Publications

2019

• Regularity result for a shape optimization problem under perimeter constraint
  
  • Bogosel Beniamin
  Communications in Analysis and Geometry, International Press, 2019, 27 (7), pp.1523-1547. We study the problem of optimizing the eigenvalues of the Dirichlet Laplace operator under perimeter constraint. We prove that optimal sets are analytic outside a closed singular set of dimension at most d−8 by writing a general optimality condition in the case the optimal eigenvalue is multiple. As a consequence we find that the optimal k-th eigenvalue is strictly smaller than the optimal (k + 1)-th eigenvalue. We also provide an elliptic regularity result for sets with positive and bounded weak curvature. (10.4310/CAG.2019.v27.n7.a3)
  DOI : 10.4310/CAG.2019.v27.n7.a3
• A MICROSCOPIC VIEW ON THE FOURIER LAW
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  Comptes Rendus. Physique, Académie des sciences (Paris), 2019. The Fourier law of heat conduction describes heat diffusion in macroscopic systems. This physical law has been experimentally tested for a large class of physical systems. A natural question is to know whether it can be derived from the microscopic models using the fundamental laws of mechanics.
• THE INCOMPATIBILITY OPERATOR: FROM RIEMANN'S INTRINSIC VIEW OF GEOMETRY TO A NEW MODEL OF ELASTO-PLASTICITY
  
  • Amstutz Samuel
  • van Goethem Nicolas
  , 2019. The mathematical modelling in mechanics has a long-standing history as related to geometry, and significant progresses have often been achieved by the invention of new geometrical tools. Also, it happened that the elucidation of practical issues led to the invention of new scientific concepts, and possibly new paradigms, with potential impact far beyond. One such example is Riemann's intrinsic view in geometry, that offered a radically new insight in the Physics of the early 20-th century. On the other hand, the rather recent intrinsic approaches in elasticity and elasto-plasticity also share this philosophical standpoint of looking from inside, i.e., from the "manifold" point of view. Of course, this approach requires smoothness, and is thus incomplete for an analyst. Nevertheless, its first aim is to highlight the concepts of metric, curvature and torsion; these notions are addressed in the first part of this survey paper. In a second part, they are given a precise functional meaning and their properties are studied systematically. Further, a novel approach to elasto-plasticity constructed upon a model of incompatible elasticity is designed, carrying this intrinsic spirit. The main mathematical object in this theory is the incompatibility operator, i.e., a linearized version of Riemann's curvature tensor. So far, this route not only has led the authors to a new model with a solid functional foundation and proof of existence results, but also to a framework with a minimal amount of ad-hoc assumptions, and complying with both the basic principles of thermodynamics and invariance principles of Physics. The questions arising from this novel approach are complex and intriguing, but we believe that the model is now sufficiently well-posed to be studied simultaneously as a problem of mathematics and of mechanics. Most of the research program remains to be done, and this survey paper is written to present our model, with a particular care to put this approach into a historical perspective.
• Curvature: a variational approach
  
  • Agrachev Andrei
  • Barilari Davide
  • Rizzi Luca
  Memoirs of the American Mathematical Society, American Mathematical Society, 2019, 256 (1225). The curvature discussed in this paper is a rather far going generalization of the Riemann sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces. (10.1090/memo/1225)
  DOI : 10.1090/memo/1225
• A breakdown of injectivity for weighted ray transforms in multidimensions
  
