CNRS Laboratory of Analysis, Topology, Probabilities

Marseille, France

CNRS Laboratory of Analysis, Topology, Probabilities

Marseille, France
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Nachtergaele B.,University of California at Davis | Vershynina A.,Princeton University | Zagrebnov V.A.,CNRS Laboratory of Analysis, Topology, Probabilities | Zagrebnov V.A.,Aix - Marseille University
Annales Henri Poincare | Year: 2014

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the total energy variation in both the ideal and the open cavities as well as the entropy production in the ideal cavity. © 2013 Springer Basel.

Le Rousseau J.,CNRS Laboratory of Analysis, Topology, Probabilities | Le Rousseau J.,CNRS Physics Laboratory | Robbiano L.,University of Versailles
Archive for Rational Mechanics and Analysis | Year: 2010

In a bounded domain of Rn+1, n ≧ 2, we consider a second-order elliptic operator, A = ∂2x0 - ∇x · (c(x)∇x), where the (scalar) coefficient c(x) is piecewise smooth yet discontinuous across a smooth interface S. We prove a local Carleman estimate for A in the neighborhood of any point of the interface. The "observation" region can be chosen independently of the sign of the jump of the coefficient c at the considered point. The derivation of this estimate relies on the separation of the problem into three microlocal regions and the Calderón projector technique. Following the method of Lebeau and Robbiano (Comm Partial Differ Equ 20:335-356, 1995) we then prove the null controllability for the linear parabolic initial problem with Dirichlet boundary conditions associated with the operator ∂t - ∇x · (c(x)∇x. © Springer-Verlag 2009.

Kuijlaars A.B.J.,Catholic University of Leuven | Martinez-Finkelshtein A.,University of Almeria | Martinez-Finkelshtein A.,University of Granada | Wielonsky F.,CNRS Laboratory of Analysis, Topology, Probabilities
Communications in Mathematical Physics | Year: 2011

We consider the double scaling limit for a model of n non-intersecting squared Bessel processes in the confluent case:all paths start at time t = 0 at the same positive value x = a, remain positive, and are conditioned to end at time t = 1 at x = 0. After appropriate rescaling, the paths fill a region in the tx-plane as n → ∞ that intersects the hard edge at x = 0 at a critical time t = t*. In a previous paper, the scaling limits for the positions of the paths at time t ≠ t* were shown to be the usual scaling limits from random matrix theory. Here, we describe the limit as n → ∞ of the correlation kernel at critical time t* and in the double scaling regime. We derive an integral representation for the limit kernel which bears some connections with the Pearcey kernel. The analysis is based on the study of a 3 × 3 matrix valued Riemann-Hilbert problem by the Deift-Zhou steepest descent method. The main ingredient is the construction of a local parametrix at the origin, out of the solutions of a particular third-order linear differential equation, and its matching with a global parametrix. © 2011 Springer-Verlag.

Keller J.,CNRS Laboratory of Analysis, Topology, Probabilities
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

In the 40's, C.R. Rao considered probability distributions for a statistical model as the points of a Riemannian smooth manifold, where the considered Riemannian metric is the so-called Fisher metric. When extended to the complex projective space, this metric is actually the Fubini-Study metric. For certain models, it is quite remarkable that one actually needs to consider data with complex values. © 2013 Springer-Verlag.

Ramulu H.G.,CNRS Laboratory of Analysis, Topology, Probabilities
Frontiers in cellular and infection microbiology | Year: 2012

The increase in huge number of genomic sequences in recent years has contributed to various genetic events such as horizontal gene transfer (HGT), gene duplication and hybridization of species. Among them HGT has played an important role in the genome evolution and was believed to occur only in Bacterial and Archaeal genomes. As a result, genomes were found to be chimeric and the evolution of life was represented in different forms such as forests, networks and species evolution was described more like a rhizome, rather than a tree. However, in the last few years, HGT has also been evidenced in other group such as metazoa (for example in root-knot nematodes, bdelloid rotifers and mammals). In addition to HGT, other genetic events such as transfer by retrotransposons and hybridization between more closely related lineages are also well established. Therefore, in the light of such genetic events, whether the evolution of metazoa exists in the form of a tree, network or rhizome is highly questionable and needs to be determined. In the current review, we will focus on the role of HGT, retrotransposons and hybridization in the metazoan evolution.

