Publications

2011

• Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes
  
  • Colonna Jean-François
  , 2011. Rotation about the Y (vertical) axis of an intertwining that can also be viewed as a set of 4x3 stereograms (Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes)
• Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes
  
  • Colonna Jean-François
  , 2011. Rotation about the Y (vertical) axis of an intertwining that can also be viewed as a set of 4x3 stereograms (Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes)
• Modeling and imaging of attenuation in biological media.
  
  • Wahab Abdul
  , 2011. The thesis is devoted to study inverse problems related to acoustic and elastic source localization in attenuating media from boundary measurements and their applications in biomedical imaging. We present efficient and stable algorithms to compensate for the effects of attenuation on image resolution. We develop Radon transform based algorithms to recover initial pressure distribution in attenuating media with and without imposed boundary conditions. We apply stationary phase theorem on an ill-conditioned attenuation operator to rectify attenuation effect and use TV-Tikhonov regularization methods to handle partial measurement problems. We revisit time reversal methods for loss-less media and extend them to attenuating media. As the attenuated waves are not time reversible, we use the strategy of back-propagating the regular approximations of adjoint attenuated waves to reconstruct sources stably with first order attenuation correction. For acoustic media, we present an alternative strategy based on data pre-processing for higher order corrections. As the data in elastic media consists of coupled shear and pressure waves, we propose an original approach based on weighted Helmholtz decomposition. Further, we introduce efficient weighted imaging algorithms for locating acoustic noise sources by cross correlation techniques and using regularized back-propagators for attenuation correction. We also localize spatially correlated noise sources and estimate correlation matrix between them. In order to extend elastic anomaly detection algorithms to visco-elastic media, we derive a closed form expression for an isotropic visco-elastic Green function. Then, we propose an attenuation correction technique for a quasi-incompressible medium and prove that one can access, approximately, the ideal (inviscid) Green function from the visco-elastic one by inverting an ordinary diff erential operator. Finally, we provide some anisotropic visco-elastic Green functions, with an aim to extend our results to anisotropic media.
• A rigorous model study of the adaptative dynamics of Mendelian diploids
  
  • Collet Pierre
  • Méléard Sylvie
  • Metz J.A.J.
  , 2011. Adaptive dynamics so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like dynamics and single locus genetics (as in Kimura's 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale (the 'long' time scale of the literature on the genetical foundations of ESS theory) as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature). Essential technical ingredients are a rigorous estimate for the probability of invasion in a dynamic diploid population, a rigorous, geometric singular perturbation theory based, invasion implies substitution theorem, and the use of the Skorohod $M_1$ topology to arrive at a functional convergence result. In the small mutational steps limit this process in turn gives rise to a differential equation in allele or in phenotype space of a type referred to in the adaptive dynamics literature as 'canonical equation'.
• La montagne de la table
  
  • Colonna Jean-François
  , 2011. Table mountain (La montagne de la table)
• Entrelacs
  
  • Colonna Jean-François
  , 2011. Intertwining (Entrelacs)
• Entrelacs
  
  • Colonna Jean-François
  , 2011. Intertwining (Entrelacs)
• LNG portfolio optimization, approach by stochastic programming techniques
  
  • Cen Zhihao
  , 2011. The work presented in this Ph.D dissertation is motivated by the problem of management of a fleet of cargos transporting lique ed natural gas (LNG) initially proposed by Total. The holder of the portfolio has to meet its commitments towards its counterparts while trying to generate pro ts through arbitrating different commodities market. Thus, the management of portfolio can be modeled as a stochastic, dynamic and integer optimization problem. This Ph.D dissertation is organised as follows: 1 We introduce a numerical method for solving continuous relaxation problem. We propose an algorithm based on the combination of the vectorial quantization method as discretization method and the dual dynamic programming approach. We show the convergence of numerical schema and give the error analysis on the discretization by quantization. Some numerical tests on real energy market problem are performed. 2 We also study the risk averse optimization by using conditional value at risk (CVaR) as criterion. We show that the algorithm proposed is also adapted to such formulation. Furthermore, we propose the technique of changes in probability measure in stochastic programming in order to improve rare scenario simulation. Same numerical test as in risk neutral problem is performed in order to make comparison. 3 We study the sensitivity of the portfolio with respect to several parameters in the market price model. We proposed a numerical method to compute sensitivity value based on Danskin's theorem. The convergence of sensitivity value of discretized problem to the one of original problem is proved. Comparison between result obtained by our algorithm and other classical methods are provided. 4 We study the stochastic integer programming problem. The integrality cutting plane method is applied to approximate the integer problem. We show that it is impossible to converge to the integer solution because of the non convexity and discontinuity of the Bellman value function. We apply an heuristic method and propose a small improvement. Some numerical tests are also provided.
• Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes
  
