Publications

2017

• Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges
  
  • Conforti Giovanni
  • von Renesse Max-K.
  Probability Theory and Related Fields, Springer Verlag, 2017. In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, bounds of the distance between bridges of different Langevin dynamics, and a logarithmic Sobolev inequality for bridge measures. The existence of an invariant measure for the bridges is also discussed and quantitative bounds for the convergence to the invariant measure are proven. All results are based on a seemingly new expression of the drift of a bridge in terms of the reciprocal characteristic, which, roughly speaking, quantifies the “mean acceleration” of a bridge. (10.1007/s00440-017-0814-9)
  DOI : 10.1007/s00440-017-0814-9
• A central limit theorem for the spatial Lambda-Fleming-Viot process with selection
  
  • Forien Raphaël
  • Penington Sarah
  Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (0), pp.1-68. We study the evolution of gene frequencies in a population living in Rd, modelled by the spatial Λ-Fleming-Viot process with natural selection. We suppose that the population is divided into two genetic types, a and A, and consider the proportion of the population which is of type a at each spatial location. If we let both the selection intensity and the fraction of individuals replaced during reproduction events tend to zero, the process can be rescaled so as to converge to the solution to a reaction-diffusion equation (typically the Fisher-KPP equation). We show that the rescaled fluctuations converge in distribution to the solution to a linear stochastic partial differential equation. Depending on whether offspring dispersal is only local or if large scale extinction-recolonization events are allowed to take place, the limiting equation is either the stochastic heat equation with a linear drift term driven by space-time white noise or the corresponding fractional heat equation driven by a coloured noise which is white in time. If individuals are diploid (i.e. either AA, Aa or aa) and if natural selection favours heterozygous (Aa) individuals, a stable intermediate gene frequency is maintained in the population. We give estimates for the asymptotic effect of random fluctuations around the equilibrium frequency on the local average fitness in the population. In particular, we find that the size of this effect - known as the drift load - depends crucially on the dimension d of the space in which the population evolves, and is reduced relative to the case without spatial structure. (10.1214/16-EJP20)
  DOI : 10.1214/16-EJP20
• A new accurate residual-based a posteriori error indicator for the BEM in 2D-acoustics
  
  • Bakry Marc
  • Pernet Sebastien
  • Collino Francis
  Computers & Mathematics with Applications, Elsevier, 2017, 73 (12), pp.2501 - 2514. In this work we construct a new reliable, efficient and local a posteriori error estimate for the single layer and hyper-singular boundary integral equations associated to the Helmholtz equation in two dimensions. It uses a localization technique based on a generic operator Λ which is used to transport the residual into L2. Under appropriate conditions on the construction of Λ, we show that it is asymptotically exact with respect to the energy norm of the error. The single layer equation and the hyper-singular equation are treated separately. While the current analysis requires the boundary to be smooth, numerical experiments show that the new error estimators also perform well for non-smooth boundaries. (10.1016/j.camwa.2017.03.016)
  DOI : 10.1016/j.camwa.2017.03.016
• Avis en réponse à la saisine HCB - dossier C/NL/04/02_001. Paris, le 13 mars 2017
  
