Publications

2020

• Modulation of homogeneous and isotropic turbulence by sub-Kolmogorov particles: Impact of particle field heterogeneity
  
  • Letournel Roxane
  • Laurent Frédérique
  • Massot Marc
  • Vié Aymeric
  International Journal of Multiphase Flow, Elsevier, 2020, 125, pp.103233. The modulation of turbulence by sub-Kolmogorov particles has been thoroughly characterized in the literature, showing either enhancement or reduction of kinetic energy at small or large scale depending on the Stokes number and the mass loading. However , the impact of a third parameter, the number density of particles, has not been independently investigated. In the present work, we perform direct numerical simulations of decaying Homogeneous Isotropic Turbulence loaded with monodisperse sub-Kolmogorov particles, varying independently the Stokes number, the mass loading and the number density of particles. Like previous investigators, crossover and modulations of the fluid energy spectra are observed consistently with the change in Stokes number and mass loading. Additionally, DNS results show a clear impact of the particle number density, promoting the energy at small scales while reducing the energy at large scales. For high particle number density, the turbulence statistics and spectra become insensitive to the increase of this parameter, presenting a two-way asymptotic behavior. Our investigation identifies the energy transfer mechanisms, and highlights the differences between the influence of a highly concentrated disperse phase (high particle number density, limit behavior) and that of heterogeneous concentration fields (low particle number density). In particular, a measure of this heterogeneity is proposed and discussed which allows to identify specific regimes in the evolution of turbulence statistics and spectra. (10.1016/j.ijmultiphaseflow.2020.103233)
  DOI : 10.1016/j.ijmultiphaseflow.2020.103233
• Modèles Génératifs Profonds : l'échantillonnage en haute dimension revisité
  
  • Moulines Eric
  , 2020. Les modèles génératifs (GM) permettent d’inférer des modèles de loi pour des observations structurées de grande dimension, qui sont typiques de l'IA moderne. Les modèles génératifs peuvent également être utilisés pour échantillonner de nouveaux exemples, en reliant le problème d'inférence à l'échantillonnage.L'apprentissage de modèles génératifs profonds (MGD) capables de capturer les structures de dépendance complexe de lois à partir de grands ensemble de données dans un cadre non-ou semi-supervisé apparaît aujourd'hui comme l'un des principaux défis de l'IA. Les modèles génératifs profonds ont de nombreuses applications passionnantes pour résoudre la pénurie de données en générant de " nouveaux " exemples, pour préserver la confidentialité en diffusant le modèle génératif à laplace des données mais aussi pour détecter les observations aberrantes.Dans cette présentation, je vais couvrir trois directions de recherche sur lesquelles je travaille actuellement.Une première approche est basée sur la minimisation de l'entropie croisée (divergence de Kullback-Leibler) entre la distribution des observations et un modèle paramétré soit par des réseaux de neurones profonds, soit par des fonctions d’energies plus adaptées, reliant les modèles génératifs et les « energy based models » quiont été introduits pour l’apprentissage non-supervisé (mais dans un cadre non-probabiliste). Cette approche est séduisante mais elle pose des problèmes de calcul difficiles, liés à la nécessité d'estimer la constante de normalisation et son gradient.Une deuxième approche repose sur les méthodes d'entropie maximale. Cette approche trouve son origine dans les quantités de physique statistique pour apprendre une distribution maximisant l'entropie sous contrainte de moment, qui sont construites à partir d'unereprésentation issue d’un réseau de neurones profondsUne troisième approche consiste à utiliser des auto-encodeurs variationnels (Variational Autoencoder, VAE), un cas particulier d'inférence variationnelle. Les VAE apprennent conjointement un algorithme pour générer des échantillons à partir de la distribution ainsi qu'un espace latent qui résume la distribution des observations.J’illustrerai ces approches par des exemples et je discuterai des challenges théoriques et numériques que ces approches posent. <a href="https://videos-rennes.inria.fr/video/HJt6vEaXI" target="_blank">[Vidéo en ligne]</a>
• Comparative study of harmonic and Rayleigh-Ritz procedures with applications to deflated conjugate gradients
  
