Publications

2014

• Coupes dans un milieu tridimensionnel érodé
  
  • Colonna Jean-François
  , 2014. Cross-sections inside an eroded tridimensional medium (Coupes dans un milieu tridimensionnel érodé)
• Limit theorems for nearly unstable Hawkes processes: Version with technical appendix
  
  • Jaisson Thibault
  • Rosenbaum Mathieu
  , 2014. Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high frequency finance. However, in practice, the statistical estimation results seem to show that very often, only "nearly unstable Hawkes processes" are able to fit the data properly. By nearly unstable, we mean that the L1 norm of their kernel is close to unity. We study in this work such processes for which the stability condition is almost violated. Our main result states that after suitable rescaling, they asymptotically behave like integrated Cox Ingersoll Ross models. Thus, modeling financial order flows as nearly unstable Hawkes processes may be a good way to reproduce both their high and low frequency stylized facts. We then extend this result to the Hawkes based price model introduced by Bacry et al. We show that under a similar criticality condition, this process converges to a Heston model. Again, we recover well known stylized facts of prices, both at the microstructure level and at the macroscopic scale.
• A semi-discrete scheme for the stochastic Landau-Lifshitz equation
  
  • Alouges François
  • de Bouard Anne
  • Hocquet Antoine
  , 2014. We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the scheme up to a subsequence.
• 10.000 chiffres aléatoires -base 10- visualisées comme une marche aléatoire bidimensionnelle 'absolue
  
  • Colonna Jean-François
  , 2014. 10.000 random digits -base 10- displayed as an 'absolute' bidimensional random walk (10.000 chiffres aléatoires -base 10- visualisées comme une marche aléatoire bidimensionnelle 'absolue')
• Tropical Cramer Determinants Revisited
  
  • Akian Marianne
  • Gaubert Stéphane
  • Guterman Alexander
  , 2014, 616, pp.45. We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness results, which extend or refine earlier results of Gondran and Minoux (1978), Plus (1990), Gaubert (1992), Richter-Gebert, Sturmfels and Theobald (2005) and Izhakian and Rowen (2009). Computational issues are also discussed; in particular, some of our proofs lead to Jacobi and Gauss-Seidel type algorithms to solve linear systems in suitably extended tropical semirings.
• Optimization of joint p-variations of Brownian semimartingales
  
  • Gobet Emmanuel
  • Landon Nicolas
  Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2014, 19 (none). We study the optimization of the joint $(p^Y,p^Z)-$variations of two continuous semimartingales $(Y,Z)$ driven by the same Itô process $X$. The $p$-variations are defined on random grids made of finitely many stopping times. We establish an explicit asymptotic lower bound for our criterion, valid in rather great generality on the grids, and we exhibit minimizing sequences of hitting time form. The asymptotics is such that the spatial increments of $X$ and the number of grid points are suitably converging to 0 and $+\infty$ respectively. (10.1214/ECP.v19-2975)
  DOI : 10.1214/ECP.v19-2975
• Two properties of two-velocity two-pressure models for two-phase flows
  
  • Coquel Frédéric
  • Hérard Jean-Marc
  • Saleh Khaled
  • Seguin Nicolas
  Communications in Mathematical Sciences, International Press, 2014, 12 (3). We study a class of models of compressible two-phase flows. This class, which includes the Baer-Nunziato model, is based on the assumption that each phase is described by its own pressure, velocity and temperature and on the use of void fractions obtained from averaging process. These models are nonconservative and non-strictly hyperbolic. We prove that the mixture entropy is non-strictly convex and that the system admits a symmetric form.
• Inversion of weighted Radon transforms via finite Fourier series weight approximations
  
  • Guillement Jean-Pol
  • Novikov Roman
  Inverse Problems in Science and Engineering, Taylor & Francis, 2014, 22 (5), pp.787–802. We consider weighted Radon transforms on the plane. We show that the Chang approximate inversion formula for these transforms admits a principal refinement as inversion via finite Fourier series weight approximations. We illustrate this inversion approach by numerical examples for the case of the attenuated Radon transforms in the framework of the single-photon emission computed tomography (SPECT).
• Hausdorff measures and dimensions in non equiregular sub-Riemannian manifolds
  