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie-Anne
  • Berny Philippe
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Eychenne Nathalie
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Jestin André
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie
  • Lefèvre François
  • Lemaire Olivier
  • Lereclus Didier D.
  • Maximilien Rémi
  • Meurs Eliane
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Parzy Daniel
  • Raynaud Xavier
  • Regnault-Roger Catherine
  • Renard Michel M.
  • Renault Tristan
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2017. Le Haut Conseil des biotechnologies (HCB) a été saisi d’une demande d’avis relative au dossier C/NL/04/02_001 dans le but d’éclairer les autorités compétentes françaises, à la suite de leur objection de principe à la mise sur le marché de cet OGM auprès de la Commission européenne dans l’attente de l’évaluation du dossier par le HCB. Déposé par la société Suntory Flowers Limited, Tokyo, Japan (anciennement Florigene) auprès des autorités compétentes néerlandaises sur le fondement de la directive 2001/18/CE, ce dossier est une demande de renouvellement d’autorisation de mise sur le marché d’œillets génétiquement modifiés FLO-40644-6 à des fins d’importation et de commercialisation de fleurs coupées dans l’Union européenne Description du produit La lignée d’œillets 123.2.38 (Evénement Florigene MoonliteTMFLO-40644-6) est modifiée génétiquement par introduction de deux gènes de pétunia, dfret f3’5’h, impliqués dans la voie de biosynthèse des anthocyanes. Leur expression confère aux fleurs une coloration violette résultant de l’accumulation de delphinidine. Cette lignée exprime également le gène muté SuRB(als) d’acétolactate synthase de Nicotiana tabacumconférant une tolérance aux herbicides de la famille des sulfonylurées, utilisée uniquement pour la sélection des transformants primaires. La transformation génétique a été réalisée à l’aide la souche désarmée d’Agrobacterium tumefaciens AGL0 contenant les cassettes d’expression au sein de l’ADN-T du plasmide pCGP1470. Les analyses initiales du dossier datant de 2006 ont montré l’insertion de deux copiesde l’ADN-T en des sites différents du génome des plantes hôtes. La première copie exprime l’ensemble des gènes transférés et comporte un fragment du plasmide vecteur situé à l’extérieur de la bordure gauche de l’ADN-T. La seconde copie contient un ADN-T incomplet, comprenant un fragment tronqué du gène dfr et de son terminateur.Grâce à la séquence d’un génome d’œillet publiée en 2014, les deux loci d’insertion ont pu être situés sur deux fragments génomiques («scaffolds») différents. Aucune séquence codante n’est interrompue par les insertions. Le caractère de coloration est stable dans les fleurs produites depuis 1998 par bouturages successifs. Impact sur la santé humaine et animale La demande concerne un usage exclusivement ornemental; les œillets ne sont pas destinés à l’alimentation humaine et animale. Dans l’hypothèse d’une consommation fortuite, le pétitionnaire a évalué la toxicité ainsi que le potentiel allergénique de la lignée 123.2.38. La delphinidine existe naturellement dans beaucoup d’autres plantes et fruits comestibles (myrtilles, mûres), elle n’est pas connue pour être toxique ou allergène. L’acétolactate synthase (ALS) est une enzyme présente dans les plantes, les bactéries et les champignons. La forme mutée du gène de l’ALS du tabac (SuRB) présente dans la lignée d’œillets 123.2.38n’est pas associée à un risque sanitaire particulier. Dans la demande de renouvellement, une analyse complémentaire des ORF potentiellement créés à la jonction des deux sites d’insertion a été réalisée. Les analyses bioinformatiques datant de 2016 indiquent l’absence d’homologie avec des allergènes ou des toxines. Risques de dispersion et impact sur l’environnement Les risques potentiels pour l’environnement concernent les risques de dispersion des transgènes et leurs conséquences. Suite à la mise sur le marché de fleurs coupées d’œillets génétiquement modifiés, les transgènes qu’ils portent pourraient théoriquement être dispersés suite à une multiplication végétative, une dispersion de pollen vers d’autres œillets ou espèces apparentées, ou une dispersion de graines qui se seraient développées sur les fleurs coupées. En pratique: - une multiplication végétative serait impossible naturellement à partir de fleurs coupées; elle serait difficile mais possible par des techniques de bouturage spécifiques appliquées par des individus expérimentés; - une dispersion de pollen vers d’autres œillets ou espèces apparentées serait peu probable compte tenu: (1) de l’environnement dans lequel les fleurs coupées sont placées (essentiellement des habitations), (2) de la relative faiblesse de la production de pollen des œillets cultivés comparée à celle des œillets «sauvages», (3) du caractère uniquement entomophile de la pollinisation (principalement via des lépidoptères, qui n’ont pas un comportement de butinage optimal), 4) de la faible viabilité du pollen une fois qu’il est accessible aux insectes, c’est-à-dire une fois que la fleur est ouverte, (5) de la durée de vie et des