Publications

2019

• Copula-like Variational Inference
  
  • Hirt Marcel
  • Dellaportas Petros
  • Durmus Alain
  , 2019. This paper considers a new family of variational distributions motivated by Sklar's theorem. This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i.e. with a complexity linear in the dimension of state space. Then, the proposed variational densities that we suggest can be seen as arising from these copula-like densities used as base distributions on the hypercube with Gaussian quantile functions and sparse rotation matrices as normalizing flows. The latter correspond to a rotation of the marginals with complexity $\mathcal{O}(d \log d)$. We provide some empirical evidence that such a variational family can also approximate non-Gaussian posteriors and can be beneficial compared to Gaussian approximations. Our method performs largely comparably to state-of-the-art variational approximations on standard regression and classification benchmarks for Bayesian Neural Networks.
• Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains
  
  • Lin Yiqing
  • Soumana-Hima Abdoulaye
  Stochastics and Dynamics, World Scientific Publishing, 2019, 19 (3), pp.n°1950025. In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with $\alpha$-H\"older continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected $G$-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by $G$-Brownian motion are investigated via a fixed-point argument. (10.1142/S0219493719500254)
  DOI : 10.1142/S0219493719500254
• Commentaires sur le rapport de surveillance de culture du MON 810 en 2017. Paris, le 23 décembre 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
  • 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
  , 2019, pp.41 p.. Les analyses contenues dans le rapport de surveillance de Monsanto ne font apparaître aucun problème majeur associé à la culture de maïs MON 810 en 2017. Cependant, le Comité scientifique (CS) du Haut Conseil des biotechnologies (HCB) a identifié une erreur significative d’analyse statistique remettant en question l’analyse du suivi de la sensibilité des sésamies à la toxine Cry1Ab, et suggérant un possible développement de résistance dans les populations du nord-est de la péninsule Ibérique. Par ailleurs, le CS du HCB identifie encore certaines faiblesses et limites méthodologiques concernant la surveillance de la résistance et la mise en oeuvre des zones refuges. Le HCB estime notamment que l’utilisation d’une dose diagnostic présente certaines limites pour la détection précoce de l’évolution de la résistance, 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. Enfin, le HCB demande à obtenir les données brutes des différents essais biologiques pour évaluer la qualité des données et de leur analyse. 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 d’une sélection d’agriculteurs. 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.
• Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data
  
  • Marguet Aline
  • Lavielle Marc
  • Cinquemani Eugenio
  Bioinformatics, Oxford University Press (OUP), 2019, 35 (14), pp.i586-i595. Motivation: Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, most existing methods to infer stochastic gene expression models from single-cell data dedicate little attention to the reconstruction of mother-daughter inheritance dynamics. Results: Starting from a transcription and translation model of gene expression, we propose a sto-chastic model for the evolution of gene expression dynamics in a population of dividing cells. Based on this model, we develop a method for the direct quantification of inheritance and variability of kinetic gene expression parameters from single-cell gene expression and lineage data. We demonstrate that our approach provides unbiased estimates of mother-daughter inheritance parameters, whereas indirect approaches using lineage information only in the post-processing of individual-cell parameters underestimate inheritance. Finally, we show on yeast osmotic shock response data that daughter cell parameters are largely determined by the mother, thus confirming the relevance of our method for the correct assessment of the onset of gene expression variability and the study of the transmission of regulatory factors. Availability and implementation: Software code is available at https://github.com/almarguet/IdentificationWithARME. Lineage tree data is available upon request. (10.1093/bioinformatics/btz378)
  DOI : 10.1093/bioinformatics/btz378
• Climatic niche change of fish is faster at high latitude and in marine environments
  
  • Bourgeaud Luana
  • Rolland Jonathan
  • Carvajal-Quintero Juan David
  • Jézéquel Céline
  • Tedesco Pablo
  • Murienne Jérôme
  • Grenouillet Gaël
  , 2019. Change in species’ climatic niches is a key mechanism influencing species distribution patterns. The question of which factors impact niche change remains a highly debated topic in evolutionary biology. Previous studies have proposed that rates of climatic niche change might be correlated with climatic oscillations at high latitude or adaptation to new environmental conditions. Yet, very few studies have asked if those factors are also predominant in aquatic environments. Here, we reconstruct the climatic niche changes of fish species on a new phylogeny encompassing 12,616 species. We first confirm that the rate of niche change is faster at high latitude and show that this association is steeper for freshwater than for marine species. We also show that freshwater species have slower rates of niche change than marine species. These results may be explained by the fact that freshwater species have larger climatic niche breadth and thermal safety margin than marine species at high latitude. Overall, our study sheds a new light on the environmental conditions and species features impacting rates of climatic niche change in aquatic habitats. (10.1101/853374)
  DOI : 10.1101/853374
• Relationship between biodiversity and agricultural production
  
