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')
• 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.
• 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
• 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.
• 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.
• 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).
• 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
• Global weak solutions to the equations of thermal convection in micropolar fluids subjected to Hall current
  
  • Amirat Youcef
  • Hamdache Kamel
  Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2014, 102, pp.186-207. In this paper we study the equations describing the thermal convection in an incompressible viscous electrically conducting micropolar fluid in the presence of a magnetic field, taking into account the effect of Hall current. The system is a combination of the generalized magnetic induction, the equations of micropolar fluids and the temperature equation. We prove long-time and large-data existence of a weak solution with decreasing energy to the system posed in a bounded domain of R3 and equipped with initial and boundary conditions.
• Hawkes model for price and trades high-frequency dynamics
  
  • Bacry Emmanuel
  • Muzy Jean-François
  Quantitative Finance, Taylor & Francis (Routledge), 2014, 14 (7), pp.1147-1166. no abstract (10.1080/14697688.2014.897000)
  DOI : 10.1080/14697688.2014.897000
• Material interface effects on the topology optimization of multi-phase structures using a level set method
  
  • Vermaak Natasha
  • Michailidis Georgios
  • Parry Guillaume
  • Estevez Raphael
  • Allaire Grégoire
  • Brechet Yves
  Structural and Multidisciplinary Optimization, Springer Verlag, 2014, 50 (4), pp.623-644. A level set method is used as a framework to study the effects of including material interface properties in the optimization of multi-phase elastic and thermoelastic structures. In contrast to previous approaches, the material properties do not have a discontinuous change across the interface that is often represented by a sharp geometric boundary between material regions. Instead, finite material interfaces with monotonic and non-monotonic property variations over a physically motivated interface zone are investigated. Numerical results are provided for several 2D problems including compliance and displacement minimization of structures composed of two and three materials. The results highlight the design performance changes attributed to the presence of the continuously graded material interface properties. (10.1007/s00158-014-1074-2)
  DOI : 10.1007/s00158-014-1074-2
• Strong solutions to the equations of electrically conductive magnetic fluids
  
  • Amirat Youcef
  • Hamdache Kamel
  Journal of Mathematical Analysis and Applications, Elsevier, 2014, 421 (1), pp.75-104. We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier-Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution. (10.1016/j.jmaa.2014.06.073)
  DOI : 10.1016/j.jmaa.2014.06.073
• Second-order necessary conditions in Pontryagin form for optimal control problems
  
  • Bonnans J. Frederic
  • Dupuis Xavier
  • Pfeiffer Laurent
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (6), pp.3887-3916. In this report, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima. (10.1137/130923452)
  DOI : 10.1137/130923452
• Efficiency of the Wang-Landau Algorithm: A Simple Test Case
  
  • Fort Gersende
  • Jourdain Benjamin
  • Kuhn Estelle
  • Lelièvre Tony
  • Stoltz Gabriel
  Applied Mathematics Research eXpress, Oxford University Press (OUP): Policy H - Oxford Open Option A, 2014, 2014 (2), pp.275-311. We analyze the convergence properties of the Wang-Landau algorithm. This sampling method belongs to the general class of adaptive importance sampling strategies which use the free energy along a chosen reaction coordinate as a bias. Such algorithms are very helpful to enhance the sampling properties of Markov Chain Monte Carlo algorithms, when the dynamics is metastable. We prove the convergence of the Wang-Landau algorithm and an associated central limit theorem. (10.1093/amrx/abu003)
  DOI : 10.1093/amrx/abu003
• Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints
  
  • Granato Giovanni
  • Zidani Hasnaa
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (1), pp.606--628. This study aims at characterizing a reachable set of a hybrid dynamical system with a lag constraint in the switch control. The setting does not consider any controllability assumptions and uses a level-set approach. The approach consists in the introduction of on adequate hybrid optimal control problem with lag constraints on the switch control whose value function allows a characterization of the reachable set. The value function is in turn characterized by a system of quasi-variational inequalities (SQVI). We prove a comparison principle for the SQVI which shows uniqueness of its solution. A class of numerical finite differences schemes for solving the system of inequalities is proposed and the convergence of the numerical solution towards the value function is studied using the comparison principle. Some numerical examples illustrating the method are presented. Our study is motivated by an industrial application, namely, that of range extender electric vehicles. This class of electric vehicles uses an additional module -- the range extender -- as an extra source of energy in addition to its main source -- a high voltage battery. The reachability study of this system is used to establish the maximum range of a simple vehicle model. (10.1137/120874205)
  DOI : 10.1137/120874205
• 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
• 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
• 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
• 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
• 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
• 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