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'))
• 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'))
• 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'))
• Biogeographic and diversification patterns of Neotropical Troidini butterflies (Papilionidae) support a museum model of diversity dynamics for Amazonia
  
  • Condamine Fabien F.
  • Silva-Brandão Karina L.
  • Kergoat Gael G.
  • Sperling Felix A.H.
  BMC Evolutionary Biology, BioMed Central, 2012, 12, pp.17 p.. BACKGROUND: The temporal and geographical diversification of Neotropical insects remains poorly understood because of the complex changes in geological and climatic conditions that occurred during the Cenozoic. To better understand extant patterns in Neotropical biodiversity, we investigated the evolutionary history of three Neotropical swallowtail Troidini genera (Papilionidae). First, DNA-based species delimitation analyses were conducted to assess species boundaries within Neotropical Troidini using an enlarged fragment of the standard barcode gene. Molecularly delineated species were then used to infer a time-calibrated species-level phylogeny based on a three-gene dataset and Bayesian dating analyses. The corresponding chronogram was used to explore their temporal and geographical diversification through distinct likelihood-based methods. RESULTS: The phylogeny for Neotropical Troidini was well resolved and strongly supported. Molecular dating and biogeographic analyses indicate that the extant lineages of Neotropical Troidini have a late Eocene (33-42 Ma) origin in North America. Two independent lineages (Battus and Euryades + Parides) reached South America via the GAARlandia temporary connection, and later became extinct in North America. They only began substantive diversification during the early Miocene in Amazonia. Macroevolutionary analysis supports the "museum model" of diversification, rather than Pleistocene refugia, as the best explanation for the diversification of these lineages. CONCLUSIONS: This study demonstrates that: (i) current Neotropical biodiversity may have originated ex situ; (ii) the GAARlandia bridge was important in facilitating invasions of South America; (iii) colonization of Amazonia initiated the crown diversification of these swallowtails; and (iv) Amazonia is not only a species-rich region but also acted as a sanctuary for the dynamics of this diversity. In particular, Amazonia probably allowed the persistence of old lineages and contributed to the steady accumulation of diversity over time with constant net diversification rates, a result that contrasts with previous studies on other South American butterflies (10.1186/1471-2148-12-82)
  DOI : 10.1186/1471-2148-12-82
• Preliminary report on the darkling beetles (Coleoptera, Tenebrionidae) collected during the SANTO 2006 expedition to Vanuatu and description of a new species from the genus [i]Uloma [/i]Dejean, 1821
  
  • Soldati Laurent
  • Kergoat Gael
  • Condamine Fabien L.
  Zoosystema, Museum Nationale d'Histoire Naturelle Paris, 2012, 34 (2), pp.305-317. An annotated list of Tenebrionidae Latreille, 1802 (Coleoptera Linnaeus, 1758) collected by one of the authors (LS) during the SANTO 2006 expedition is given. It concerns the period covered by the section “Fallow & Aliens” during October 2006. These faunistic data are completed with the description of a new species: [i]Uloma vanuatensis[/i] L. Soldati n. sp. Furthermore, biogeographic hypotheses on the colonisation of the Vanuatu archipelago are presented to explain the origin of the tenebrionid fauna. (10.5252/z2012n2a8)
  DOI : 10.5252/z2012n2a8
• Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges
  
  • Barrieu Pauline
  • Bensusan Harry
  • El Karoui Nicole
  • Hillairet Caroline
  • Loisel Stéphane
  • Ravanelli Claudia
  • Salhi Yahia
  Scandinavian Actuarial Journal, Taylor & Francis (Routledge), 2012, 2012 (3), pp.203-231. This article investigates the latest developments in longevity risk modelling, and explores the key risk management challenges for both the financial and insurance industries. The article discusses key definitions that are crucial for the enhancement of the way longevity risk is understood; providing a global view of the practical issues for longevity-linked insurance and pension products that have evolved concurrently with the steady increase in life expectancy since 1960s. In addition, the article frames the recent and forthcoming developments that are expected to action industry-wide changes as more effective regulation, designed to better assess and efficiently manage inherited risks, is adopted. Simultaneously, the evolution of longevity is intensifying the need for capital markets to be used to manage and transfer the risk through what are known as Insurance-Linked Securities (ILS). Thus, the article will examine the emerging scenarios, and will finally highlight some important potential developments for longevity risk management from a financial perspective with reference to the most relevant modelling and pricing practices in the banking industry.
• Homogenization and concentration for a diffusion equation with large convection in a bounded domain
  
