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
• From Hammersley's lines to Hammersley's trees
  
  • Basdevant Anne-Laure
  • Gerin Lucas
  • Gouere Jean-Baptiste
  • Singh Arvind
  Probability Theory and Related Fields, Springer Verlag, 2018, 171 (1-2), pp.1-51. We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends the usual Hammersley's line process. Just as Hammersley's process is related to the problem of the longest increasing subsequence, this model also has a combinatorial interpretation: it counts the number of heaps (i.e. increasing trees) required to store a random permutation. This problem was initially considered by Byers et. al (2011) and Istrate and Bonchis (2015) in the case of regular trees. We show, in particular, that the number of heaps grows logarithmically with the size of the permutation. (10.1007/s00440-017-0772-2)
  DOI : 10.1007/s00440-017-0772-2
• The Quasispecies for the Wright–Fisher Model
  
  • Cerf Raphaël
  • Dalmau Joseba
  Evolutionary Biology, Springer, 2018, 45 (3), pp.318-323. We consider the classical Wright-Fisher model of population genetics. We prove the existence of an error threshold for the mutation probability per nucleotide, below which a quasispecies is formed. We show a new phenomenon, specific to a finite population model, namely the existence of a population threshold: to ensure the stability of the quasispecies, the population size has to be at least of the same order as the genome length. We derive an explicit formula describing the quasispecies. (10.1007/s11692-018-9452-0)
  DOI : 10.1007/s11692-018-9452-0
• Impact of subsampling and tree depth on random forests
  
  • Duroux Roxane
  • Scornet Erwan
  ESAIM: Probability and Statistics, EDP Sciences, 2018, 22, pp.96-128. Random forests are ensemble learning methods introduced by Breiman [Mach. Learn. 45 (2001) 5–32] that operate by averaging several decision trees built on a randomly selected subspace of the data set. Despite their widespread use in practice, the respective roles of the different mechanisms at work in Breiman’s forests are not yet fully understood, neither is the tuning of the corresponding parameters. In this paper, we study the influence of two parameters, namely the subsampling rate and the tree depth, on Breiman’s forests performance. More precisely, we prove that quantile forests (a specific type of random forests) based on subsampling and quantile forests whose tree construction is terminated early have similar performances, as long as their respective parameters (subsampling rate and tree depth) are well chosen. Moreover, experiments show that a proper tuning of these parameters leads in most cases to an improvement of Breiman’s original forests in terms of mean squared error. (10.1051/ps/2018008)
  DOI : 10.1051/ps/2018008
• Commentaires sur le projet de document consensus de l’OCDE sur les considérations environnementales relatives à l’évaluation des risques associé. Paris, le 23 mai 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 sollicité le 4 avril 2018 par la direction générale de l’alimentation du ministère de l’Agriculture et de l’Alimentation et par la direction générale de la prévention des risques du ministère de la Transition écologique et solidaire pour examiner et commenter le projet de document consensus de l’OCDE (version du 3 avril 2018) sur les considérations environnementales relatives à l’évaluation des risques associés à la dissémination de plantes génétiquement modifiées en vue de la réunion du groupe de travail de l’OCDE sur l’harmonisation de la surveillance réglementaire en biotechnologie les 21 et 22 juin 2018. Le Comité scientifique (CS)1 du HCB a examiné ce document en séance du 26 avril 2018 sous la présidence de Jean-Christophe Pagès. Les commentaires du CS du HCB à destination de l’OCDE, en version française et anglaise2, ont été validés par voie électronique et transmis aux autorités compétentes françaises le 23 mai 2018, et publiés après envoi à l’OCDE le 30 mai 2018.
• Sensing Von Economo Neurons in the Insula with Multi-shell Diffusion MRI
  
  • Wassermann Demian
  • Nguyen Dang Van
  • Gallardo Guillermo
  • Li Jing-Rebecca
  • Cai Weidong
  • Menon Vinod
  , 2018.
• Vertices with fixed outdegrees in large Galton-Watson trees
  
  • Thévenin Paul
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 25 (none). We are interested in nodes with fixed outdegrees in large conditioned Galton--Watson trees. We first study the scaling limits of processes coding the evolution of the number of such nodes in different explorations of the tree (lexicographical order and contour order) starting from the root. We give necessary and sufficient conditions for the limiting processes to be centered, thus measuring the linearity defect of the evolution of the number of nodes with fixed outdegrees. This extends results by Labarbe & Marckert in the case of the contour-ordered counting process of leaves in uniform plane trees. Then, we extend results obtained by Janson concerning the asymptotic normality of the number of nodes with fixed outdegrees. (10.1214/20-EJP465)
  DOI : 10.1214/20-EJP465
• Markov chains
  
  • Douc Randal
  • Moulines Eric
  • Priouret Pierre
  • Soulier Philippe
  , 2018, pp.757. This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature (10.1007/978-3-319-97704-1)
  DOI : 10.1007/978-3-319-97704-1
• 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.
• 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.
• 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
• 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.
• 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
• 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
• 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.
• 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
• 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.