Boutellis A.,Aix - Marseille University | Abi-Rached L.,CNRS Laboratory of Analysis, Topology, Probabilities | Raoult D.,Aix - Marseille University
Infection, Genetics and Evolution | Year: 2014

Two genera of lice parasitize humans: Pthirus and Pediculus. The latter is of significant public health importance and comprises two ecotypes: the body louse and the head louse. These ecotypes are morphologically and genetically notably similar; the body louse is responsible for three infectious diseases: Louse-borne epidemic typhus, relapsing fever, and trench fever. Mitochondrial DNA studies have shown that there are three obviously divergent clades of head lice (A, B and C), and only one clade of body lice is shared with head lice (clade A). Each clade has a unique geographic distribution. Lice have been parasitizing humans for millions of years and likely dispersed throughout the World with the human migrations out of Africa, so they can be good markers for studying human evolution. Here, we present an overview of the origin of human lice and their role in vector pathogenic bacteria that caused epidemics, and we review the association between lice clades and human migrations. © 2014 Elsevier B.V.

Mentrelli A.,CNRS Laboratory of Analysis, Topology, Probabilities | Negulescu C.,CNRS Laboratory of Analysis, Topology, Probabilities
Journal of Computational Physics | Year: 2012

Heat transfer in magnetically confined plasmas is a process characterized by non-linear and extremely high anisotropic diffusion phenomena. Standard numerical methods, successfully employed in the numerical treatment of classical diffusion problems, are generally inefficient, or even prone to break down, when such high anisotropies come into play, leading thus to the need of new numerical techniques suitable for this kind of problems.In the present paper, the authors propose a numerical scheme based on an asymptotic-preserving (AP) reformulation of this non-linear evolution problem, generalizing the ideas introduced in a previous paper for the case of elliptic anisotropic problems [P. Degond, A. Lozinski, J. Narski, C. Negulescu, An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition, J. Comput. Phys. 231 (7) (2012) 2724-2740]. The performances of the here proposed AP scheme are tested numerically; in particular it is shown that the scheme is capable to deal with problems characterized by a high degree of anisotropy, thus proving to be suitable for the study of anisotropic diffusion in magnetically confined plasmas. © 2012 Elsevier Inc..

Bardos C.,University Paris Diderot | Nouri A.,CNRS Laboratory of Analysis, Topology, Probabilities
Journal of Mathematical Physics | Year: 2012

Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This pathology appears on the full nonlinear problem, well-posed locally in time with analytic initial data, but generally ill-posed in the Hadamard sense. Eventually with a very different class of solutions, mono-kinetic, which constrains the structure of the density distribution, the problem becomes locally in time well-posed. © 2012 American Institute of Physics.

Bufetov A.I.,CNRS Laboratory of Analysis, Topology, Probabilities | Bufetov A.I.,National Research University Higher School of Economics | Solomyak B.,University of Washington
Communications in Mathematical Physics | Year: 2013

We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings. © 2012 Springer-Verlag Berlin Heidelberg.

Hachama M.,University of Khemis Miliana | Desolneux A.,Ecole Normale Superieure de Cachan | Richard F.J.P.,CNRS Laboratory of Analysis, Topology, Probabilities
IEEE Transactions on Image Processing | Year: 2012

In this paper, we address a complex image registration issue arising while the dependencies between intensities of images to be registered are not spatially homogeneous. Such a situation is frequently encountered in medical imaging when a pathology present in one of the images modifies locally intensity dependencies observed on normal tissues. Usual image registration models, which are based on a single global intensity similarity criterion, fail to register such images, as they are blind to local deviations of intensity dependencies. Such a limitation is also encountered in contrast-enhanced images where there exist multiple pixel classes having different properties of contrast agent absorption. In this paper, we propose a new model in which the similarity criterion is adapted locally to images by classification of image intensity dependencies. Defined in a Bayesian framework, the similarity criterion is a mixture of probability distributions describing dependencies on two classes. The model also includes a class map which locates pixels of the two classes and weighs the two mixture components. The registration problem is formulated both as an energy minimization problem and as a maximum a posteriori estimation problem. It is solved using a gradient descent algorithm. In the problem formulation and resolution, the image deformation and the class map are estimated simultaneously, leading to an original combination of registration and classification that we call image classifying registration. Whenever sufficient information about class location is available in applications, the registration can also be performed on its own by fixing a given class map. Finally, we illustrate the interest of our model on two real applications from medical imaging: template-based segmentation of contrast-enhanced images and lesion detection in mammograms. We also conduct an evaluation of our model on simulated medical data and show its ability to take into account spatial variations of intensity dependencies while keeping a good registration accuracy. © 1992-2012 IEEE.

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