Publications

2012

• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb')
  
  • Colonna Jean-François
  , 2012. Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') (Agrandissement d'un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'Mandelbulb'))
• Volume-constrained minimizers for the prescribed curvature problem in periodic media
  
  • Goldman Michael
  • Novaga Matteo
  Calculus of Variations and Partial Differential Equations, Springer Verlag, 2012. We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence after rescaling of the volume-constrained minimizers towards a suitable Wulff Shape, when the volume tends to infinity.
• Tropical bounds for the eigenvalues of structured matrices
  
  • Akian Marianne
  • Gaubert Stéphane
  • Sharify M.
  , 2012. We establish several inequalities of log-majorization type, relating the moduli of the eigenvalues of a complex matrix or matrix polynomial with the tropical eigenvalues of auxiliary matrix polynomials. This provides bounds which can be computed by combinatorial means. We consider in particular structured matrices and obtain bounds depending on the norms of block submatrices and on the pattern (graph structure) of the matrix.
• Min-max spaces and complexity reduction in min-max expansions
  
  • Gaubert Stéphane
  • Mceneaney W.M.
  Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 65 (3), pp.315--348. Idempotent methods have been found to be extremely helpful in the numerical solution of certain classes of nonlinear control problems. In those methods, one uses the fact that the value function lies in the space of semiconvex functions (in the case of maximizing controllers), and approximates this value using a truncated max-plus basis expansion. In some classes, the value function is actually convex, and then one specifically approximates with suprema (i.e., max-plus sums) of affine functions. Note that the space of convex functions is a max-plus linear space, or moduloid. In extending those concepts to game problems, one finds a different function space, and different algebra, to be appropriate. Here we consider functions which may be represented using infima (i.e., min-max sums) of max-plus affine functions. It is natural to refer to the class of functions so represented as the min-max linear space (or moduloid) of max-plus hypo-convex functions. We examine this space, the associated notion of duality and min-max basis expansions. In using these methods for solution of control problems, and now games, a critical step is complexity-reduction. In particular, one needs to find reduced-complexity expansions which approximate the function as well as possible. We obtain a solution to this complexity-reduction problem in the case of min-max expansions. (10.1007/s00245-011-9158-5)
  DOI : 10.1007/s00245-011-9158-5
• Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data
  
  • Bacry Emmanuel
  • Muzy Khalil Dayri Jean-François
  The European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2012, 85 (5), pp.1--12. We define a numerical method that provides a non-parametric estimation of the kernelshape in symmetric multivariate Hawkes processes. This method relies on second orderstatistical properties of Hawkes processes that relate the covariance matrix of theprocess to the kernel matrix. The square root of the correlation function is computedusing a minimal phase recovering method. We illustrate our method on some examples andprovide an empirical study of the estimation errors. Within this framework, we analyzehigh frequency financial price data modeled as 1D or 2D Hawkes processes. We find slowlydecaying (power-law) kernel shapes suggesting a long memory nature of self-excitationphenomena at the microstructure level of price dynamics. (10.1140/epjb/e2012-21005-8)
  DOI : 10.1140/epjb/e2012-21005-8
• Modified Lees-Edwards Boundary conditions and viscous contact for numerical simulations of particles in a shear flow
  
  • Verdon Nicolas
  • Lefebvre-Lepot Aline
  • Laure Patrice
  • Lobry Laurent
  Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, Hermès / Paris : Lavoisier, 2012, 121 (3-6 / Special Issue: French Conference on Computational Mechanics 2011: selected contributions), pp.397-406. We present a way to handle contacts between rigid particles in shear flow. The influence of such a modeling is shown by studying an example with 13 particles in 3D. Studying a concentrated suspension in 2D, we demonstrate that contact modelling as well as choice of boundary conditions influences the macroscopic properties of the suspension. (10.1080/17797179.2012.714851)
  DOI : 10.1080/17797179.2012.714851
• Solving multi-stage stochastic mixed integer linear programs by the dual dynamic programming approach
  
  • Cen Zhihao
  , 2012. We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In our previous article, we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to solve the continuous relaxation problem. In this paper, we study the multi-stage stochastic mixed integer linear program (SMILP) and show the difficulty when using dual programming type algorithm. We propose an approach based on the cutting plane method combined with the algorithm in our previous article, which gives an upper and a lower bound of the optimal value and a sub-optimal integer solution. Finally, a numerical test on a real problem in energy market is provided.
• A la recherche de l'inégalité perdue
  