  • Ghezzi Roberta
  • Jean Frédéric
  , 2014, 5, pp.201-218. (10.1007/978-3-319-02132-4_13)
  DOI : 10.1007/978-3-319-02132-4_13
• Almost sure optimal hedging strategy
  
  • Gobet Emmanuel
  • Landon Nicolas
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2014, 24 (4), pp.1652--1690. In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error.
• Avis en réponse à la saisine du 7 novembre 2013, de Madame Marie-Christine Blandin, relative à l’article de Snell et al. (Food and Chemical Toxicology, 2012)
  
  • Bagnis Claude
  • Bar-Hen Avner
  • Barny Marie Anne M. A.
  • Bellivier Florence
  • Berny Philippe
  • Bertheau Yves
  • Boireau Pascal
  • Brévault Thierry
  • Chauvel Bruno B.
  • Coléno François
  • Couvet Denis
  • Dassa Elie
  • de Verneuil Hubert
  • Eychenne Nathalie
  • Franche Claudine
  • Guerche Philippe
  • Guillemain Joël
  • Hernandez Raquet Guillermina
  • Jestin André
  • Klonjkowski Bernard
  • Lavielle Marc
  • Le Corre Valérie V.
  • Lemaire Olivier O.
  • Lereclus Didier
  • Maximilien Rémi
  • Meurs Eliane
  • Moreau de Bellaing Cédric
  • Naffakh Nadia
  • Négre Didier
  • Noyer Jean-Louis
  • Ochatt Sergio
  • Pages Jean-Christophe
  • Parzy Daniel
  • Regnault-Roger Catherine
  • Renard Michel
  • Saindrenan Patrick
  • Simonet Pascal
  • Troadec Marie-Bérengère
  • Vaissière Bernard
  • Vilotte Jean-Luc
  , 2014. Le Haut Conseil des biotechnologies (HCB) a été saisi le 7 novembre 2013 par Madame la Sénatrice Marie-Christine Blandin, en vertu de l’article L531-3 du code de l’environnement, d’une demande d’avis relative à l’article de Snell et al., intitulé «Assessment of the health impact of GM plant diets in long-term and multigenerational animal feeding trials: A literature review», publié dans la revue Food and Chemical Toxicology (Snellet al.,2012). Pour répondre aux questions de la saisine, le Comité Scientifique (CS) du HCB a constitué un groupe de travail ad hoc. A la suite du compte-rendu de ce dernier, le CS du HCB a procédé à l’examen du projet de réponse le 25 février 2014 sous la présidence de Jean-Christophe Pagès.
• The Factorization Method for a Cavity in an Inhomogeneous Medium
  
  • Meng Shixu
  • Haddar Houssem
  • Cakoni Fioralba
  Inverse Problems, IOP Publishing, 2014, 30 (045008). We consider the inverse scattering problem for a cavity that is bounded by a penetrable anisotropic inhomogeneous medium of compact support and seek to determine the shape of the cavity from internal measurements on a curve or surface inside the cavity. We derive a factorization method which provides a rigorous characterization of the support of the cavity in terms of the range of an operator which is computable from the measured data. The support of the cavity is determined without a-priori knowledge of the constitutive parameters of the surrounding anisotropic medium provided they satisfy appropriate physical as well as mathematical assumptions imposed by our analysis. Numerical examples are given showing the viability of our method. (10.1088/0266-5611/30/4/045008)
  DOI : 10.1088/0266-5611/30/4/045008
• Stochastic Approximation Finite Element method: analytical formulas for multidimensional diffusion process
  
  • Bompis Romain
  • Gobet Emmanuel
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2014, 52 (6), pp.3140-3164. We derive an analytical weak approximation of a multidimensional diffusion process as coefficients or time are small. Our methodology combines the use of Gaussian proxys to approximate the law of the diffusion and a Finite Element interpolation of the terminal function applied to the diffusion. We call this method Stochastic Approximation Finite Element (SAFE for short) method. We provide error bounds of our global approximation depending on the diffusion process coefficients, the time horizon and the regularity of the terminal function. Then we give estimates of the computational cost of our algorithm. This shows an improved efficiency compared to Monte-Carlo methods in small and medium dimensions (up to 10), which is confirmed by numerical experiments. (10.1137/130928431)
  DOI : 10.1137/130928431
• Unsupervised Segmentation of Spectral Images with a Spatialized Gaussian Mixture Model and Model Selection
  