conditions de conservation des fleurs coupées, et (6) de la distance de dispersion relativement courte (quelques centaines de mètres). - une dispersion de graines qui se seraient développées sur les fleurs coupées serait très improbable considérant notamment que le processus de développement des graines dure cinq semaines à deux mois et qu’une fleur coupée en vase ne survit pas sur cette durée. Par ailleurs, dans le cas peu probable d’une dispersion dans l’environnement, des plantes porteuses du transgène SurB ne présenteraient pas d’avantage sélectif, sauf dans le cas particulier où elles seraient exposées à des herbicides dont la seule matière active est le flazasulfuron. L’évaluation phénotypique comparative présentée dans le dossier de renouvellement ne met pas en évidence de risque accru de dispersion par reproduction sexuée et flux de gènes. Le CS du HCB recommande cependant, que, si elle était autorisée, la mise sur le marché des œillets FLO-40644-6 soit accompagnée de mesures propres à répondre au risque de dispersion par bouturage par une communication à l’attention des sociétés d’amateurs quant aux possibilités de diffusion non contrôlée des œillets transgéniques. Plans de surveillance post-commercialisation Considérant les résultats de l’analyse de risques et l’utilisation prévue des œillets dans la demande d’autorisation de mise sur le marché C/NL/04/02, le CS du HCB s’accorde avec le pétitionnaire sur le fait qu’un plan de surveillance spécifique n’est pas nécessaire. Le CS du HCB approuve l’approche générale et les méthodes du plan de surveillance générale indiquées par le pétitionnaire en accord avec la directive 2001/18/CE. Il inclut l’étiquetage spécifique des fleurs, la constitution de réseaux d’experts, une surveillance des populations de Dianthus sauvages à travers des institutions spécialisées, et une veille documentaire et bibliographique. Il n’apparaît pas utile de prolonger la surveillance post-commercialisation au-delà de la période couverte par l’autorisation, sachant que la surveillance générale réalisée sur une période de 10 ans n’a montré aucun effet adverse pour la santé humaine et animale ou l’environnement. Pour améliorer la surveillance de terrain sur les espèces endémiques de Dianthus en France, des experts français du secteur public ou privé, comme par exemple des experts de conservatoires botaniques, devraient être incités par les autorités compétentes à se rapprocher du pétitionnaire pour conduire avec lui la veille de terrain qu’il souhaite réaliser et qui contribue à faire progresser la connaissance scientifique. Conclusions Au terme de l’analyse de l’ensemble des données fournies par le pétitionnaire et de données supplémentaires disponibles dans la littérature scientifique, le CS du HCB note que: -Aucun risque particulier de toxicité ni d’allergénicité n’a été identifié suite à l’évaluation et l’analyse bioinformatique de lignée d’œillets 123.2.38 (Evénement Florigene Moonlite TM FLO-40644-6), de la delphinidine, de l’enzyme mutante ALS, ou des ORFs potentiels créés par la modification génétique. - Il est improbable que les fleurs coupées d’œillet produisent des graines; le risque de dispersion par des graines produites par ces fleurs est donc quasi nul. - Le risque de dispersion de gènes par le pollen de fleurs coupées d’œillet est faible mais non nul. Il ne lui serait cependant pas associé d’impact environnemental significatif. - La dispersion par bouturage est difficile à réaliser mais possible par des techniques adaptées. Le CS du HCB recommande que, si elle était autorisée, la mise sur le marché des œillets FLO-40644-6 soit accompagnée de mesures propres à répondre au risque de dispersion par bouturage par une communication à l’attention des sociétés d’amateurs quant aux possibilités de diffusion non contrôlée des œillets transgéniques. - Le plan de surveillance proposé par le pétitionnaire est adapté à l’utilisation prévue des œillets Florigene Moonlite TM FLO-40644-6 dans la demande d’autorisation de renouvellement de mise sur le marché. Le CS du HCB considère qu’il n’apparaît pas utile de prolonger la surveillance post-commercialisation au-delà de la période couverte par l’autorisation, sachant que la surveillance générale réalisée sur une période de 10 ans n’a montré aucun effet adverse pour la santé humaine et animale ou l’environnement. - Pour améliorer la surveillance de terrain sur les espèces endémiques de Dianthus en France, des experts français du secteur public ou privé, comme par exemple des experts de conservatoires botaniques, devraient être incités par les Autorités compétentes à se rapprocher du pétitionnaire pour conduire avec lui la veille de terrain qu’il souhaite réaliser et qui contribue à faire progresser la connaissance scientifique. De plus, afin de vérifier le bon fonctionnement de la surveillance générale, il pourrait être envisagé de s’assurer de la puissance du dispositif et de la robustesse de la surveillance, ceci par une collaboration entre le pétitionnaire et les autorités compétentes des Etats membres ou d’autres organisations.
• Generalized and hybrid Metropolis-Hastings overdamped Langevin algorithms
  