  • Venkovic Nicolas
  • Mycek Paul
  • Giraud Luc
  • Le Maitre Olivier
  , 2020. Harmonic Rayleigh-Ritz and Raleigh-Ritz projection techniques are compared in the context of iterative procedures to solve for small numbers of least dominant eigenvectors of large symmetric positive definite matrices. The procedures considered are (i) locally optimal conjugate gradient (CG) methods, i.e., LOBCG, (ii) thick-restart Lanczos methods, and (iii) recycled linear CG solvers, e.g., eigCG. Approaches based on principles of local optimality are adapted to enable the use of harmonic projection techniques. Upon investigating the search spaces generated by these methods, it is found that LOBCG and thick-restart Lanczos methods can be adapted, which is not the case of eigCG. Explanations are also given as to why eigCG works so well in comparison to other recycling strategies. Numerical experiments show that, while approaches based on harmonic projections consistently result in a faster convergence of eigen-residuals, they generally do not yield better convergence of the forward error of eigenvectors, until the Rayleigh quotients have converged. Then, the effect of recycling strategies is investigated on deflation for the resolution of sequences of linear systems. While non-locally optimal recycling strategies need to solve more linear systems in order to fully develop their effect on convergence, they eventually reach similar behaviors to those of locally optimal recycling procedures. While implementations based on Init-CG are robust for systems with multiple right-hand sides, this is not the case for multiple operators.
• Quantitative modeling links in vivo microstructural and macrofunctional organization of human and macaque insular cortex, and predicts cognitive control abilities
  
  • Menon Vinod
  • Gallardo Guillermo
  • Pinsk Mark
  • Nguyen Van-Dang
  • Li Jing-Rebecca
  • Cai Weidong
  • Wassermann Demian
  , 2020. (10.1101/662601)
  DOI : 10.1101/662601
• Computing bi-tangents for transmission belts
  
  • Chouly Franz
  • Loubani Jinan
  • Lozinski Alexei
  • Méjri Bochra
  • Merito Kamil
  • Passos Sébastien
  • Pineda Angie
  , 2020. In this note, we determine the bi-tangents of two rotated ellipses, and we compute the coordinates of their points of tangency. For these purposes, we develop two approaches. The first one is an analytical approach in which we compute analytically the equations of the bi-tangents. This approach is valid only for some cases. The second one is geometrical and is based on the determination of the normal vector to the tangent line. This approach turns out to be more robust than the first one and is valid for any configuration of ellipses.
• Adaptive Bayesian SLOPE—High-dimensional Model Selection with Missing Values
  
  • Jiang Wei
  • Bogdan Malgorzata
  • Josse Julie
  • Miasojedow Blazej
  • Rockova Veronika
  , 2020. We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure -- adaptive Bayesian SLOPE -- which effectively combines the SLOPE method (sorted l1 regularization) together with the Spike-and-Slab LASSO method. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation, despite the missing values. As with the Spike-and-Slab LASSO, the coefficients are regarded as arising from a hierarchical model consisting of two groups: (1) the spike for the inactive and (2) the slab for the active. However, instead of assigning independent spike priors for each covariate, here we deploy a joint "SLOPE" spike prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. Through extensive simulations, we demonstrate satisfactory performance in terms of power, FDR and estimation bias under a wide range of scenarios. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent a severe trauma, where we show excellent performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into an R package ABSLOPE for public use.
• Nonparametric imputation by data depth
  
  • Mozharovskyi Pavlo
  • Josse Julie
  • Husson François
  Journal of the American Statistical Association, Taylor & Francis, 2020, 115 (529), pp.241-253. The presented methodology for single imputation of missing values borrows the idea from data depth --- a measure of centrality defined for an arbitrary point of the space with respect to a probability distribution or a data cloud. This consists in iterative maximization of the depth of each observation with missing values, and can be employed with any properly defined statistical depth function. On each single iteration, imputation is narrowed down to optimization of quadratic, linear, or quasiconcave function being solved analytically, by linear programming, or the Nelder-Mead method, respectively. Being able to grasp the underlying data topology, the procedure is distribution free, allows to impute close to the data, preserves prediction possibilities different to local imputation methods (k-nearest neighbors, random forest), and has attractive robustness and asymptotic properties under elliptical symmetry. It is shown that its particular case --- when using Mahalanobis depth --- has direct connection to well known treatments for multivariate normal model, such as iterated regression or regularized PCA. The methodology is extended to the multiple imputation for data stemming from an elliptically symmetric distribution. Simulation and real data studies positively contrast the procedure with existing popular alternatives. The method has been implemented as an R-package. (10.1080/01621459.2018.1543123)
  DOI : 10.1080/01621459.2018.1543123
• Commentaires sur le rapport de surveillance de culture du MON 810 en 2018. Paris, le 25 février 2020
  