  • Allaire Grégoire
  Matapli, Société de Mathématiques Appliquées et Industrielles (SMAI), 2012 (98), pp.52-64. A l'occasion du centenaire de la disparition de Henri Poincaré on s'intéresse à l'origine de la célèbre inégalité de Poincaré, si utile dans l'analyse de certaines équations aux dérivées partielles. Comme souvent en mathématiques les bons résultats ne sont pas attribués aux bonnes personnes... En fait, cette inégalité est probablement due à Neumann, Schwarz ou Scheeffer et on doit plutôt à Henri Poincaré une variante, appelée communément inégalité de Poincaré-Wirtinger. Sa démonstration originale est très intéressante car elle est constructive, au contraire d'une démonstration ultérieure par contradiction, utilisant le théorème de compacité de Rellich, que l'on trouve désormais dans la plupart des ouvrages sur les équations aux dérivées partielles. La motivation de cette inégalité est l'étude des valeurs propres et fonctions propres du Laplacien.
• Convergence of time-space adaptive algorithms for nonlinear conservation laws
  
  • Coquel F.
  • Postel M.
  • Tran Q.-H.
  IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2012, 32 (4), pp.1440 - 1483. A family of explicit adaptive algorithms is designed to solve nonlinear scalar one-dimensional conservation laws. Based on the Godunov scheme on a uniform grid, a first strategy uses the multiresolution analysis of the solution to design an adaptive grid that evolves in time according to the time-dependent local smoothness. The method is furthermore enhanced by a local time-stepping strategy. Both numerical schemes are shown to converge towards the unique entropy solution. (10.1093/imanum/drr054)
  DOI : 10.1093/imanum/drr054
• Palaeoenvironmental shifts drove the adaptive radiation of a noctuid stemborer tribe (Lepidoptera, Noctuidae, Apameini) in the Miocene
  
  • Toussaint Emmanuel F.A.
  • Condamine Fabien L.
  • Kergoat Gael
  • Capdevielle-Dulac Claire
  • Barbut Jérôme
  • Silvain Jean-François
  • Le Ru Bruno P.
  PLoS ONE, Public Library of Science, 2012, 7 (7), pp.np. Between the late Oligocene and the early Miocene, climatic changes have shattered the faunal and floral communities and drove the apparition of new ecological niches. Grassland biomes began to supplant forestlands, thus favouring a large-scale ecosystem turnover. The independent adaptive radiations of several mammal lineages through the evolution of key innovations are classic examples of these changes. However, little is known concerning the evolutionary history of other herbivorous groups in relation with this modified environment. It is especially the case in phytophagous insect communities, which have been rarely studied in this context despite their ecological importance. Here, we investigate the phylogenetic and evolutionary patterns of grass-specialist moths from the species-rich tribe Apameini (Lepidoptera, Noctuidae). The molecular dating analyses carried out over the corresponding phylogenetic framework reveal an origin around 29 million years ago for the Apameini. Ancestral state reconstructions indicate (i) a potential Palaearctic origin of the tribe Apameini associated with a major dispersal event in Afrotropics for the subtribe Sesamiina; (ii) a recent colonization from Palaearctic of the New World and Oriental regions by several independent lineages; and (iii) an ancestral association of the tribe Apameini over grasses (Poaceae). Diversification analyses indicate that diversification rates have not remained constant during the evolution of the group, as underlined by a significant shift in diversification rates during the early Miocene. Interestingly, this age estimate is congruent with the development of grasslands at this time. Rather than clade ages, variations in diversification rates among genera better explain the current differences in species diversity. Our results underpin a potential adaptive radiation of these phytophagous moths with the family Poaceae in relation with the major environmental shifts that have occurred in the Miocene. (10.1371/journal.pone.0041377)
  DOI : 10.1371/journal.pone.0041377
• Un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'MandelBulb')
  
  • Colonna Jean-François
  , 2012. A pseudo-octonionic Mandelbrot set (a 'MandelBulb') (Un ensemble de Mandelbrot dans l'ensemble des pseudo-octonions (un 'MandelBulb'))
• Transmission eigenvalues for inhomogeneous media containing obstacles
  
  • Cakoni Fioralba
  • Cossonnière Anne
  • Haddar Houssem
  Inverse Problems and Imaging, AIMS American Institute of Mathematical Sciences, 2012, 6 (3), pp.373-398. (10.3934/ipi.2012.6.373)
  DOI : 10.3934/ipi.2012.6.373
• Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal condition
  
