Publications

2012

• 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'))
• 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'))
• 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.
• 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
• 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
• Shape Optimization of a Sodium Fast Reactor Core
  
  • Dombre Emmanuel
  • Allaire Grégoire
  • Pantz Olivier
  , 2012.
• 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
• 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
• Heat transfer in incompressible magnetic fluid
  
  • Amirat Youcef
  • Hamdache Kamel
  Journal of Mathematical Fluid Mechanics, Springer Verlag, 2012, 14, pp.217--247.
• 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.
• 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.
• 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
• 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
• 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.
• 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
• 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.
• 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.
• Representation formula for stochastic Schrödinger evolution equations and applications
  
  • de Bouard Anne
  • Fukuizumi Reika
  Nonlinearity, IOP Publishing, 2012, 25 (11), pp.2993-3022. We prove a representation formula for solutions of Schrödinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L2 or in the energy space of model equations arising in Bose-Einstein condensation or in fiber optics. Our results also give a justification of diffusion-approximation for stochastic nonlinear Schrödinger equations. (10.1088/0951-7715/25/11/2993)
  DOI : 10.1088/0951-7715/25/11/2993