Publications

2013

• An improved time domain linear sampling method for Robin and Neumann obstacles
  
  • Haddar Houssem
  • Lechleiter Armin
  • Marmorat Simon
  Applicable Analysis, Taylor & Francis, 2013, pp.1-22. We consider inverse obstacle scattering problems for the wave equation with Robin or Neu- mann boundary conditions. The problem of reconstructing the geometry of such obstacles from measurements of scattered waves in the time domain is tackled using a time domain linear sampling method. This imaging technique yields a picture of the scatterer by solving a linear operator equation involving the measured data for many right-hand sides given by singular so- lutions to the wave equation. We analyze this algorithm for causal and smooth impulse shapes, we discuss the effect of different choices of the singular solutions used in the algorithm, and finally we propose a fast FFT-based implementation. (10.1080/00036811.2013.772583)
  DOI : 10.1080/00036811.2013.772583
• Statistics of animal movement
  
  • Berthelot Geoffroy C.B.
  • Bansaye Vincent
  • Calenge C.
  , 2013.
• 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
• 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
• A numerical method for kinetic equations with discontinuous equations : application to mathematical modeling of cell dynamics
  
  • Aymard Benjamin
  • Clément Frédérique
  • Coquel Frédéric
  • Postel Marie
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2013, 35 (6), pp.27 pages. Abstract: In this work, we propose a numerical method to handle discontinuous fluxes arising in transport-like equations. More precisely, we study hyperbolic PDEs with flux transmission conditions at interfaces between subdomains where coefficients are discontinuous. A dedicated finite volume scheme with a limited high order enhancement is adapted to treat the discontinuities arising at interfaces. The validation of the method is done on 1D and 2D toy problems for which exact solutions are available, allowing us to do a thorough convergence study. We then apply the method to a biological model focusing on complex cell dynamics, that initially motivated this study, and illustrates the full potentialities of the scheme. (10.1137/120904238)
  DOI : 10.1137/120904238