Publications

2013

• A new non linear shell modeling combining flexural and membrane effects
  
  • Pantz Olivier
  • Trabelsi Karim
  , 2013.
• Statistical models for deformable templates in image and shape analysis (Modèles statistiques d'atlas déformables pour l'analyse d'images et de formes)
  
  • Allassonnière Stéphanie
  • Bigot Jérémie
  • Glaunès Joan Alexis
  • Maire Florian
  • Richard Frederic J.P.
  Annales Mathématiques Blaise Pascal, Université Blaise-Pascal - Clermont-Ferrand, 2013, 20 (1), pp.1-35. Les données de grande dimensions sont de plus en plus fréquemment collectées dans de nombreux domaines d'application. Il devient alors particulièrement important d'être capable d'extraire des caractéristiques significatives de ces bases de données. Le modèle d'atlas déformable (Deformable template model) est un outil maintenant répandu pour atteindre ce but. Cet article présente un panorama des aspects statistiques de ce modèle ainsi que ses généralisations. Nous décrivons les différents cadres mathématiques permettant de prendre en compte des types variés de données et de déformations. Nous rappelons les propriétés théoriques de convergence des estimateurs et des algorithmes permettant l'estimation de ces caractéristiques. Nous terminons cet article par la présentation de quelques résultats publiés utilisant des données réelles. (10.5802/ambp.320)
  DOI : 10.5802/ambp.320
• The Moutard transformation and two-dimensional multi-point delta-type potentials
  
  • Novikov Roman
  • Taimanov Iskander
  Russian Mathematical Surveys, Turpion, 2013, 68 (5), pp.957–959. In the framework of the Moutard transformation formalism we find multi-point delta-type potentials for two-dimensional Schrodinger operators and their isospectral deformations on the zero energy level. In particular, these potentials are "reflectionless" in the sense of the Faddeev generalized "scattering" data.
• Diffraction of Bloch Wave Packets for Maxwell's Equations
  
  • Allaire Grégoire
  • Palombaro Mariapia
  • Rauch Jeffrey
  Communications in Contemporary Mathematics, World Scientific Publishing, 2013, 15 (6), pp.1350040. We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity and dispersed by a Schrödinger equation given by the quadratic approximation of the Bloch dispersion relation. A weak ray average hypothesis guarantees stability. Compared to earlier work on scalar wave equations, the generator is no longer elliptic. Coercivity holds only on the complement of an infinite dimensional kernel. The system structure requires many innovations. (10.1142/S0219199713500405)
  DOI : 10.1142/S0219199713500405
• Adaptation and migration of a population between patches
  
  • Mirrahimi Sepideh
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2013, 18, pp.753-768. A Hamilton-Jacobi formulation has been established previously for phenotypically structured population models where the solution concentrates as Dirac masses in the limit of small diffusion. Is it possible to extend this approach to spatial models? Are the limiting solutions still in the form of sums of Dirac masses? Does the presence of several habitats lead to polymorphic situations? We study the stationary solutions of a structured population model, while the population is structured by continuous phenotypical traits and discrete positions in space. The growth term varies from one habitable zone to another, for instance because of a change in the temperature. The individuals can migrate from one zone to another with a constant rate. The mathematical modeling of this problem, considering mutations between phenotypical traits and competitive interaction of individuals within each zone via a single resource, leads to a system of coupled parabolic integro-differential equations. We study the asymptotic behavior of the stationary solutions to this model in the limit of small mutations. The limit, which is a sum of Dirac masses, can be described with the help of an effective Hamiltonian. The presence of migration can modify the dominant traits and lead to polymorphic situations. (10.3934/dcdsb.2013.18.753)
  DOI : 10.3934/dcdsb.2013.18.753
• Lineage selection and the maintenance of sex
  
  • de Vienne Damien M.
  • Giraud Tatiana
  • Gouyon Pierre-Henri
  PLoS ONE, Public Library of Science, 2013, 8 (6), pp.e66906. Sex predominates in eukaryotes, despite its short-term disadvantage when compared to asexuality. Myriad models have suggested that short-term advantages of sex may be sufficient to counterbalance its twofold costs. However, despite decades of experimental work seeking such evidence, no evolutionary mechanism has yet achieved broad recognition as explanation for the maintenance of sex. We explore here, through lineage-selection models, the conditions favouring the maintenance of sex. In the first model, we allowed the rate of transition to asexuality to evolve, to determine whether lineage selection favoured species with the strongest constraints preventing the loss of sex. In the second model, we simulated more explicitly the mechanisms underlying the higher extinction rates of asexual lineages than of their sexual counterparts. We linked extinction rates to the ecological and/ or genetic features of lineages, thereby providing a formalisation of the only figure included in Darwin's "The origin of species". Our results reinforce the view that the long-term advantages of sex and lineage selection may provide the most satisfactory explanations for the maintenance of sex in eukaryotes, which is still poorly recognized, and provide figures and a simulation website for training and educational purposes. Short-term benefits may play a role, but it is also essential to take into account the selection of lineages for a thorough understanding of the maintenance of sex. (10.1371/journal.pone.0066906)
  DOI : 10.1371/journal.pone.0066906