  • Colonna Jean-François
  , 2011. Rotation about the Y (vertical) axis of an intertwining that can also be viewed as a set of 4x3 stereograms (Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes)
• Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes
  
  • Colonna Jean-François
  , 2011. Rotation about the Y (vertical) axis of an intertwining that can also be viewed as a set of 4x3 stereograms (Rotation autour de l'axe Y (vertical) d'un entrelacs qui peut être vue comme un ensemble de 4x3 stéréogrammes)
• Un ensemble de Julia brumeux dans l'ensemble des pseudo-octonions (comme un 'MandelBulb' : un 'JuliaBulb') calculé pour A=(0,1,0,0,0,0,0,0) et avec un exposant variable localement entre 2 et 12
  
  • Colonna Jean-François
  , 2011. A foggy pseudo-octonionic Julia set ('MandelBulb' like : a 'JuliaBulb') computed with A=(0,1,0,0,0,0,0,0) and with a locally variable exponent between 2 and 12 (Un ensemble de Julia brumeux dans l'ensemble des pseudo-octonions (comme un 'MandelBulb' : un 'JuliaBulb') calculé pour A=(0,1,0,0,0,0,0,0) et avec un exposant variable localement entre 2 et 12)
• La dynamique d'un espace fractal
  
  • Colonna Jean-François
  , 2011. Fractal space dynamics (La dynamique d'un espace fractal)
• Global optimization of pipe networks by the interval analysis approach: the Belgium network case
  
  • Bonnans Joseph Frederic
  • Spiers Grégoire
  • Vie Jean-Léopold
  , 2011, pp.13. We show that global optimization techniques, based on interval analysis and constraint propagation, succeed in solving the classical problem of optimization of the Belgium gas network.
• Optimal multiple stopping problem and financial applications
  
  • Ben Latifa Imene
  • Bonnans Joseph Frederic
  • Mnif Mohamed
  , 2011, pp.30. In their paper [2], Carmona and Touzi have studied an optimal multiple stopping time problem in a market where the price process is continuous. In this paper, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of swing options to the context of jump diffusion processes. Then we relate our problem to a sequence of ordinary stopping time problems. We characterize the value function of each ordinary stopping time problem as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman Variational Inequality.
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme (4xO+1)/(1xO-1) dans l'ensemble des pseudo-octonions
  
  • Colonna Jean-François
  , 2011. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the pseudo-octonionic space (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme (4xO+1)/(1xO-1) dans l'ensemble des pseudo-octonions)
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme (4xO+1)/(1xO-1) dans l'ensemble des pseudo-octonions
  
  • Colonna Jean-François
  , 2011. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the pseudo-octonionic space (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme (4xO+1)/(1xO-1) dans l'ensemble des pseudo-octonions)
• Complementary proofs to "Approximation of discrete BSDE using least-squares regression
  
  • Gobet Emmanuel
  • Turkedjiev Plamen
  , 2011. This short note gives complementary proofs to our work "Approximation of discrete BSDE using least-squares regression" (Gobet-Turkedjiev 2011), of which we follow the notations and assumptions.
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme OxO dans l'ensemble des pseudo-octonions
  