  • Goncharov Fedor O
  • Novikov Roman G
  Arkiv för Matematik, Royal Swedish Academy of Sciences, Institut Mittag-Leffler, 2019, 57, pp.333–371. We consider weighted ray-transforms $P_W$ (weighted Radon transforms along straight lines) in $\mathbb{R}^d, \, d\geq 2,$ with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel in the space of infinitely smooth compactly supported functions on $\mathbb{R}^d$. In addition, the constructed weight $W$ is rotation-invariant continuous and is infinitely smooth almost everywhere on $\mathbb{R}^d \times \mathbb{S}^{d-1}$. In particular, by this construction we give counterexamples to some well-known injectivity results for weighted ray transforms for the case when the regularity of $W$ is slightly relaxed. We also give examples of continous strictly positive $W$ such that $\dim \ker P_W \geq n$ in the space of infinitely smooth compactly supported functions on $\mathbb{R}^d$ for arbitrary $n\in \mathbb{N}\cup \{\infty\}$, where $W$ are infinitely smooth for $d=2$ and infinitely smooth almost everywhere for $d\geq 3$. (10.4310/ARKIV.2019.v57.n2.a5)
  DOI : 10.4310/ARKIV.2019.v57.n2.a5
• Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector
  
  • Cerf Raphaël
  • Dalmau Joseba
  ESAIM: Probability and Statistics, EDP Sciences, 2019, 23, pp.797-802. Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A , as well as of a multitype branching process with mean matrix e ( A − I ) t . These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain. (10.1051/ps/2019007)
  DOI : 10.1051/ps/2019007
• Topological derivative for the nonlinear magnetostatic problem
  
  • Amstutz Samuel
  • Gangl Peter
  Electronic Transactions on Numerical Analysis, Kent State University Library, 2019, 51, pp.169-218. (10.1553/etna_vol51s169)
  DOI : 10.1553/etna_vol51s169
• Initiation of a validation strategy of reduced-order two-fluid flow models using direct numerical simulations in the context of jet atomization
  
  • Cordesse Pierre
  • Murrone A.
  • Ménard T.
  • Massot Marc
  NASA Technical Memorandum, National Aeronautics and Space Administration, 2019, pp.1-11. In industrial applications, developing predictive tools relying on numerical simulations using reduced-order models nourish the need of building a validation strategy. In the context of cryogenic atomization, we propose to build a hierarchy of direct numerical simulation test cases to assess qualitatively and quantitatively diffuse interface models. The present work proposes an initiation of the validation strategy with an air-assisted water atomization using a coaxial injector.
• On a Wasserstein-type distance between solutions to stochastic differential equations
  
  • Bion-Nadal Jocelyne
  • Talay Denis
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2019, 29 (3), pp.1609-1639. In this paper, we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic differential equations. This new distance is defined by restricting the set of possible coupling measures. We prove that it may also be defined by means of the value function of a stochastic control problem whose Hamilton–Jacobi–Bellman equation has a smooth solution, which allows one to deduce a priori estimates or to obtain numerical evaluations. We exhibit an optimal coupling measure and characterize it as a weak solution to an explicit stochastic differential equation, and we finally describe procedures to approximate this optimal coupling measure. A notable application concerns the following modeling issue: given an exact diffusion model, how to select a simplified diffusion model within a class of admissible models under the constraint that the probability distribution of the exact model is preserved as much as possible? (10.1214/18-AAP1423)
  DOI : 10.1214/18-AAP1423
• Derivation of a two-phase flow model with two-scale kinematics, geometric variables and surface tension using variational calculus
  
  • Cordesse Pierre
  • Kokh Samuel
  • Di Battista Ruben
  • Drui Florence
  • Massot Marc
  NASA Technical Memorandum, National Aeronautics and Space Administration, 2019. The present paper proposes a two-phase flow model that is able to account for two-scale kinematics and two-scale surface tension effects based on geometric variables at small scale. At large scale, the flow and the full geometry of the interface may be retrieved thanks to the bulk variables, while at small scale the interface is accurately described by volume fraction, interfacial area density and mean curvature, called the geometric variables. Our work mainly relies on the Least Action Principle. The resulting system is an extension of a previous work modeling small scale pulsation in which surface tension was not taken into account at large or small scale. Whereas the original derivation assumes a cloud of monodispersed spherical bubbles, the present context allows for polydispersed, non-spherical bubbles. The resulting system of equations solely involves small scale geometric variables, thus contributing in the construction of a unified model describing both large and small scales.
• Pointwise Besov Space Smoothing of Images
  