  • Du Haut Conseil Des Biotechnologies Comité Scientifique
  • Angevin Frédérique
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Collonnier Cécile
  • Couvet Denis
  • Dassa Elie
  • 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
  • de Verneuil Hubert
  • Vilotte Jean-Luc
  , 2020, pp.35 p.. Les analyses contenues dans le rapport de surveillance de Bayer Agriculture BVBA ne font apparaître aucun problème majeur associé à la culture de maïs MON 810 en 2018. Toutefois, le CS du HCB identifie encore certaines faiblesses et limites méthodologiques concernant la surveillance de la sensibilité des ravageurs ciblés à la toxine Cry1Ab, remettant en question les conclusions du rapport. Le HCB estime notamment que l’utilisation d’une dose diagnostic présente certaines limites pour la détection précoce de l’évolution de la résistance, tant dans son principe intrinsèque que dans sa mise en oeuvre par Bayer, et recommande une méthode alternative de type F2 screen permettant de déterminer la fréquence des allèles de résistance au sein d’une population de ravageurs cibles. Par ailleurs, le HCB formule des recommandations destinées à renforcer la mise en oeuvre des zones refuges pour prévenir ou retarder le développement de résistance à la toxine Cry1Ab chez les ravageurs ciblés. Concernant la surveillance générale, le CS du HCB relève un problème de pertinence méthodologique quant aux questions étudiées, avec des règles de décision arbitraires, des conclusions incorrectement justifiées et un possible biais associé au format d’enquête auprès du panel d’agriculteurs qui ont accepté de répondre au questionnaire. Enfin, le CS du HCB recommande que le rapport de surveillance considère la présence de téosinte dans des zones de culture du maïs MON 810 en Espagne et les risques potentiels associés à une éventuelle introgression de gènes de maïs MON 810 chez le téosinte.
• Kinetic derivation of diffuse-interface fluid models
  
  • Giovangigli Vincent
  Physical Review E, American Physical Society (APS), 2020, 102. We present a full derivation of capillary fluid equations from the kinetic theory of dense gases. These equations involve van der Waals' gradient energy, Korteweg's tensor, and Dunn and Serrin's heat flux as well as viscous and heat dissipative fluxes. Starting from macroscopic equations obtained from the kinetic theory of dense gases, we use a second-order expansion of the pair distribution function in order to derive the diffuse interface model. The capillary extra terms and the capillarity coefficient are then associated with intermolecular forces and the pair interaction potential. (10.1103/physreve.102.012110)
  DOI : 10.1103/physreve.102.012110
• Regression Monte Carlo methods for HJB-type equations: which approximation space?
  
  • Barrera David
  • Gobet Emmanuel
  • Lopez-Salas Jose
  • Turkedjiev Plamen
  • Vasquez Carlos
  • Zubelli Jorge
  , 2020.
• A quantitative McDiarmid’s inequality for geometrically ergodic Markov chains
  
  • Havet Antoine
  • Lerasle Matthieu
  • Moulines Éric
  • Vernet Elodie
  Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2020, 25. (10.1214/20-ECP286)
  DOI : 10.1214/20-ECP286
• Tropical planar networks
  
  • Gaubert Stéphane
  • Niv Adi
  Linear Algebra and its Applications, Elsevier, 2020, 595, pp.123-144. We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniqueness theorem for the factorization of a tropical totally positive in terms of elementary Jacobi matrices. (10.1016/j.laa.2020.02.019)
  DOI : 10.1016/j.laa.2020.02.019
• Optimal Hedging Under Fast-Varying Stochastic Volatility
  
  • Garnier Josselin
  • Sølna Knut
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2020, 11 (1), pp.274-325. In a market with a rough or Markovian mean-reverting stochastic volatility thereis no perfect hedge. Here it is shown how various delta-type hedging strategies perform and canbe evaluated in such markets in the case of European options.A precise characterization of thehedging cost, the replication cost caused by the volatilityfluctuations, is presented in an asymptoticregime of rapid mean reversion for the volatility fluctuations. The optimal dynamic asset basedhedging strategy in the considered regime is identified as the so-called “practitioners” delta hedgingscheme. It is moreover shown that the performances of the delta-type hedging schemes are essentiallyindependent of the regularity of the volatility paths in theconsidered regime and that the hedgingcosts are related to a Vega risk martingale whose magnitude is proportional to a new market riskparameter. It is also shown via numerical simulations that the proposed hedging schemes whichderive from option price approximations in the regime of rapid mean reversion, are robust: the“practitioners” delta hedging scheme that is identified as being optimal by our asymptotic analysiswhen the mean reversion time is small seems to be optimal witharbitrary mean reversion times. (10.1137/18M1221655)
  DOI : 10.1137/18M1221655
• The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
  
