Center for Applied Mathematics – Ecole Polytechnique
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Publications

Publications

CMAP Theses  are available by following this link:
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Listed below, are sorted by year, the publications appearing in the HAL open archive.

2012

  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Un ruban de Möbius fractal
    • Colonna Jean-François
    , 2012. A fractal Möbius strip (Un ruban de Möbius fractal)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Un ruban de Möbius fractal
    • Colonna Jean-François
    , 2012. A fractal Möbius strip (Un ruban de Möbius fractal)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Structure aléatoire N-dimensionnelle
    • Colonna Jean-François
    , 2012. N-dimensional random structure (Structure aléatoire N-dimensionnelle)
  • Structure fractale filamenteuse tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional filamentous fractal structure (Structure fractale filamenteuse tridimensionnelle)
  • Structure aléatoire N-dimensionnelle
    • Colonna Jean-François
    , 2012. N-dimensional random structure (Structure aléatoire N-dimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Policy iteration algorithm for zero-sum multichain stochastic games with mean payoff and perfect information
    • Akian Marianne
    • Cochet-Terrasson Jean
    • Detournay Sylvie
    • Gaubert Stéphane
    , 2012. We consider zero-sum stochastic games with finite state and action spaces, perfect information, mean payoff criteria, without any irreducibility assumption on the Markov chains associated to strategies (multichain games). The value of such a game can be characterized by a system of nonlinear equations, involving the mean payoff vector and an auxiliary vector (relative value or bias). We develop here a policy iteration algorithm for zero-sum stochastic games with mean payoff, following an idea of two of the authors (Cochet-Terrasson and Gaubert, C. R. Math. Acad. Sci. Paris, 2006). The algorithm relies on a notion of nonlinear spectral projection (Akian and Gaubert, Nonlinear Analysis TMA, 2003), which is analogous to the notion of reduction of super-harmonic functions in linear potential theory. To avoid cycling, at each degenerate iteration (in which the mean payoff vector is not improved), the new relative value is obtained by reducing the earlier one. We show that the sequence of values and relative values satisfies a lexicographical monotonicity property, which implies that the algorithm does terminate. We illustrate the algorithm by a mean-payoff version of Richman games (stochastic tug-of-war or discrete infinity Laplacian type equation), in which degenerate iterations are frequent. We report numerical experiments on large scale instances, arising from the latter games, as well as from monotone discretizations of a mean-payoff pursuit-evasion deterministic differential game.
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure (Structure fractale tridimensionnelle)
  • Structure fractale tridimensionnelle -la 'mousse' de l'espace-temps ?
    • Colonna Jean-François
    , 2012. Tridimensional fractal structure -the space-time foam ?- (Structure fractale tridimensionnelle -la 'mousse' de l'espace-temps ?-)
  • Fixed points of discrete convex monotone dynamical systems
    • Akian Marianne
    , 2012.
  • Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration
    • Bouin Emeric
    • Calvez Vincent
    • Meunier Nicolas
    • Mirrahimi Sepideh
    • Perthame Benoît
    • Raoul Gael
    • Voituriez Raphael
    Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2012, 350 (15-16), pp.761–766. Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the motility is unbounded we show that the position of the front scales as $t^{3/2}$. When the mutation rate is low we show that the canonical equation for the dynamics of the fittest trait should be stated as a PDE in our context. It turns out to be a type of Burgers equation with source term. (10.1016/j.crma.2012.09.010)
    DOI : 10.1016/j.crma.2012.09.010
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