La question de la modélisation en sciences humaines : mathématiques et informatique, année 2008/2009

Retour à l’année en cours

  • Mardi 9 juin 2009 à 15 h salle 206 (54, bd Raspail Paris 6e)

    Odo Diekmann
    Mathematical Institute, Utrecht University, Professeur invité à l’EHESS
    The evolution of virulence
    The individual host is a cul-de-sac for parasites that reproduce within it and so parasite persistence relies on host-to-host transmission. As a consequence, natural selection acts on two intertwined levels. Adopting the Adaptive Dynamics approach, we study some of the consequences in the context of caricatural models for within-host dynamics. The inspiration came from a paper of Gilchrist & Coombs (TPB 69(2006)145-153) but we incorporate superinfection and thus deal with a variant of the milker-killer dilemma. We find that dimorphism may arise by a degenerate form of branching. The lecture is based on joint work with Barbara Boldin.

  • Mardi 10 mars 2009 à 15 h 30, exceptionnellement même adresse, salle 206, 2e étage

    Jean Petitot
    Géométrie sous-riemannienne en perception visuelle
    De nombreuses données expérimentales sur l’architecture fonctionnelle de la première aire corticale visuelle (V1) montrent que celle-ci implémente la fibration  V ayant pour base le plan rétinien R et pour fibre la droite projective P des orientations du plan. En fait, c’est même la structure de contact naturelle de V ainsi que sa géométrie sous-riemannienne qui ont un sens neurophysiologique. Cela explique certaines propriétés « gestaltistes » de la perception visuelle.

  • Mardi 24 février 2009 à 15h

    Nicola Bellomo
    Department of Mathematics, Politecnico di Torino, Italy, e-mail:
    On the Modelling Vehicular Traffic, Crowds, and Swarms Mathematics, Complexity and Multiscale Issues
    This lecture deals with a review of models of vehicular traffic and crowd phenomena, with some preliminary results on swarm modelling. The survey covers modelling approaches related to the different representation scales (from micro to macroscopic), and is constantly referred to a critical analysis focused on research perspectives and hints to deal with them. The mathematical approach is based on the methods of the mathematical kinetic theory for active particles with interactions modelled by stochastic games.

The presentation is focused on general aspects of the modelling complex large systems of individuals interacting in a non-linear manner and who have a self-organizing ability. These systems, as known, are difficult to model and understand at a global level, based only on the knowledge of the dynamics of their individual elements. On the other hand, the mathematical approach leads to the description various interesting emerging collective behavior of the complex system under consideration.

N. Bellomo, Modelling Complex Living Systems – A Kinetic Theory and Stochastic Game Approach, Birkhäuser, Boston, 2008.