  • Poncet Romain
  , 2017. It has been shown that the nonreversible overdamped Langevin dynamics enjoy better convergence properties in terms of spectral gap and asymptotic variance than the reversible one. In this article we propose a variance reduction method for the Metropolis-Hastings Adjusted Langevin Algorithm (MALA) that makes use of the good behaviour of the these nonreversible dynamics. It consists in constructing a nonreversible Markov chain (with respect to the target invariant measure) by using a Generalized Metropolis-Hastings adjustment on a lifted state space. We present two variations of this method and we discuss the importance of a well-chosen proposal distribution in terms of average rejection probability. We conclude with numerical experimentations to compare our algorithms with the MALA, and show variance reduction of several orders of magnitude in some favourable toy cases.
• Quantitative DLA-based compressed sensing for T1-weighted acquisitions.
  
  • Svehla Pavel
  • Nguyen Khieu-Van
  • Li Jing-Rebecca
  • Ciobanu Luisa
  Journal of Magnetic Resonance, Elsevier, 2017. (10.1016/j.jmr.2017.05.002)
  DOI : 10.1016/j.jmr.2017.05.002
• Resolution Analysis of Passive Synthetic Aperture Imaging of Fast Moving Objects
  
  • Garnier Josselin
  • Borcea L.
  • Papanicolaou G.
  • Solna K.
  • Tsogka C.
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, 10 (2), pp.665 - 710. (10.1137/16M109716X)
  DOI : 10.1137/16M109716X
• An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations
  
  • Giacomini Matteo
  Journal of Scientific Computing, Springer Verlag, 2017. The certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It relies on the computation of an upper bound of the error introduced by the finite element approximation of the shape gradient. In this paper, we present a goal-oriented error estimator which depends solely on local quantities and is fully-computable. By means of the equilibrated fluxes approach, we construct a unified strategy valid for both conforming finite element approximations and discontinuous Galerkin discretizations. The new variant of the CDA is tested on the inverse identification problem of electrical impedance tomography: both its ability to identify a genuine descent direction at each iteration and its reliable stopping criterion are confirmed. (10.1007/s10915-017-0545-1)
  DOI : 10.1007/s10915-017-0545-1
• Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles
  