  • Buzzard Gregery
  • Chambolle Antonin
  • Cohen Jonathan
  • Levine Stacey
  • Lucier Bradley
  Journal of Mathematical Imaging and Vision, Springer Verlag, 2019, 61 (1), pp.1-20. (10.1007/s10851-018-0821-1)
  DOI : 10.1007/s10851-018-0821-1
• On the stability of matrix-valued Riccati diffusions
  
  • Bishop Adrian N
  • del Moral Pierre
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2019, 24. The stability properties of matrix-valued Riccati diffusions are investigated. The matrix-valued Riccati diffusion processes considered in this work are of interest in their own right, as a rather prototypical model of a matrix-valued quadratic stochastic process. Under rather natural observability and controllability conditions, we derive time-uniform moment and fluctuation estimates and exponential contraction inequalities. Our approach combines spectral theory with nonlinear semigroup methods and stochastic matrix calculus. This analysis seem to be the first of its kind for this class of matrix-valued stochastic differential equation. This class of stochastic models arise in signal processing and data assimilation, and more particularly in ensemble Kalman-Bucy filtering theory. In this context, the Riccati diffusion represents the flow of the sample covariance matrices associated with McKean-Vlasov-type interacting Kalman-Bucy filters. The analysis developed here applies to filtering problems with unstable signals. (10.1214/19-EJP342)
  DOI : 10.1214/19-EJP342
• Avis en réponse à la saisine HCB - habilitation agents 2019. Paris, le 4 juillet 2019
  
  • 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
  , 2019, pp.2 p..
• Avis en réponse à la saisine HCB - dossier EFSA-GMO-RX-013. Paris, le 30 janvier 2019
  
  • 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
  , 2019.
• Avis en réponse à la saisine HCB - EFSA-GMO-ES-2018-154. Paris, le 5 avril 2019
  
  • 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
  • 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
  , 2019.
• Mean field model for collective motion bistability
  
  • Garnier Josselin
  • Papanicolaou George
  • Yang Tzu-Wei
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2019, 24 (2), pp.851-879. (10.3934/dcdsb.2018210)
  DOI : 10.3934/dcdsb.2018210
• Existence of strong solutions to the Dirichlet problem for the Griffith energy
  
  • Chambolle Antonin
  • Crismale Vito
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2019, 58 (136). In this paper we continue the study of the Griffith brittle fracture energy minimisation under Dirichlet boundary conditions, suggested by Francfort and Marigo in 1998. In a recent paper, we proved the existence of weak minimisers of the problem. Now we show that these minimisers are indeed strong solutions, namely their jump set is closed and they are smooth away from the jump set and continuous up to the Dirichlet boundary. This is obtained by extending up to the boundary the recent regularity results of Conti, Focardi, Iurlano, and of Chambolle, Conti, Iurlano. (10.1007/s00526-019-1571-7)
  DOI : 10.1007/s00526-019-1571-7
• Incomplete graphical model inference via latent tree aggregation
  
  • Robin Geneviève
  • Ambroise Christophe
  • Robin Stephane S.
  Statistical Modelling, SAGE Publications, 2019, 19 (5), pp.545-568. Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical cases, not all variables involved in the network have been observed, and the samples are actually drawn from a distribution where some variables have been marginalized out. This challenges the sparsity assumption commonly made in graphical model inference, since marginalization yields locally dense structures, even when the original network is sparse. We present a procedure for inferring Gaussian graphical models when some variables are unobserved, that accounts both for the influence of missing variables and the low density of the original network. Our model is based on the aggregation of spanning trees, and the estimation procedure on the Expectation-Maximization algorithm. We treat the graph structure and the unobserved nodes as missing variables and compute posterior probabilities of edge appearance. To provide a complete methodology, we also propose several model selection criteria to estimate the number of missing nodes. A simulation study and an illustration flow cytometry data reveal that our method has favorable edge detection properties compared to existing graph inference techniques. The methods are implemented in an R package. (10.1177/1471082X18786289)
  DOI : 10.1177/1471082X18786289
• Longest increasing paths with gaps
  
