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.
• 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')
• 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.
• 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
• 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.
• 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
• 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.
• Quick reachability and proper extension for problems with unbounded controls
  
  • Aronna Maria Soledad
  • Motta Monica
  • Rampazzo Franco
  , 2014. For a CONTROL SYSTEM of the form _ x = f (x; u; v) + Σm =1 g (x)u_ ; on [0;T]; (x; u)(0) = ( x; u); with x : [0;T] ! IRn; u : [0;T] ! U IRm; v : [0;T] ! V IRl ; we rely on the notion of LIMIT SOLUTION, and we investigate whether minimum problems with L1controls are PROPER EXTENSIONS of regular problems with more regular controls (AC or BV). Motivation: optimality conditions, numerical methods, etc.
• 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.
• The $\Gamma$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension
  
  • Bellettini Giovanni
  • Chambolle Antonin
  • Goldman Michael
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014. In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functionals with discontinuities penalized with a ''cohesive'' energy, that is, whose cost depends on the actual opening of the discontinuity.
• 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.
• Beyond first-order finite element schemes in micromagnetics
  
  • Kritsikis E.
  • Vaysset A.
  • Buda-Prejbeanu L.D.
  • Alouges F.
  • Toussaint Jean-Christophe
  Journal of Computational Physics, Elsevier, 2014, 256, pp.357. (10.1016/j.jcp.2013.08.035)
  DOI : 10.1016/j.jcp.2013.08.035
• A generalized formulation of the Linear Sampling Method with exact characterization of targets in terms of farfield measurements
  
  • Audibert Lorenzo
  • Haddar Houssem
  Inverse Problems, IOP Publishing, 2014, 30 (035011). We propose and analyze a new formulation of the Linear Sampling Method that uses an exact characterization of the targets shape in terms of the so-called farfield operator (at a fixed frequency). This characterization is based on constructing nearby solutions of the farfield equation using minimizing sequences of a least squares cost functional with an appropriate penalty term. We first provide a general framework for the theoretical foundation of the method in the case of noise-free and noisy measurements operator. We then explicit applications for the case of inhomogeneous inclusions and indicate possible straightforward generalizations. We finally validate the method through some numerical tests and compare the performances with classical LSM and the factorization methods. (10.1088/0266-5611/30/3/035011)
  DOI : 10.1088/0266-5611/30/3/035011
• On certain hyperelliptic signals that are natural controls for nonholonomic motion planning
  
  • Gauthier Jean-Paul
  • Monroy-Perez Felipe
  , 2014. In this paper we address the general problem of approximating, in a certain optimal way, non admissible motions of a kinematic system with nonholonomic constraints. Since this kind of problems falls into the general subriemannian geometric setting, it is natural to consider optimality in the sense of approximating by means of subriemannian geodesics. We consider sys-tems modeled by a subriemannian Goursat structure, a particular case being the well known system of a car with trailers, along with the associated parallel parking problem. Several authors approximate the successive Lie brackets by using trigonometric functions. By contrast, we show that the more natural op-timal motions are related with closed hyperelliptic plane curves with a certain number of loops.
• 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.
• Geometric Control Theory and sub-Riemannian Geometry
  
  • Stefani Gianna
  • Boscain Ugo
  • Gauthier Jean-Paul
  • Sarychev Andrey
  • Sigalotti Mario
  , 2014, pp.372. This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
• 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
• 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
• 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
• 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