  • Cohen Serge X.
  • Le Pennec E.
  Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, Institut Français du Pétrole (IFP), 2014, 69 (2), pp.245-259. In this article, we describe a novel unsupervised spectral image segmentation algorithm. This algorithm extends the classical Gaussian Mixture Model-based unsupervised classification technique by incorporating a spatial flavor into the model: the spectra are modelized by a mixture of K classes, each with a Gaussian distribution, whose mixing proportions depend on the position. Using a piecewise constant structure for those mixing proportions, we are able to construct a penalized maximum likelihood procedure that estimates the optimal partition as well as all the other parameters, including the number of classes. We provide a theoretical guarantee for this estimation, even when the generating model is not within the tested set, and describe an efficient implementation. Finally, we conduct some numerical experiments of unsupervised segmentation from a real dataset. (10.2516/ogst/2014013)
  DOI : 10.2516/ogst/2014013
• Higher level molecular phylogeny of darkling beetles (Coleoptera: Tenebrionidae)
  
  • Kergoat Gael G.
  • Soldati Laurent L.
  • Clamens Anne Laure
  • Jourdan Hervé
  • Jabbour-Zahab Roula
  • Genson Guénaëlle
  • Bouchard Patrice
  • Condamine Fabien
  Systematic Entomology, Wiley-Blackwell, 2014, 39 (3), pp.486-499. Insect diversity represents about 60% of the estimated million-and-a-half described eukaryotic species worldwide, yet comprehensive and well-resolved intra-ordinal phylogenies are still lacking for the majority of insect groups. This is the case especially for the most species-rich insect group, the beetles (Coleoptera), a group for which less than 4% of the known species have had their DNA sequenced. In this study, we reconstruct the first higher level phylogeny based on DNA sequence data for the species-rich darkling beetles, a family comprising at least 20000 species. Although amongst all families of beetles Tenebrionidae ranks seventh in terms of species diversity, the lack of knowledge on the phylogeny and systematics of the group is such that its monophyly has been questioned (not to mention those of the subfamilies and tribes contained within it). We investigate the evolutionary history of Tenebrionidae using multiple phylogenetic inference methods (Bayesian inference, maximum likelihood and parsimony) to analyse a dataset consisting of eight gene fragments across 404 taxa (including 250 tenebrionid species). Although the resulting phylogenetic framework only encompasses a fraction of the known tenebrionid diversity, it provides important information on their systematics and evolution. Whatever the methods used, our results provide strong support for the monophyly of the family, and highlight the likely paraphyletic or polyphyletic nature of several important tenebrionid subfamilies and tribes, notably the polyphyletic subfamilies Diaperinae and Tenebrioninae that clearly require substantial revision in the future. Some interesting associations in several groups are also revealed by the phylogenetic analyses, such as the pairing of Aphtora Bates with Phrenapatinae. Furthermore this study advances our knowledge of the evolution of the group, providing novel insights into much-debated theories, such as the apparent relict distribution of the tribe Elenophorini. (10.1111/syen.12065)
  DOI : 10.1111/syen.12065
• Hypoelliptic Diffusion and Human Vision: A Semidiscrete New Twist
  
  • Boscain U.
  • Chertovskih R. A.
  • Gauthier Jean-Paul
  • Remizov A. O.
  SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2014, 7 (2), pp.669–695. (10.1137/130924731)
  DOI : 10.1137/130924731
• Integrative taxonomy of New Caledonian beetles: species delimitation and definition of the [i]Uloma isoceroides[/i] species group (Coleoptera, Tenebrionidae, Ulomini), with the description of four new species
  
