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'))
• 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
• Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues
  
  • Boscain Ugo
  • Chittaro Francesca
  • Mason Paolo
  • Sigalotti Mario
  IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2012, 57 (8), pp.1970-1983. In this paper, we present a constructive method to control the bilinear Schrödinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if the latter are conical (as it happens generically). In this framework, we are able to spread on several levels connected by conical intersections a state initially concentrated in a single energy level. We provide sharp estimates on the dependence of the error with respect to the controllability time. Moreover, we identify some special curves in the space of controls that improve the precision of the adiabatic approximation, when passing through conical intersections, with respect to classical adiabatic theory. (10.1109/TAC.2012.2195862)
  DOI : 10.1109/TAC.2012.2195862
• A general stochastic model for sporophytic self-incompatibility
  
  • Billiard Sylvain
  • Tran Viet Chi
  Journal of Mathematical Biology, Springer, 2012, 64 (1-2), pp.163-210. Disentangling the processes leading populations to extinction is a major topic in ecology and conservation biology. The difficulty to find a mate in many species is one of these processes. Here, we investigate the impact of self-incompatibility in flowering plants, where several inter-compatible classes of individuals exist but individuals of the same class cannot mate. We model pollen limitation through different relationships between mate availability and fertilization success. After deriving a general stochastic model, we focus on the simple case of distylous plant species where only two classes of individuals exist. We first study the dynamics of such a species in a large population limit and then, we look for an approximation of the extinction probability in small populations. This leads us to consider inhomogeneous random walks on the positive quadrant. We compare the dynamics of distylous species to self-fertile species with and without inbreeding depression, to obtain the conditions under which self-incompatible species could be less sensitive to extinction while they can suffer more pollen limitation. (10.1007/s00285-011-0410-z)
  DOI : 10.1007/s00285-011-0410-z
• Analysis of exposure–response of CI-945 in patients with epilepsy: application of novel mixed hidden Markov modeling methodology
  
  • Delattre Maud
  • Savic Radojka M.
  • Miller Raymond
  • Karlsson Mats O.
  • Lavielle Marc
  Journal of Pharmacokinetics and Pharmacodynamics, Springer Verlag, 2012, 39 (3), pp.263 - 271. We propose to describe exposure–response relationship of an antiepileptic agent, using mixed hidden Markov modeling methodology, to reveal additional insights in the mode of the drug action which the novel approach offers. Daily seizure frequency data from six clinical studies including patients who received gabapentin were available for the analysis. In the model, seizure frequencies are governed by underlying unobserved disease activity states. Individual neighbouring states are dependent, like in reality and they exhibit their own dynamics with patients transitioning between low and high disease states, according to a set of transition probabilities. Our methodology enables estimation of unobserved disease dynamics and daily seizure frequencies in all disease states. Additional modes of drug action are achievable: gabapentin may influence both daily seizure frequencies and disease state dynamics. Gabapentin significantly reduced seizure frequencies in both disease activity states; however it did not significatively affect disease dynamics. Mixed hidden Markov modeling is able to mimic dynamics of seizure frequencies very well. It offers novel insights into understanding disease dynamics in epilepsy and gabapentin mode of action. (10.1007/s10928-012-9248-2)
  DOI : 10.1007/s10928-012-9248-2
• On Simultaneous Identification of the Shape and Generalized Impedance Boundary Condition in Obstacle Scattering
  
  • Bourgeois Laurent
  • Chaulet Nicolas
  • Haddar Houssem
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (3), pp.A1824-A1848. We consider the inverse obstacle scattering problem of determining both the shape and the "equiva- lent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface differential operator (refer to as generalized impedance boundary condition) as opposed to a scalar function. The generalized impedance boundary condition can be seen as a more accurate model for effective impedances and is widely used in the scattering problem for thin coatings. Our approach is based on a least square optimization technique. A major part of our analysis is to characterize the derivative of the cost function with respect to the boundary and this complex surface impedance configuration. In particular, we provide an extension of the notion of shape derivative to the case where the involved impedance parameters do not need to be surface traces of given functions, which leads (in general) to a non-vanishing tangential boundary perturbation. The efficiency of considering this type of derivative is illustrated by several 2D numerical experiments based on a (classical) steepest descent method. The feasibility of retrieving both the shape and the impedance parameters is also discussed in our numerical experiments. (10.1137/110850347)
  DOI : 10.1137/110850347
• Asymptotic and non asymptotic approximations for option valuation
  
  • Bompis Romain
  • Gobet Emmanuel
  , 2012, pp.80. We give a broad overview of approximation methods to derive analytical formulas for accurate and quick evaluation of option prices. We compare different approaches, from the theoretical point of view regarding the tools they require, and also from the numerical point of view regarding their performances. In the case of local volatility models with general time-dependency, we derive new formulas using the local volatility function at the mid-point between strike and spot: in general, our approximations outperform previous ones by Hagan and Henry-Labordère. We also provide approximations of the option delta.
• Noise Source Localization in an Attenuating Medium
  
  • Bretin Elie
  • Ammari Habib
  • Garnier Josselin
  • Wahab Abdul
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2012, 72 (1), pp.317 - 336. (10.1137/11083191X)
  DOI : 10.1137/11083191X