  • Basdevant Anne-Laure
  • Gerin Lucas
  ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....], 2019, 16 (2), pp.1141--1163. We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal gaps between abscissae and ordinates of successive points of the path. For both cases (continuous and discrete) our approach rely on couplings with well-studied models: respectively the classical Ulam-Hammersley problem and last-passage percolation with geometric weights. Thanks to these couplings we obtain explicit limiting shapes in both settings. We also establish that, as in the classical Ulam-Hammersley problem, the fluctuations around the mean are given by the Tracy-Widom distribution.
• Statistical estimation in a randomly structured branching population
  
  • Hoffmann Marc
  • Marguet Aline
  Stochastic Processes and their Applications, Elsevier, 2019, 129 (12), pp.5236-5277. We consider a binary branching process structured by a stochastic trait that evolves according to a diffusion process that triggers the branching events, in the spirit of Kimmel's model of cell division with parasite infection. Based on the observation of the trait at birth of the first n generations of the process, we construct nonparametric estimator of the transition of the associated bifurcating chain and study the parametric estimation of the branching rate. In the limit $n → ∞$, we obtain asymptotic efficiency in the parametric case and minimax optimality in the nonparametric case. (10.1016/j.spa.2019.02.015)
  DOI : 10.1016/j.spa.2019.02.015
• On the Essential Self-Adjointness of Singular Sub-Laplacians
  
  • Franceschi Valentina
  • Prandi Dario
  • Rizzi Luca
  Potential Analysis, Springer Verlag, 2019, 53, pp.89-112. (10.1007/s11118-018-09760-w)
  DOI : 10.1007/s11118-018-09760-w
• The asymptotic geometry of the Teichmüller metric
  
  • Walsh Cormac
  Geometriae Dedicata, Springer Verlag, 2019, 200 (1), pp.115-152. We determine the asymptotic behaviour of extremal length along arbitrary Teichmüller rays. This allows us to calculate the endpoint in the Gardiner-Masur boundary of any Teichmüller ray. We give a proof that this compactification is the same as the horofunction compactification. An important subset of the latter is the set of Busemann points. We show that the Busemann points are exactly the limits of the Teichmüller rays, and we give a necessary and sufficient condition for a sequence of Busemann points to converge to a Busemann point. Finally, we determine the detour metric on the boundary. (10.1007/s10711-018-0364-z)
  DOI : 10.1007/s10711-018-0364-z
• Avis en réponse à la saisine HCB - dossier RX-015. Paris, le 26 février 2019
  
  • 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
  , 2019.
• Avis en réponse à la saisine HCB - dossier 2018-151. Paris, le 10 janvier 2019
  
  • 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
  , 2019.
• C-mix: a high dimensional mixture model for censored durations, with applications to genetic data
  
  • Bussy Simon
  • Guilloux Agathe
  • Gaïffas Stéphane
  • Jannot Anne-Sophie
  Statistical Methods in Medical Research, SAGE Publications, 2019, 28 (5), pp.1523--1539. We introduce a supervised learning mixture model for censored durations (C-mix) to simultaneously detect subgroups of patients with different prognosis and order them based on their risk. Our method is applicable in a high-dimensional setting, i.e. with a large number of biomedical covariates. Indeed, we penalize the negative log-likelihood by the Elastic-Net, which leads to a sparse parameterization of the model and automatically pinpoints the relevant covariates for the survival prediction. Inference is achieved using an efficient Quasi-Newton Expectation Maximization (QNEM) algorithm, for which we provide convergence properties. The statistical performance of the method is examined on an extensive Monte Carlo simulation study, and finally illustrated on three publicly available genetic cancer datasets with high-dimensional co-variates. We show that our approach outperforms the state-of-the-art survival models in this context, namely both the CURE and Cox proportional hazards models penalized by the Elastic-Net, in terms of C-index, AUC(t) and survival prediction. Thus, we propose a powerfull tool for personalized medicine in cancerology. (10.1177/0962280218766389)
  DOI : 10.1177/0962280218766389