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
• 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.
• 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.
• 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
• 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.
• 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.
• 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.
• 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
• Full Likelihood Inference from the Site Frequency Spectrum based on the Optimal Tree Resolution
  
  • Sainudiin Raazesh
  • Véber Amandine
  Theoretical Population Biology, Elsevier, 2018.
• 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
• 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
• 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.
• 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.
• 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
• 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
• Avis en réponse à la saisine HCB - dossier EFSA-GMO-RX009. Paris, le 4 juin 2018
  
  • Comité Scientifique Du Haut Conseil Des Biotechnologies .
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Demeneix Barbara
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Khalife Jamal
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémy
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2018.
• Fluctuations and Temperature Effects in Bose-Einstein Condensation
  
  • de Bouard Anne
  • Debussche Arnaud
  • Fukuizumi Reika
  • Poncet Romain
  ESAIM: Proceedings and Surveys, EDP Sciences, 2018, 61, pp.55-67. The modeling of cold atoms systems has known an increasing interest in the theoretical physics community, after the first experimental realizations of Bose Einstein condensates, some twenty years ago. We here review some analytical and numerical results concerning the influence of fluctuations , either arising from fluctuations of the confining parameters, or due to temperature effects, in the models describing the dynamics of such condensates. (10.1051/proc/201861055)
  DOI : 10.1051/proc/201861055
• 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
• 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