  • Soldati Laurent
  • Kergoat Gael
  • Clamens Anne Laure
  • Jourdan Hervé
  • Jabbour-Zahab Roula
  • Condamine Fabien L.
  Zookeys, Pensoft, 2014, 415, pp.133-167. New Caledonia is an important biodiversity hotspot with much undocumented biodiversity, especially in many insect groups. Here we used an integrative approach to explore species diversity in the tenebrionid genus Uloma (Coleoptera, Tenebrionidae, Ulomini), which encompasses about 150 species, of which 22 are known from New Caledonia. To do so, we focused on a morphologically homogeneous group by comparing museum specimens with material collected during several recent field trips. We also conducted molecular phylogenetic analyses based on a concatenated matrix of four mitochondrial and three nuclear genes for 46 specimens. The morphological study allowed us to discover and describe four new species that belong to the group of interest, the Uloma isoceroides group. Molecular analyses confirmed the species boundaries of several of the previously described species and established the validity of the four new species. The phylogenetic analyses also provided additional information on the evolutionary history of the group, highlighting that a species that was thought to be unrelated to the group was in fact a member of the same evolutionary lineage. Molecular species delimitation confirmed the status of the sampled species of the group and also suggested some hidden (cryptic) biodiversity for at least two species of the group. Altogether this integrative taxonomic approach has allowed us to better define the boundaries of the Uloma isoceroides species group, which comprises at least 10 species: Uloma isoceroides (Fauvel, 1904), Uloma opacipennis (Fauvel, 1904), Uloma caledonica Kaszab, 1982, Uloma paniei Kaszab, 1982, Uloma monteithi Kaszab, 1986, Uloma robusta Kaszab, 1986, Uloma clamensae sp. n., Uloma condaminei sp. n., Uloma jourdani sp. n., and Uloma kergoati sp. n. We advocate more studies on other New Caledonian groups, as we expect that much undocumented biodiversity can be unveiled through the use of similar approaches (10.3897/zookeys.415.6623)
  DOI : 10.3897/zookeys.415.6623
• Asymptotic analysis of the transmission eigenvalue problem for a Dirichlet obstacle coated by a thin layer of non-absorbing media
  
  • Cakoni Fioralba
  • Haddar Houssem
  • Chaulet Nicolas
  IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2014, pp.36. We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first transmission eigenvalue with respect to the thickness of the thin layer. Our convergence analysis is based on a Max–Min principle and an iterative approach which involves estimates on the corresponding eigenfunctions. We provide explicit expressions for the terms in the asymptotic expansion up to order 3. (10.1093/imamat/hxu045)
  DOI : 10.1093/imamat/hxu045
• A finite elements method to solve the Bloch–Torrey equation applied to diffusion magnetic resonance imaging
  
  • Nguyen Dang Van
  • Li Jing-Rebecca
  • Grebenkov Denis S
  • Le Bihan Denis
  Journal of Computational Physics, Elsevier, 2014, pp.283–302. The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation (PDE). In addition, steady-state Laplace PDEs can be formulated to produce the homogenized diffusion tensor that describes the diffusion characteristics of the medium in the long time limit. In spatial domains that model biological tissues at the cellular level, these two types of PDEs have to be completed with permeability conditions on the cellular interfaces. To solve these PDEs, we implemented a finite elements method that allows jumps in the solution at the cell interfaces by using double nodes. Using a transformation of the Bloch-Torrey PDE we reduced oscillations in the searched-for solution and simplified the implementation of the boundary conditions. The spatial discretization was then coupled to the adaptive explict Runge-Kutta-Chebychev time-stepping method. Our proposed method is second order accurate in space and second order accurate in time. We implemented this method on the FEniCS C++ platform and show time and spatial convergence results. Finally, this method is applied to study some relevant questions in diffusion MRI. (10.1016/j.jcp.2014.01.009)
  DOI : 10.1016/j.jcp.2014.01.009
• Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling
  
  • Allaire Grégoire
  • Brizzi Robert
  • Dufrêche Jean-François
  • Mikelic Andro
  • Piatnitski Andrey
  Physica D: Nonlinear Phenomena, Elsevier, 2014, 282, pp.39-60. This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic non-ideal effects are taken into account by an approach based on the mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. We first consider equilibrium solutions in the absence of external forces. In such a case, the velocity and diffusive fluxes vanish and the equilibrium electrostatic potential is the solution of a variant of Poisson-Boltzmann equation coupled with algebraic equations. Contrary to the ideal case, this nonlinear equation has no monotone structure. However, based on invariant region estimates for Poisson-Boltzmann equation and for small characteristic value of the solute packing fraction, we prove existence of at least one solution. To our knowledge this existence result is new at this level of generality. When the motion is governed by a small static electric field and a small hydrodynamic force, we generalize O'Brien's argument to deduce a linearized model. Our second main result is the rigorous homogenization of these linearized equations and the proof that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. We eventually make numerical comparisons with the ideal case. Our numerical results show that the MSA model confirms qualitatively the conclusions obtained using the ideal model but there are quantitative differences arising that can be important at high charge or high concentrations. (10.1016/j.physd.2014.05.007)
  DOI : 10.1016/j.physd.2014.05.007
• Estimating the duration of speciation from phylogenies
  