  • Backhoff Julio
  • Conforti Giovanni
  • Gentil Ivan
  • Léonard Christian
  Probability Theory and Related Fields, Springer Verlag, 2020, 178, pp.475-530. (10.1007/s00440-020-00977-8)
  DOI : 10.1007/s00440-020-00977-8
• State-constrained control-affine parabolic problems I: First and Second order necessary optimality conditions
  
  • Aronna M Soledad
  • Bonnans J. Frederic
  • Kröner Axel
  Set-Valued and Variational Analysis, Springer, 2020. In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimen-sional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results.
• Variance Reduction Methods and Multilevel Monte Carlo Strategy for Estimating Densities of Solutions to Random Second-Order Linear Differential Equations
  
  • Jornet Marc
  • Calatayud Julia
  • Le Maitre Olivier
  • Cortés Juan Carlos
  International Journal for Uncertainty Quantification, Begell House Publishers, 2020, 10 (5), pp.467-497. This paper concerns the estimation of the density function of the solution to a random nonautonomous second-order linear differential equation with analytic data processes. In a recent contribution, we proposed to express the density function as an expectation, and we used a standard Monte Carlo algorithm to approximate the expectation. Although the algorithms worked satisfactorily for most test problems, some numerical challenges emerged for others, due to large statistical errors. In these situations, the convergence of the Monte Carlo simulation slows down severely, and noisy features plague the estimates. In this paper, we focus on computational aspects and propose several variance reduction methods to remedy these issues and speed up the convergence. First, we introduce a pathwise selection of the approximating processes which aims at controlling the variance of the estimator. Second, we propose a hybrid method, combining Monte Carlo and deterministic quadrature rules, to estimate the expectation. Third, we exploit the series expansions of the solutions to design a multilevel Monte Carlo estimator. The proposed methods are implemented and tested on several numerical examples to highlight the theoretical discussions and demonstrate the significant improvements achieved.
• Error estimates for phase recovering from phaseless scattering data
  
  • Novikov Roman
  • Sivkin Vladimir
  Eurasian Journal of Mathematical and Computer Applications, Eurasian National University, Kazakhstan (Nur-Sultan), 2020, 8 (1), pp.44-61. We study the simplest explicit formulas for approximate finding the complex scattering amplitude from modulus of the scattering wave function. We obtain detailed error estimates for these formulas in dimensions d = 3 and d = 2.
• Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions
  
  • Bansaye Vincent
  • Cloez Bertrand
  • Gabriel Pierre
  Acta Applicandae Mathematicae, Springer Verlag, 2020, 166 (1), pp.29-72. We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and Doeblin's type conditions for coupling the associated process. Our aim is to provide quantitative estimates for linear partial differential equations and we develop several applications for population dynamics in varying environment. We start with the asymptotic profile for a growth diffusion model with time and space non-homogeneity. Moreover we provide general estimates for semigroups which become asymptotically homogeneous, which are applied to an age-structured population model. Finally, we obtain a speed of convergence for periodic semi-groups and new bounds in the homogeneous setting. They are are illustrated on the renewal equation. (10.1007/s10440-019-00253-5)
  DOI : 10.1007/s10440-019-00253-5
• Hölder-logarithmic stability in Fourier synthesis
  
  • Isaev Mikhail
  • Novikov Roman G
  Inverse Problems, IOP Publishing, 2020, 36 (12), pp.125003(17 pp.). We prove a Hölder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function v on R^d from its Fourier transform Fv given on [−r, r]^d. This estimate relies on a Hölder stable continuation of Fv from [−r, r]^d to a larger domain. The related reconstruction procedures are based on truncated series of Chebyshev polynomials. We also give an explicit example showing optimality of our stability estimates. (10.1088/1361-6420/abb5df)
  DOI : 10.1088/1361-6420/abb5df
• An Eco-Routing Algorithm for HEVs Under Traffic Conditions
  
