Publications

2008

• Entrelacs base sur la géométrie de la surface de Boy
  
  • Colonna Jean-François
  , 2008. Intertwining based on the geometry of the Boy surface (Entrelacs base sur la géométrie de la surface de Boy)
• Entrelacs base sur la géométrie de la surface de Boy
  
  • Colonna Jean-François
  , 2008. Intertwining based on the geometry of the Boy surface (Entrelacs base sur la géométrie de la surface de Boy)
• Entrelacs base sur la géométrie de la sphère
  
  • Colonna Jean-François
  , 2008. Intertwining based on the geometry of the sphere (Entrelacs base sur la géométrie de la sphère)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Structure paradoxale
  
  • Colonna Jean-François
  , 2008. Paradoxal structure (Structure paradoxale)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2008. Intertwining (Entrelacs)
• On the shooting algorithm for optimal control problems with state constraints
  
  • Hermant Audrey
  , 2008. This thesis deals with (deterministic) optimal control problems of an ordinary differential equation subject to one or several state constraints, of arbitrary orders, in the case when the strengthened Legendre-Clebsch condition is satisfied. Pontryagin's minimum principle provides us with a well-known first-order optimality condition. In this thesis we first obtain a second-order sufficient optimality condition which is the weakest possible, i.e. which is as close as possible to the second-order necessary condition and characterizes quadratic growth. This condition allows us to obtain a characterization of the well-posedness of the shooting algorithm in presence of state constraints. Then stability and sensitivity analysis of solutions under perturbation of the data is investigated. We obtain for the first time stability results for state constraints of order greater than or equal to two that make no assumption on the structure of the trajectory. Moreover, results on structural stability of Pontryagin's extremals are given. Finally, the above results on the well-posedness of the shooting algorithm and on stability analysis allow us to design a new continuation method, for state constraints of first and second-order, whose novelty is to automatically detect the structure of the trajectory and initialize the associated shooting parameters.
• Orthogonal Bandlet Bases for Geometric Images Approximation
  
  • Mallat Stéphane
  • Peyré Gabriel
  Communications on Pure and Applied Mathematics, Wiley, 2008, 61 (9), pp.1173-1212. This paper introduces orthogonal bandelet bases to approximate images having some geometrical regularity. These bandelet bases are computed by applying parametrized Alpert transform operators over an orthogonal wavelet basis. These bandeletization operators depend upon a multiscale geometric flow that is adapted to the image at each wavelet scale. This bandelet construction has a hierarchical structure over wavelet coefficients taking advantage of existing regularity among these coefficients. It is proved that C˛ -images having singularities along Calpha-curves are approximated in a best orthogonal bandelet basis with an optimal asymptotic error decay. Fast algorithms and compression applications are described.