  • Brunetti Ilaria
  • Tidball Mabel
  • Couvet Denis
  Natural Resource Modeling, Rocky Mountain Mathematics Consortium, 2019, 32 (2), pp.e12204. The intensification of agriculture is one of the main causes of biodiversity loss. We model the interdependent relationship between agriculture and wild biodiversity providing regulating services to agriculture on farmed land. We suppose that while agriculture has a negative impact on wild biodiversity, the latter can increase agricultural production. Farmers act as myopic agents, who maximize their instantaneous profit without considering the negative effects of their practice on the evolution of biodiversity. Two unexpected results arise (a) a tax on inputs can have a positive effect on yield since it can be considered as a social signal helping farmers to avoid myopic behavior concerning the positive effect of biodiversity on yield; (b) increasing biodiversity productivity, a proposal of ecological intensification, affects negatively the level of biodiversity, a counter‐intuitive result; due to the fact that when biodiversity is more productive, farmers can maintain lower biodiversity to get the same yield. (10.1111/nrm.12204)
  DOI : 10.1111/nrm.12204
• Hamiltonian models of interacting fermion fields in Quantum Field Theory
  
  • Alvarez Benjamin
  • Faupin Jérémy
  • Guillot Jean-Claude
  Letters in Mathematical Physics, Springer Verlag, 2019, 109 (11), pp.2403-2437. We consider Hamiltonian models representing an arbitrary number of spin 1 / 2 fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction form factors are supposed to satisfy some regularity conditions in both position and momentum space. Without any restriction on the strength of the interaction, we prove that the Hamiltonian identifies to a self-adjoint operator on a tensor product of antisymmetric Fock spaces and we establish the existence of a ground state. Our results rely on new interpolated $N_\tau $ estimates. They apply to models arising from the Fermi theory of weak interactions, with ultraviolet and spatial cutoffs. (10.1007/s11005-019-01193-9)
  DOI : 10.1007/s11005-019-01193-9
• High Pressure Flames with Multicomponent Transport
  
  • Giovangigli Vincent
  • Matuszewski Lionel
  • Gaillard Pierre
  , 2019. The thermodynamic formulation and the traditional formulation of multicomponent transport fluxes in high pressure fluids are discussed. The impact of high pressure transport models on mixing layers, premixed plane flames and strained diffusion flames is then investigated. Multicomponent fluxes in diffuse-interface transcritical diffusion flames are further addressed.
• A variational approach to nonlinear and interacting diffusions
  
  • Arnaudon Marc
  • del Moral Pierre
  Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2019, 37 (5), pp.717-748. The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward stochastic interpolations, Lyapunov linearization techniques as well as spectral theory. This framework applies to a large class of stochastic models including nonhomogeneous diffusions, as well as stochastic processes evolving on differentiable manifolds, such as constraint-type embedded manifolds on Euclidian spaces and manifolds equipped with some Riemannian metric. We derive uniform as well as almost sure exponential contraction inequalities at the level of the nonlinear diffusion flow, yielding what seems to be the first result of this type for this class of models. Uniform propagation of chaos properties w.r.t. the time parameter is also provided. Illustrations are provided in the context of a class of gradient flow diffusions arising in fluid mechanics and granular media literature. The extended versions of these nonlinear Langevin-type diffusions on Riemannian manifolds are also discussed. (10.1080/07362994.2019.1609985)
  DOI : 10.1080/07362994.2019.1609985
• An explicit Floquet-type representation of Riccati aperiodic exponential semigroups
  
  • Bishop Adrian N
  • del Moral Pierre
  International Journal of Control, Taylor & Francis, 2019, pp.1-9. The article presents a rather surprising Floquet-type representation of time-varying transition matri-ces associated with a class of nonlinear matrix differentialRiccati equations. The main difference withconventional Floquet theory comes from the fact that the underlying flow of the solution matrix is aperi-odic. The monodromy matrix associated with this Floquet representation coincides with the exponential(fundamental) matrix associated with the stabilizing fixedpoint of the Riccati equation. The second partof this article is dedicated to the application of this representation to the stability of matrix differentialRiccati equations. We provide refined global and local contraction inequalities for the Riccati exponentialsemigroup that depend linearly on the spectral norm of the initial condition. These refinements improveupon existing results and are a direct consequence of the Floquet-type representation, yielding whatseems to be the first results of this type for this class of models. (10.1080/00207179.2019.1590647)
  DOI : 10.1080/00207179.2019.1590647
• Moutard transforms for the conductivity equation
  
  • Grinevich Piotr G
  • Novikov Roman G
  Letters in Mathematical Physics, Springer Verlag, 2019, 109 (10), pp.2209-2222. We construct Darboux-Moutard type transforms for the two-dimensional conductivity equation. This result continues our recent studies of Darboux-Moutard type transforms for generalized analytic functions. In addition, at least, some of the Darboux-Moutard type transforms of the present work admit direct extension to the conductivity equation in multidimensions. Relations to the Schrödinger equation at zero energy are also shown. (10.1007/s11005-019-01183-x)
  DOI : 10.1007/s11005-019-01183-x