  • Geiss Christel
  • Geiss Stefan
  • Gobet Emmanuel
  Stochastic Processes and their Applications, Elsevier, 2012, 122 (5), pp.2078--2116. We relate the $L_p$-variation, $2\le p < \infty$, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.
• A Patchy Dynamic Programming Scheme for a Class of Hamilton-Jacobi-Bellman Equations
  
  • Cacace Simone
  • Cristiani Emiliano
  • Falcone Maurizio
  • Picarelli Athena
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (5), pp.A2625-A2649. In this paper we present a new parallel algorithm for the solution of Hamilton-Jacobi- Bellman equations related to optimal control problems. The main idea is to divide the domain of computation into subdomains following the dynamics of the control problem. This results in a rather complex geometrical subdivision, but has the advantage that every subdomain is invariant with respect to the optimal controlled vector field, so that we can compute the value function in each subdomain assigning the task to a processor and avoiding the classical transmission condition on the boundaries of the subdomains. For this specific feature the subdomains are patches in the sense introduced by Ancona and Bressan in [1]. Several examples in dimension two and three illustrate the properties of the new method. (10.1137/110841576)
  DOI : 10.1137/110841576
• Marchenko-Pastur Theorem and Bercovici-Pata bijections for heavy-tailed or localized vectors
  
  • Benaych-Georges Florent
  • Cabanal-Duvillard Thierry
  ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada (Rio de Janeiro, Brasil) [2006-....], 2012, 9 (2), pp.685-715. The celebrated Marchenko-Pastur theorem gives the asymptotic spectral distribution of sums of random, independent, rank-one projections. Its main hypothesis is that these projections are more or less uniformly distributed on the first grassmannian, which implies for example that the corresponding vectors are delocalized, i.e. are essentially supported by the whole canonical basis. In this paper, we propose a way to drop this delocalization assumption and we generalize this theorem to a quite general framework, including random projections whose corresponding vectors are localized, i.e. with some components much larger than the other ones. The first of our two main examples is given by heavy tailed random vectors (as in a model introduced by Ben Arous and Guionnet or as in a model introduced by Zakharevich where the moments grow very fast as the dimension grows). Our second main example is given by vectors which are distributed as the Brownian motion on the unit sphere, with localized initial law. Our framework is in fact general enough to get new correspondences between classical infinitely divisible laws and some limit spectral distributions of random matrices, generalizing the so-called Bercovici-Pata bijection.
• Error estimates for the logarithmic barrier method in stochastic linear quadratic optimal control problems
  
  • Bonnans Joseph Frédéric
  • Silva Francisco J.
  Systems and Control Letters, Elsevier, 2012, 61 (1), pp.143-147. We consider a linear quadratic stochastic optimal control problem whith non-negativity control constraints. The latter are penalized with the classical logarithmic barrier. Using a duality argument and the stochastic minimum principle, we provide an error estimate for the solution of the penalized problem which is the natural extension of the well known estimate in the deterministic framework.
• Approximate Models for Wave Propagation Across Thin Periodic Interfaces
  
  • Delourme Bérangère
  • Haddar Houssem
  • Joly Patrick
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2012, 98 (1), pp.28-71. This work deals with the scattering of acoustic waves by a thin ring that contains regularly spaced inhomogeneities. We first explicit and study the asymptotic of the solution with respect to the period and thickness of the inhomogeneities using so-called matched asymptotic expansions. We then build simplified models replacing the thin ring with Approximate Transmission Conditions that are accurate up to third order with respect to the layer width. We pay particular attention to the study of these approximate models and the quantification of their accuracy. (10.1016/j.matpur.2012.01.003)
  DOI : 10.1016/j.matpur.2012.01.003
• Identification of small inclusions from multistatic data using the reciprocity gap concept
  
  • Haddar Houssem
  • Mdimagh Ridha
  Inverse Problems, IOP Publishing, 2012, 28 (4), pp.045011, 19. We consider the problem of identifying small inclusions (or point sources) from multistatic Cauchy data at given surface measurements associated with harmonic waves at a fixed frequency. We employ the reciprocity gap sampling method to recover the location of the inclusions and identify their equivalent dielectric properties. As opposed to the case of extended obstacles, no approximation argument is needed in the theoretical justification of the method. These aspects are numerically validated through multiple numerical experiments associated with small inclusions. (10.1088/0266-5611/28/4/045011)
  DOI : 10.1088/0266-5611/28/4/045011