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.
• 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.
• Non-abelian Radon transform and its applications
  
  • Novikov Roman G
  , 2019, pp.115–128. Considerations of the non-abelian Radon transform were started in [Manakov, Zakharov, 1981] in the framework of the theory of solitons in dimension 2+1. On the other hand, the problem of inversion of transforms of such a type arises in different tomographies, including emission tomographies, polarization tomographies, and vector field tomography. In this article we give a short review of old and recent results on this subject. This article is an extended version of the talk given at the conference "100 Years of the Radon Transform", Linz, 27-31 March 2017.
• Stochastic Approximation Schemes for Economic Capital and Risk Margin Computations
  
  • Barrera David
  • Crépey Stéphane
  • Diallo Babacar
  • Fort Gersende
  • Gobet Emmanuel
  • Stazhynski Uladzislau
  ESAIM: Proceedings and Surveys, EDP Sciences, 2019, 65, pp.182-218. We consider the problem of the numerical computation of its economic capital by an insurance or a bank, in the form of a value-at-risk or expected shortfall of its loss over a given time horizon. This loss includes the appreciation of the mark-to-model of the liabilities of the firm, which we account for by nested Monte Carlo à la Gordy and Juneja (2010) or by regression à la Broadie, Du, and Moallemi (2015). Using a stochastic approximation point of view on value-at-risk and expected shortfall, we establish the convergence of the resulting economic capital simulation schemes, under mild assumptions that only bear on the theoretical limiting problem at hand, as opposed to assumptions on the approximating problems in Gordy-Juneja (2010) and Broadie-Du-Moallemi (2015). Our economic capital estimates can then be made conditional in a Markov framework and integrated in an outer Monte Carlo simulation to yield the risk margin of the firm, corresponding to a market value margin (MVM) in insurance or to a capital valuation adjustment (KVA) in banking par- lance. This is illustrated numerically by a KVA case study implemented on GPUs. (10.1051/proc/201965182)
  DOI : 10.1051/proc/201965182
• Scaling of Sub-Ballistic 1D Random Walks Among Biased Random Conductances
  
  • Berger Quentin
  • Salvi Michele
  Markov Processes And Related Fields, Polymat Publishing Company, 2019, 25 (1), pp.171-187. We consider two models of one-dimensional random walks among biased i.i.d.\ random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random walk on a point process (the bias depending on the distance between points). We study the case when the walk is transient to the right but sub-ballistic, and identify the correct scaling of the random walk: we find Undefined control sequence \ga such that Undefined control sequence \ga. Interestingly, Undefined control sequence \ga does not depend on the intensity of the bias in the first case, but it does in the second case. %Moreover, with additional information on the distribution of the conductances, we are able to identify more sharply the correct scaling, and the limiting distribution for the rescaled Xn.
• A policy iteration algorithm for non-zero sum stochastic impulse games
  
  • Aïd René
  • Bernal Francisco
  • Mnif Mohamed
  • Zabaljauregui Diego
  • Zubelli Jorge P.
  ESAIM: Proceedings and Surveys, EDP Sciences, 2019, 65 (CEMRACS 2017). This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing. (10.1051/proc/201965027)
  DOI : 10.1051/proc/201965027
• 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
• 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
• 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.
• Hamiltonian models of interacting fermion fields in Quantum Field Theory
  
  • Alvarez Benjamin
  • Faupin Jérémy
  • Guillot Jean-Claude
  Lett.Math.Phys., 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
• 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
• 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