  • Ollivier Yann
  • Arnold Ludovic
  • Auger Anne
  • Hansen Nikolaus
  Journal of Machine Learning Research, Microtome Publishing, 2017, 18 (18), pp.1-65. We present a canonical way to turn any smooth parametric family of probability distributions on an arbitrary search space X into a continuous-time black-box optimization method on X, the information-geometric optimization (IGO) method. Invariance as a major design principle keeps the number of arbitrary choices to a minimum. The resulting IGO flow is the flow of an ordinary differential equation conducting the natural gradient ascent of an adaptive, time-dependent transformation of the objective function. It makes no particular assumptions on the objective function to be optimized. The IGO method produces explicit IGO algorithms through time discretization. It naturally recovers versions of known algorithms and offers a systematic way to derive new ones. In continuous search spaces, IGO algorithms take a form related to natural evolution strategies (NES). The cross-entropy method is recovered in a particular case with a large time step, and can be extended into a smoothed, parametrization-independent maximum likelihood update (IGO-ML). When applied to the family of Gaussian distributions on R^d, the IGO framework recovers a version of the well-known CMA-ES algorithm and of xNES. For the family of Bernoulli distributions on {0, 1}^d, we recover the seminal PBIL algorithm and cGA. For the distributions of restricted Boltzmann machines, we naturally obtain a novel algorithm for discrete optimization on {0, 1}^d. All these algorithms are natural instances of, and unified under, the single information-geometric optimization framework. The IGO method achieves, thanks to its intrinsic formulation, maximal invariance properties: invariance under reparametrization of the search space X, under a change of parameters of the probability distribution, and under increasing transformation of the function to be optimized. The latter is achieved through an adaptive, quantile-based formulation of the objective. Theoretical considerations strongly suggest that IGO algorithms are essentially characterized by a minimal change of the distribution over time. Therefore they have minimal loss in diversity through the course of optimization, provided the initial diversity is high. First experiments using restricted Boltzmann machines confirm this insight. As a simple consequence, IGO seems to provide, from information theory, an elegant way to simultaneously explore several valleys of a fitness landscape in a single run.
• Équations de Navier-Stokes incompressibles et multirésolution spatiale adaptative: sur la question des modes parasites en maillage collocalisé.
  
  • N'Guessan Marc-Arthur
  • Massot Marc
  • Tenaud Christian
  • Series Laurent
  , 2017. La simulation numérique directe (DNS) de la combustion avec chimie détaillée et transport multi-espèces représente l'un des défis les plus importants en matière de calcul scientifique dans de nombreuses applications industrielles. Un des enjeux est de coupler un solveur hydrodynamique pour la résolution des équations de Navier-Stokes, pour un mélange réactif dans la limite des faibles nombres de Mach, à une stratégie de résolution de systèmes de convection-réaction-diffusion, tout en maintenant l'efficacité algorithmique, l'adaptation temps-espace et le contrôle d'erreur. La présente communication vise à proposer une stratégie optimale pour l'élimination des modes parasites dans un contexte de maillages colocalisés en volume fini, dans un cadre de multirésolution spatiale.
• Functional Characterization of Intrinsic and Extrinsic Geometry
  
  • Corman Etienne
  • Solomon Justin
  • Ben-Chen Mirela
  • Guibas Leonidas
  • Ovsjanikov Maks
  ACM Transactions on Graphics, Association for Computing Machinery, 2017, 17. We propose a novel way to capture and characterize distortion between pairs of shapes by extending the recently proposed framework of shape differences built on functional maps. We modify the original definition of shape differences slightly and prove that, after this change, the discrete metric is fully encoded in two shape difference operators and can be recovered by solving two linear systems of equations. Then, we introduce an extension of the shape difference operators using offset surfaces to capture extrinsic or embedding-dependent distortion, complementing the purely intrinsic nature of the original shape differences. Finally, we demonstrate that a set of four operators is complete, capturing intrinsic and extrinsic structure and fully encoding a shape up to rigid motion in both discrete and continuous settings. We highlight the usefulness of our constructions by showing the complementary nature of our extrinsic shape differences in capturing distortion ignored by previous approaches. We additionally provide examples where we recover local shape structure from the shape difference operators, suggesting shape editing and analysis tools based on manipulating shape differences.
• Exploring the complexity of the integer image problem in the max-algebra
  