  • Colonna Jean-François
  , 2011. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a OxO conformal transformation in the pseudo-octonionic space (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme OxO dans l'ensemble des pseudo-octonions)
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme OxO dans l'ensemble des pseudo-octonions
  
  • Colonna Jean-François
  , 2011. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a OxO conformal transformation in the pseudo-octonionic space (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb') avec une transformation conforme OxO dans l'ensemble des pseudo-octonions)
• La montagne de la table
  
  • Colonna Jean-François
  , 2011. Table mountain (La montagne de la table)
• La montagne de la table
  
  • Colonna Jean-François
  , 2011. Table mountain (La montagne de la table)
• Numerical analysis of the Factorization Method for Electrical Impedance Tomography in inhomogeneous medium
  
  • Haddar Houssem
  • Migliorati Giovanni
  , 2011, pp.34. The retrieval of information on the coefficient in Electrical Impedance Tomography is a severely ill-posed problem, and often leads to inaccurate solutions. It is well known that numerical methods provide only low-resolution reconstructions. The aim of this work is to analyze the Factorization Method in the case of inhomogeneous background. We propose a numerical scheme to solve the dipole-like Neumann boundary-value problem, when the background coefficient is inhomogeneous. Several numerical tests show that the method is capable of recovering the location and the shape of the inclusions, in many cases where the diffusion coefficient is nonlinearly space-dependent. In addition, we test the numerical scheme after adding artificial noise.
• Infinite-dimensional idempotent analysis: the role of continuous posets
  
  • Poncet Paul
  , 2011. Idempotent analysis involves the study of infinite-dimensional linear spaces in which the usual addition is replaced by the maximum operation. We prove a series of results in this framework and stress the crucial contribution of domain and continuous lattice theory. Two themes are considered: integration and convexity. In idempotent integration, the properties of domain-valued maxitive measures such as regularity are surveyed and completed in a topological framework; we provide a converse statement to the idempotent Radon-Nikodym theorem; using the Z generalization of domain theory we gather and surpass existing results on the representation of continuous linear forms on an idempotent module. In tropical convexity, we obtain a Krein-Milman type theorem in several ordered algebraic structures, including locally-convex topological semilattices and idempotent modules; in the latter structure we prove a Choquet integral representation theorem: every point of a compact convex subset K can be represented by a possibility measure supported by the extreme points of K. The hope for a unification of classical and idempotent analysis is considered in a final step. The notion of inverse semigroup, which fairly generalizes both groups and semilattices, may be the right candidate for this; in this perspective we examine "mirror" properties between inverse semigroups and semilattices, among which continuity. The general conclusion broadens this point of view.
• New approaches of source-sink metapopulations decoupling the roles of demography and dispersal
  
  • Bansaye Vincent
  • Lambert Amaury
  , 2011. Source-sink systems are metapopulations of habitat patches with different, and possibly temporally varying, habitat qualities, which are commonly used in ecology to study the fate of spatially extended natural populations. We propose new techniques that allow to disentangle the respective contributions of demography and dispersal to the dynamics and fate of a single species in a source-sink metapopulation. Our approach is valid for a general class of stochastic, individual-based, stepping-stone models, with density-independent demography and dispersal, provided the metapopulation is finite or else enjoys some transitivity property. We provide 1) a simple criterion of persistence, by studying the motion of a single random disperser until it returns to its initial position; 2) a joint characterization of the long-term growth rate and of the asymptotic occupancy frequencies of the ancestral lineage of a random survivor, by using large deviations theory. Both techniques yield formulae decoupling demography and dispersal, and can be adapted to the case of periodic or random environments, where habitat qualities are autocorrelated in space and possibly in time. In this last case, we display examples of coupled time-averaged sinks allowing survival, as was previously known in the absence of demographic stochasticity for fully mixing \cite{JY98} and even partially mixing \cite{ERS12, Sch10} metapopulations.
• Structure en quarks et gluons du nucléon
  
  • Colonna Jean-François
  , 2011. Quark and gluon structure of the nucleon (Structure en quarks et gluons du nucléon)