Publications

2014

• 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.
• Coupes dans un milieu tridimensionnel érodé
  
  • Colonna Jean-François
  , 2014. Cross-sections inside an eroded tridimensional medium (Coupes dans un milieu tridimensionnel érodé)
• 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')
• Variational Curvature Flows
  
  • Chambolle Antonin
  • Morini Massimiliano
  • Ponsiglione Marcello
  , 2014. Variational Curvature Flows
• Policy iteration for stochastic zero-sum games
  
  • Akian Marianne
  , 2014. Recent results of Ye and Hansen, Miltersen and Zwick show that policy iteration for one or two player (perfect information) zero-sum stochastic games, restricted to instances with a fixed discount rate, is strongly polynomial. We show that policy iteration for mean-payoff zero-sum stochastic games is also strongly polynomial when restricted to instances with bounded first mean return time to a given state. The proof is based on methods of nonlinear Perron-Frobenius theory, allowing us to reduce the mean-payoff problem to a discounted problem with state dependent discount rate. Our analysis also shows that policy iteration remains strongly polynomial for discounted problems in which the discount rate can be state dependent (and even negative) at certain states, provided that the spectral radii of the nonnegative matrices associated to all strategies are bounded from above by a fixed constant strictly less than 1.
• Characterization of Glioma Microcirculation and Tissue Features Using Intravoxel Incoherent Motion Magnetic Resonance Imaging in a Rat Brain Model
  
  • Iima M.
  • Reynaud O.
  • Tsurugizawa T.
  • Ciobanu Luisa
  • Li Jing-Rebecca
  • Geffroy F.
  • Djemai B.
  • Umehana M.
  • Le Bihan Denis
  Investigative Radiology, Lippincott, Williams & Wilkins, 2014, pp.485–490. (10.1097/RLI.0000000000000040)
  DOI : 10.1097/RLI.0000000000000040
• Weak approximation of averaged diffusion processes
  
  • Gobet Emmanuel
  • Miri Mohammed
  Stochastic Processes and their Applications, Elsevier, 2014, 124, pp.475--504. We derive expansion results in order to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approximation is based on the use of proxys with normal distribution or log-normal distribution, so that the expansion terms are explicit. We provide non asymptotic error bounds, which justifies the expansion accuracy as the time or the diffusion coefficients are small in a suitable sense.
• The horofunction boundary and isometry group of the Hilbert geometry
  
  • Walsh Cormac
  , 2014, 22. The horofunction boundary is a means of compactifying metric spaces that was introduced by Gromov in the 1970s. We describe explicitly the horofunction boundary of the Hilbert geometry, and sketch how it may be used to study the isometry group of this space.
• Découverte et analyse de la biodiversité : les moyens actuels
  
  • Elias Marianne
  • Condamine Fabien
  Mémoires de la SEF, 2014 (9), pp.23-39. – Depuis l’antiquité, la diversité des formes biologiques fascine, et fait l’objet de descriptions, d’analyses et classifications. Alors que pendant des siècles la caractérisation de la biodiversité a reposé sur des critères morphologiques, l’avènement et le développement rapide des techniques moléculaires et des méthodes analytiques associées ont permis de développer des approches complexes et intégratives pour étudier la biodiversité, tout en incorporant les données issues de la morphologie. Ces approches se classent en trois catégories : 1) Les approches microévolutives de type “génétique des populations”, basées sur de nombreux marqueurs moléculaires répartis dans tout le génome, et qui renseignent sur la structure fine de la biodiversité en étudiant les processus de spéciation (formation des espèces). 2) Les approches de type barcoding, qui permettent de caractériser génétiquement un individu et de lui assigner un nom d’espèce sur la base de la variation de la séquence d’ADN d’un ou de plusieurs gènes. Éventuellement, cette approche permet de définir les limites d’espèces. Combiné à la morphologie, le barcoding moléculaire a conduit à la taxonomie intégrative. 3) Les approches macroévolutives de type “phylogénies” (établies sur des données moléculaires et/ou morphologiques), qui reconstruisent les relations de parenté entre espèces et sont donc non seulement informatives sur la systématique du groupe étudié, mais également sur les processus évolutifs qui en ont structuré la biodiversité (biogéographie historique, rôle de caractères particuliers dans la diversification du groupe, variation des taux de diversification dans le temps ou entre lignées...). Ces trois approches, qui peuvent être combinées entre elles ainsi qu’aux approches morphologiques, ont contribué à mieux caractériser et comprendre les facteurs à l’origine de la biodiversité, par exemple en mettant en évidence des espèces cryptiques (des espèces qui se ressemblent tellement qu’elles étaient considérées comme une seule et même espèce), notamment chez les Insectes; en bouleversant les classifications traditionnelles; ou en remettant en cause le paradigme de l’isolement géographique dans la formation des espèces. Bien que la contribution de ces approches modernes soit notable, elles restent cependant très complexes et perfectibles. Plus important encore, il est essentiel aujourd’hui d’intégrer des experts de divers domaines pour appréhender sous divers angles et mieux comprendre cette biodiversité.
• 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).
• 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.
• 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
• 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
• 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.
• 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
• 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
• 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
• 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