  • Maccaig Marie
  Discrete Applied Mathematics, Elsevier, 2017, 217 (2), pp.261--275. We investigate the complexity of the problem of finding an integer vector in the max-algebraic column span of a matrix, which we call the integer image problem. We show some cases where we can determine in strongly polynomial time whether such an integer vector exists, and find such an integer vector if it does exist. On the other hand we also describe a group of related problems each of which we prove to be NP-hard. Our main results demonstrate that the integer image problem is equivalent to finding a special type of integer image of a matrix satisfying a property we call column typical. For a subclass of matrices this problem is polynomially solvable but if we remove the column typical assumption then it becomes NP-hard. (10.1016/j.dam.2016.09.016)
  DOI : 10.1016/j.dam.2016.09.016
• Online Learning and Blackwell Approachability with Partial Monitoring: Optimal Convergence Rates
  
  • Kwon Joon
  • Perchet Vianney
  JMLR Papers, 2017, 54, pp.604-613. Blackwell approachability is an online learning setup generalizing the classical problem of regret minimization by allowing for instance multi-criteria optimization, global (online) optimization of a convex loss, or online linear optimization under some cumulative constraint. We consider partial monitoring where the decision maker does not necessarily observe the outcomes of his decision (unlike the traditional regret/bandit literature). Instead, he receives a random signal correlated to the decision-outcome pair, or only to the outcome. We construct, for the first time, approachability algorithms with convergence rate of order O(T −1/2) when the signal is independent of the decision and of order O(T −1/3) in the case of general signals. Those rates are optimal in the sense that they cannot be improved without further assumption on the structure of the objectives and/or the signals.
• Cell Averaging Two-Scale Convergence: Applications to Periodic Homogenization
  
  • Alouges François
  • Di Fratta Giovanni
  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2017, 15 (4), pp.1651-1671. (10.1137/16M1085309)
  DOI : 10.1137/16M1085309
• A numerical approach to determine mutant invasion fitness and evolutionary singular strategies
  
  • Fritsch Coralie
  • Campillo Fabien
  • Ovaskainen Otso
  Theoretical Population Biology, Elsevier, 2017, 115, pp.89-99. We propose a numerical approach to study the invasion fitness of a mutant and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds. Our approach is based on a dual representation, which consists of the modelling of the small size mutant population by a stochastic model and the computation of its corresponding deterministic model. The use of the deterministic model greatly facilitates the numerical determination of the feasibility of invasion as well as the convergence-stability of the evolutionary singular strategy. Our approach combines standard adaptive dynamics with the link between the mutant survival criterion in the stochastic model and the sign of the eigenvalue in the corresponding deterministic model. We present our method in the context of a mass-structured individual-based chemostat model. We exploit a previously derived mathematical relationship between stochastic and deterministic representations of the mutant population in the chemostat model to derive a general numerical method for analyzing the invasion fitness in the stochastic models. Our method can be applied to the broad class of evolutionary models for which a link between the stochastic and deterministic invasion fitnesses can be established. (10.1016/j.tpb.2017.05.001)
  DOI : 10.1016/j.tpb.2017.05.001
• Sampling method for sign changing contrast
  
  • Audibert Lorenzo
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2017. We extend the applicability of the Generalized Linear Sampling Method (GLSM) [2] and the Factorization Method (FM)[14] to the case of inhomogeneities where the contrast change sign strictly inside the obstacle. Both methods give an exact characterization of the target shapes in term of the fareld operator (at a xed frequency). One of the key ingredient to prove this exact characterization is based on a factorization of the fareld operator. This factorization involves three operators which should exhibit specic properties. This paper is concerned with the extension of the coercivity property required on one of them to the case of sign changing contrast both for isotropic and anisotropic scatters with possibly dierent supports for the isotropic and anisotropic parts. We fnally validate the method through some numerical tests in two dimensions.
• Understanding the Time-Dependent Effective Diffusion Coefficient Measured by Diffusion MRI: the Intra-Cellular Case
  