  • Allaire Grégoire
  • Pankratova I.
  • Piatnitski Andrey
  Journal of Functional Analysis, Elsevier, 2012, 262 (1), pp.300-330. We consider the homogenization of a non-stationary convection–diffusion equation posed in a bounded domain with periodically oscillating coefficients and homogeneous Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic profile of the solution and determine its rate of decay. In particular, it allows us to characterize the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to the domain boundary and is also the point of concentration. Due to the competition between convection and diffusion, the position of the “hot spot” is not always intuitive as exemplified in some numerical tests. (10.1016/j.jfa.2011.09.014)
  DOI : 10.1016/j.jfa.2011.09.014
• Homogenization of a One-Dimensional Spectral Problem for a Singularly Perturbed Elliptic Operator with Neumann Boundary Conditions
  
  • Allaire Grégoire
  • Capdeboscq Y.
  • Puel Marjolaine
  Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2012, 17, pp.1-31. We study the asymptotic behavior of the first eigenvalue and eigenfunctionof a one-dimensional periodic elliptic operator with Neumann boundaryconditions. The second order elliptic equation is not self-adjointand is singularly perturbed since, denoting by $\epsilon$ the period,each derivative is scaled by an $\epsilon$ factor.The main difficulty is that the domain size is not an integer multipleof the period. More precisely, for a domain of size $1$ and a givenfractional part $0\leq\delta<1$, we consider a sequence of periods$\epsilon_n=1/(n+\delta)$ with $n\in \mathbb{N}$. In other words, the domaincontains $n$ entire periodic cells and a fraction $\delta$ of a cellcut by the domain boundary. According to the value of the fractionalpart $\delta$, different asymptotic behaviors are possible: in somecases an homogenized limit is obtained, while in other cases thefirst eigenfunction is exponentially localized at one of theextreme points of the domain. (10.3934/dcdsb.2012.17.1)
  DOI : 10.3934/dcdsb.2012.17.1
• Approximation and relaxation of perimeter in the Wiener space
  
  • Goldman Michael
  • Novaga Matteo
  Annales de l'Institut Henri Poincaré, Presses universitaires de France — PUF, 2012. We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L^2-topology. We also show that the rescaled Allen-Cahn functionals approximate this relaxed functional in the sense of Gamma-convergence.
• Heat transfer in incompressible magnetic fluid
  
  • Amirat Youcef
  • Hamdache Kamel
  Journal of Mathematical Fluid Mechanics, Springer Verlag, 2012, 14, pp.217--247.
• Multigrid methods for two-player zero-sum stochastic games
  
  • Akian Marianne
  • Detournay Sylvie
  Numerical Linear Algebra with Applications, Wiley, 2012, 19 (2), pp.313--342. We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space zero-sum two player game or to the discretization of an Isaacs equation. We present numerical tests on discretizations of Isaacs equations or variational inequalities. We also present a full multi-level policy iteration, similar to FMG, which allows to improve substantially the computation time for solving some variational inequalities. (10.1002/nla.1815)
  DOI : 10.1002/nla.1815
• Optimized analytic reconstruction for SPECT
  
  • Guillement Jean-Pol
  • Novikov Roman
  Journal of Inverse and Ill-posed Problems, De Gruyter, 2012, 20 (4), pp.489–500. We develop optimized analytic reconstruction for the single-photon emission computed tomography (SPECT). This reconstruction is based on : (1) Novikov's exact and Chang's approximate inversion formulas for the attenuated ray transform, (2) filtering techniques, and (3) Morozov type discrepancy principle. Our numerical examples include comparisons with the standard least square and expectation maximization iterative SPECT reconstructions.
• Shape Optimization of a Sodium Fast Reactor Core
  
  • Dombre Emmanuel
  • Allaire Grégoire
  • Pantz Olivier
  , 2012.
• Large graph limit for an SIR process in random network with heterogeneous connectivity
  
  • Decreusefond Laurent
  • Dhersin Jean-Stephane
  • Moyal Pascal
  • Tran Viet Chi
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2012, 22 (2), pp.541-575. We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz (2008). (10.1214/11-AAP773)
  DOI : 10.1214/11-AAP773
• 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.
• 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.
• 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.
• 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.
• 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
• 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'))