  • Etienne R.S.
  • Morlon H.
  • Lambert A.
  Evolution - International Journal of Organic Evolution, Wiley, 2014, 68 (8), pp.2430-2440. Speciation is not instantaneous but takes time. The protracted birth-death diversification model incorporates this fact and predicts the often observed slowdown of lineage accumulation toward the present. The mathematical complexity of the protracted speciation model has barred estimation of its parameters until recently a method to compute the likelihood of phylogenetic branching times under this model was outlined (Lambert et al. ). Here, we implement this method and study using simulated phylogenies of extant species how well we can estimate the model parameters (rate of initiation of speciation, rate of extinction of incipient and good species, and rate of completion of speciation) as well as the duration of speciation, which is a combination of the aforementioned parameters. We illustrate our approach by applying it to a primate phylogeny. The simulations show that phylogenies often do not contain enough information to provide unbiased estimates of the speciation-initiation rate and the extinction rate, but the duration of speciation can be estimated without much bias. The estimate of the duration of speciation for the primate clade is consistent with literature estimates. We conclude that phylogenies combined with the protracted speciation model provide a promising way to estimate the duration of speciation. (10.1111/evo.12433)
  DOI : 10.1111/evo.12433
• Two-dimensional von Neumann--Wigner potentials with a multiple positive eigenvalue
  
  • Novikov Roman
  • Taimanov Iskander
  • Tsarev Sergey
  Functional Analysis and Its Applications, Springer Verlag, 2014, 48 (4), pp.295-297. By the Moutard transformation method we construct two-dimensional Schrodinger operators with real smooth potential decaying at infinity and with a multiple positive eigenvalue. These potentials are rational functions of spatial variables and their sines and cosines.
• Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations
  
  • Rao Zhiping
  • Siconolfi Antonio
  • Zidani Hasnaa
  Journal of Differential Equations, Elsevier, 2014, 257 (11), pp.3978--4014. We establish a comparison principle for a Hamilton-Jacobi-Bellman equation, more appropriately a system, related to an infinite horizon problem in presence of an interface. Namely a low dimensional subset of the state variable space where discontinuities in controlled dynamics and costs take place. Since corresponding Hamiltonians, at least for the subsolution part, do not enjoy any semicontinuity property, the comparison argument is rather based on a separation principle of the controlled dynamics across the interface. For this, we essentially use the notion of "-partition and minimal "-partition for intervals of definition of an integral trajectory. (10.1016/j.jde.2014.07.015)
  DOI : 10.1016/j.jde.2014.07.015
• Weighted Radon transforms and first order differential systems on the plane
  
  • Novikov Roman
  Moscow Mathematical Journal, Independent University of Moscow, 2014, 14 (4), pp.807–823. We consider weighted Radon transforms on the plane, where weights are given as finite Fourier series in angle variable. By means of additive Riemann-Hilbert problem techniques, we reduce inversion of these transforms to solving first order differential systems on $\R^2=\C$ with a decay condition at infinity. As a corollary, we obtain new injectivity and inversion results for weighted Radon transforms on the plane.
• A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging
  
  • Bonnard Bernard
  • Claeys Mathieu
  • Cots Olivier
  • Jacquemard Alain
  • Martinon Pierre
  , 2014. In this article, the contrast imaging problem by saturation in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal solution of the Maximum Principle and analyzed with the recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on shooting and continuation methods implemented in the HamPath software. The results are compared with a direct approach to the optimization problem and implemented within the Bocop toolbox. In complement lmi techniques are used to estimate a global optimum. It is completed with the analysis of the saturation problem of an ensemble of spin particles to deal with magnetic fields inhomogeneities.