, a CPU time similar to the Mixed Integer Linear Programming (MILP) approach used in [5]. We achieve this performance by introducing a trick based on the Pontryagin Maximum Principle (PMP). The trick increases the computation speed by several orders and also improves the precision of the solution. For validation purposes, simulation are performed using datasets from an actual isolated microgrid located in northern Chile. Results show that DPP method is very well suited for this type of problem when compared with the MILP approach.
• Epidemics and the Eden model : a detailed study of robustness
  
  • Gerin Lucas
  , 2018, Emergence, Complexity and Computation, vol 27, pp.165-178. We present some well-known and less well-known properties of the Probabilistic Cellular Automaton \emph{Epidemics} on a finite grid and its analogous on the infinite square lattice: the Eden model. (10.1007/978-3-319-65558-1_12)
  DOI : 10.1007/978-3-319-65558-1_12
• The geometry of random minimal factorizations of a long cycle via biconditioned bitype random trees
  
  • Féray Valentin
  • Kortchemski Igor
  Annales Henri Lebesgue, UFR de Mathématiques - IRMAR, 2018, 1, pp.149-226. (10.5802/ahl.5)
  DOI : 10.5802/ahl.5
• On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds
  
  • Sacchelli Ludovic
  • Sigalotti Mario
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2018. In this article we study the validity of the Whitney $C^1$ extension property for horizontal curves in sub-Riemannian manifolds endowed with 1-jets that satisfy a first-order Taylor expansion compatibility condition. We first consider the equiregular case, where we show that the extension property holds true whenever a suitable non-singularity property holds for the input-output maps on the Carnot groups obtained by nilpotent approximation. We then discuss the case of sub-Riemannian manifolds with singular points and we show that all step-2 manifolds satisfy the $C^1$ extension property. We conclude by showing that the $C^1$ extension property implies a Lusin-like approximation theorem for horizontal curves on sub-Riemannian manifolds.
• 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
• 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
• 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
• 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.
• 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.
• 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
• 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
• 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.
• 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.