  • Haddar Houssem
  • Li Jing-Rebecca
  • Schiavi Simona
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2017. Diffusion Magnetic Resonance Imaging (dMRI) can be used to measure a time-dependent effective diffusion coefficient that can in turn reveal information about the tissue geometry. Recently a mathematical model for the time-dependent effective diffusion coefficient was obtained using homogenization techniques after imposing a certain scaling relationship for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. With this choice of the scaling of the physical parameters, the effective diffusion coefficient of the medium can be computed after solving a diffusion equation subject to a time-dependent Neumann boundary condition, independently in the biological cells and in the extra-cellular space. In this paper, we analyze this new model, which we call the H-ADC model, in the case of finite domains, which is relevant to diffusion inside biological cells. We use both the eigenfunction expansion and the single layer potential representation for the solution of the above mentioned diffusion equation to obtain analytical expressions for the effective diffusion coefficient in different diffusion time regimes. These expressions are validated using numerical simulations in two dimensions.
• Adaptive multipreconditioned FETI: scalability results and robustness assessment
  
  • Bovet Christophe
  • Parret-Fréaud Augustin
  • Spillane Nicole
  • Gosselet Pierre
  Computers & Structures, Elsevier, 2017, 193, pp.1-20. The purpose of this article is to assess the adaptive multipreconditioned FETI solvers (AMPFETI) on realistic industrial problems and hardware. The multi-preconditioned FETI algorithm (first introduced as Simultaneous FETI [1]) is a non-overlapping domain decomposition method which exhibits good robust-ness properties without requiring the explicit knowledge of the original partial differential equation, or any a priori analysis of the algebraic system through eigenvalues problems. Multipreconditioned FETI solves critical problems in significantly fewer iterations than classical FETI but each iteration involves a larger computational effort. An adaptive strategy (known as the adaptive mul-tipreconditioned conjugate gradient algorithm [2]) has been proposed to achieve balance between robustness and efficiency and we will observe that it provides an efficient solver for the problems considered here. (10.1016/j.compstruc.2017.07.010)
  DOI : 10.1016/j.compstruc.2017.07.010
• Correction to Black--Scholes Formula Due to Fractional Stochastic Volatility
  
  • Garnier Josselin
  • Sølna Knut
  SIAM Journal on Financial Mathematics, Society for Industrial and Applied Mathematics, 2017, 8 (1), pp.560 - 588. (10.1137/15M1036749)
  DOI : 10.1137/15M1036749
• Consistent functional cross field design for mesh quadrangulation
  
  • Azencot Omri
  • Corman Etienne
  • Ben-Chen Mirela
  • Ovsjanikov Maks
  ACM Transactions on Graphics, Association for Computing Machinery, 2017, 36 (4), pp.92. We propose a novel technique for computing consistent cross fields on a pair of triangle meshes given an input correspondence, which we use as guiding fields for approximately consistent quadrangulations. Unlike the majority of existing methods our approach does not assume that the meshes share the same connectivity or even have the same number of vertices, and furthermore does not place any restrictions on the topology (genus) of the shapes. Importantly, our method is robust with respect to small perturbations of the given correspondence, as it only relies on the transportation of real-valued functions and thus avoids the costly and error-prone estimation of the map differential. Key to this robustness is a novel formulation, which relies on the previously-proposed notion of power vectors, and we show how consistency can be enforced without pre-alignment of local basis frames, in which these power vectors are computed. We demonstrate that using the same formulation we can both compute a quadrangulation that would respect a given symmetry on the same shape or a map across a pair of shapes. We provide quantitative and qualitative comparison of our method with several baselines and show that it both provides more accurate results and allows to handle more general cases than existing techniques. (10.1145/3072959.3073696)
  DOI : 10.1145/3072959.3073696
• HOMOGENIZATION OF STOKES SYSTEM USING BLOCH WAVES
  