  • Rhun Arthur Le
  • Bonnans Frédéric
  • Nunzio Giovanni De
  • Leroy Thomas
  • Martinon Pierre
  IFAC-PapersOnLine, Elsevier, 2020, 53 (2), pp.14242 - 14247. In a previous work, a bi-level optimization approach was presented for the energy management of Hybrid Electric Vehicles (HEVs), using a statistical model for traffic conditions. The present work is an extension of this framework to the eco-routing problem. The optimal trajectory is computed as the shortest path on a weighted graph whose nodes are (position, state of charge) pairs for the vehicle. The edge costs are provided by cost maps from an offline optimization at the lower level of small road segments. The error due to the discretization of the state of charge is proven to be linear if the cost maps are Lipschitz. The classical A * algorithm is used to solve the problem, with a heuristic based on a lower bound of the energy needed to complete the travel. The eco-routing method is compared to the fastest-path strategy by numerical simulations on a simple synthetic road network. (10.1016/j.ifacol.2020.12.1158)
  DOI : 10.1016/j.ifacol.2020.12.1158
• ADDITIVE MANUFACTURING SCANNING PATHS OPTIMIZATION USING SHAPE OPTIMIZATION TOOLS
  
  • Boissier M
  • Allaire G.
  • Tournier Christophe
  Structural and Multidisciplinary Optimization, Springer Verlag, 2020, 61, pp.2437–2466. This paper investigates path planning strategies for additive manufacturing processes such as powder bed fusion. The state of the art mainly studies trajectories based on existing patterns. Parametric optimization on these patterns or allocating them to the object areas are the main strategies. We propose in this work a more systematic optimization approach without any a priori restriction on the trajectories. The typical optimization problem is to melt the desired structure, without overheating (to avoid thermally induced residual stresses) and possibly with a minimal path length. The state equation is the heat equation with a source term depending on the scanning path. First, in a steady-state context, shape optimization tools are applied to trajec-tories. Second, for time-dependent problems, an optimal control method is considered instead. In both cases, gradient type algorithms are deduced and tested on 2-d examples. Numerical results are discussed, leading to a better understanding of the problem and thus to short-and long-term perspectives. (10.1007/s00158-020-02614-3)
  DOI : 10.1007/s00158-020-02614-3
• SCALPEL3: a scalable open-source library for healthcare claims databases
  
  • Bacry Emmanuel
  • Gaiffas Stéphane
  • Leroy Fanny
  • Morel Maryan
  • Nguyen D.P.
  • Sebiat Youcef
  • Sun Dian
  International Journal of Medical Informatics, Elsevier, 2020.
• Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions
  
  • Akimoto Youhei
  • Auger Anne
  • Hansen Nikolaus
  Theoretical Computer Science, Elsevier, 2020, 832, pp.42-67. Quality gain is the expected relative improvement of the function value in a single step of a search algorithm. Quality gain analysis reveals the dependencies of the quality gain on the parameters of a search algorithm, based on which one can derive the optimal values for the parameters. In this paper, we investigate evolution strategies with weighted recombination on general convex quadratic functions. We derive a bound for the quality gain and two limit expressions of the quality gain. From the limit expressions, we derive the optimal recombination weights and the optimal step-size, and find that the optimal recombination weights are independent of the Hessian of the objective function. Moreover, the dependencies of the optimal parameters on the dimension and the population size are revealed. Differently from previous works where the population size is implicitly assumed to be smaller than the dimension, our results cover the population size proportional to or greater than the dimension. Simulation results show the optimal parameters derived in the limit approximates the optimal values in non-asymptotic scenarios. (10.1016/j.tcs.2018.05.015)
  DOI : 10.1016/j.tcs.2018.05.015
• A new McKean-Vlasov stochastic interpretation of the parabolic-parabolic Keller-Segel model: The one-dimensional case
  
  • Tomasevic Milica
  • Talay Denis
  Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2020, 26 (2), pp.1323-1353. In this paper we analyze a stochastic interpretation of the one-dimensional parabolic-parabolic Keller-Segel system without cut-off. It involves an original type of McKean-Vlasov interaction kernel. At the particle level, each particle interacts with all the past of each other particle by means of a time integrated functional involving a singular kernel. At the mean-field level studied here, the McKean-Vlasov limit process interacts with all the past time marginals of its probability distribution in a similarly singular way. We prove that the parabolic-parabolic Keller-Segel system in the whole Euclidean space and the corresponding McKean-Vlasov stochastic differential equation are well-posed for any values of the parameters of the model. (10.3150/19-BEJ1158)
  DOI : 10.3150/19-BEJ1158
• The boundary of random planar maps via looptrees
  
  • Kortchemski Igor
  • Richier Loïc
  Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc, 2020, 29 (2), pp.391-430. (10.5802/afst.1636)
  DOI : 10.5802/afst.1636