  • Allaire Grégoire
  • Ghosh Tuhin
  • Vanninathan Muthusamy
  Networks and Heterogeneous Media, American Institute of Mathematical Sciences, 2017, 12 (4), pp.525-550. In this work, we study the Bloch wave homogenization for the Stokes system with periodic viscosity coefficient. In particular, we obtain the spectral interpretation of the homogenized tensor. The presence of the incompressibility constraint in the model raises new issues linking the homogenized tensor and the Bloch spectral data. The main difficulty is a lack of smoothness for the bottom of the Bloch spectrum, a phenomenon which is not present in the case of the elasticity system. This issue is solved in the present work, completing the homogenization process of the Stokes system via the Bloch wave method.
• On perturbed proximal gradient algorithms
  
  • Atchadé Yves
  • Fort Gersende
  • Moulines Éric
  Journal of Machine Learning Research, Microtome Publishing, 2017, 18 (10), pp.1-33.
• An approximation of the M 2 closure: application to radiotherapy dose simulation
  
  • Pichard T
  • Alldredge G W
  • Brull Stéphane
  • Dubroca B
  • Frank M
  Journal of Scientific Computing, Springer Verlag, 2017. Particle transport in radiation therapy can be modelled by a kinetic equation which must be solved numerically. Unfortunately, the numerical solution of such equations is generally too expensive for applications in medical centers. Moment methods provide a hierarchy of models used to reduce the numerical cost of these simulations while preserving basic properties of the solutions. Moment models require a closure because they have more unknowns than equations. The entropy-based closure is based on the physical description of the particle interactions and provides desirable properties. However, computing this closure is expensive. We propose an approximation of the closure for the first two models in the hierarchy, the M 1 and M 2 models valid in one, two or three dimensions of space. Compared to other approximate closures, our method works in multiple dimensions. We obtain the approximation by a careful study of the domain of realizability and by invariance properties of the entropy minimizer. The M 2 model is shown to provide significantly better accuracy than the M 1 model for the numerical simulation of a dose computation in radiotherapy. We propose a numerical solver using those approximated closures. Numerical experiments in dose computation test cases show that the new method is more efficient compared to numerical solution of the minimum entropy problem using standard software tools.
• The infinitesimal model: definition, derivation, and implications
  
  • Barton Nick
  • Etheridge Alison M
  • Véber Amandine
  Theoretical Population Biology, Elsevier, 2017. Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation , population structure, ... We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1/\sqrt{M}. Simulations suggest that in some cases the convergence may be as fast as 1/\sqrt{M} .
• Optimal control of slender microswimmers
  
  • Zoppello Marta
  • Desimone Antonio
  • Alouges François
  • Giraldi Laetitia
  • Martinon Pierre
  , 2017, pp.21. We discuss a reduced model to compute the motion of slender swimmers which propel themselves by changing the curvature of their body. Our approach is based on the use of Resistive Force Theory for the evaluation of the viscous forces and torques exerted by the surrounding fluid, and on discretizing the kinematics of the swimmer by representing its body through an articulated chain of N rigid links capable of planar deformations. The resulting system of ODEs governing the motion of the swimmer is easy to assemble and to solve, making our reduced model a valuable tool in the design and optimization of bio-inspired artificial microdevices. We prove that the swimmer is controllable in the whole plane for N is greater of equal to 3 and for almost every set of stick lengths. As a direct result, there exists an optimal swimming strategy to reach a desired configuration in minimum time. Numerical experiments for N = 3 (Purcell swimmer) suggest that the optimal strategy is periodic, namely a sequence of identical strokes. Our results indicate that this candidate for an optimal stroke indeed gives a better displacement speed than the classical Purcell stroke. (10.1007/978-3-319-73371-5_8)
  DOI : 10.1007/978-3-319-73371-5_8