Protocole de routage à chemins multiples pour des réseaux ad hoc

Ad hoc networks consist of a collection of wireless mobile nodes which dynamically exchange data without reliance on any fixed based station or a wired backbone network. They are by definition self-organized. The frequent topological changes make multi-hops routing a crucial issue for these networks. In this PhD thesis, we propose a multipath routing protocol named Multipath Optimized Link State Routing (MP-OLSR). It is a multipath extension of OLSR, and can be regarded as a hybrid routing scheme because it combines the proactive nature of topology sensing and reactive nature of multipath computation. The auxiliary functions as route recovery and loop detection are introduced to improve the performance of the network. The usage of queue length metric for link quality criteria is studied and the compatibility between single path and multipath routing is discussed to facilitate the deployment of the protocol. The simulations based on NS2 and Qualnet softwares are performed in different scenarios. A testbed is also set up in the campus of Polytech’Nantes. The results from the simulator and testbed reveal that MP-OLSR is particularly suitable for mobile, large and dense networks with heavy network load thanks to its ability to distribute the traffic into different paths and effective auxiliary functions. The H.264/SVC video service is applied to ad hoc networks with MP-OLSR. By exploiting the scalable characteristic of H.264/SVC, we propose to use Priority Forward Error Correction coding based on Finite Radon Transform (FRT) to improve the received video quality. An evaluation framework called SVCEval is built to simulate the SVC video transmission over different kinds of networks in Qualnet. This second study highlights the interest of multiple path routing to improve quality of experience over self-organized networks.Les réseaux ad hoc sont constitués d’un ensemble de nœuds mobiles qui échangent des données sans infrastructure de type point d’accès ou artère filaire. Ils sont par définition auto-organisés. Les changements fréquents de topologie des réseaux ad hoc rendent le routage multi-sauts très problématique. Dans cette thèse, nous proposons un protocole de routage à chemins multiples appelé Multipath Optimized Link State Routing (MP-OLSR). C’est une extension d’OLSR à chemins multiples qui peut être considérée comme une méthode de routage hybride. En effet, MP-OLSR combine la caractéristique proactive de la détection de topologie et la caractéristique réactive du calcul de chemins multiples qui est effectué à la demande. Les fonctions auxiliaires comme la récupération de routes ou la détection de boucles sont introduites pour améliorer la performance du réseau. L’utilisation de la longueur des files d’attente des nœuds intermédiaires comme critère de qualité de lien est étudiée et la compatibilité entre routage à chemins multiples et chemin unique est discutée pour faciliter le déploiement du protocole. Les simulations basées sur les logiciels NS2 et Qualnet sont effectuées pour tester le routage MP-OLSR dans des scénarios variés. Une mise en œuvre a également été réalisée au cours de cette thèse avec une expérimentation sur le campus de Polytech’Nantes. Les résultats de la simulation et de l’expérimentation révèlent que MP-OLSR est particulièrement adapté pour les réseaux mobiles et denses avec des trafics élevés grâce à sa capacité à distribuer le trafic dans des chemins différents et à des fonctions auxiliaires efficaces. Au niveau application, le service vidéo H.264/SVC est appliqué à des réseaux ad hoc MP-OLSR. En exploitant la hiérarchie naturelle délivrée par le format H.264/SVC, nous proposons d’utiliser un codage à protection inégale (PFEC) basé sur la Transformation de Radon Finie (FRT) pour améliorer la qualité de la vidéo à la réception. Un outil appelé SVCEval est développé pour simuler la transmission de vidéo SVC sur différents types de réseaux dans le logiciel Qualnet. Cette deuxième étude témoigne de l’intérêt du codage à protection inégale dans un routage à chemins multiples pour améliorer une qualité d’usage sur des réseaux auto-organisés

Project OASIS: The Design of a Signal Detector for the Search for Extraterrestrial Intelligence

An 8 million channel spectrum analyzer (MCSA) was designed the meet to meet the needs of a SETI program. The MCSA puts out a very large data base at very high rates. The development of a device which follows the MCSA, is presented

Asymptotic theory for Bayesian nonparametric inference in statistical models arising from partial differential equations

Partial differential equations (PDEs) are primary mathematical tools to model the behaviour of complex real-world systems. PDEs generally include a collection of parameters in their formulation, which are often unknown in applications and need to be estimated from the data. In the present thesis, we investigate the theoretical performance of nonparametric Bayesian procedures in such parameter identification problems in PDEs. In particular, inverse regression models for elliptic equations and stochastic diffusion models are considered. In Chapter 2, we study the statistical inverse problem of recovering an unknown function from a linear indirect measurement corrupted by additive Gaussian white noise. We employ a nonparametric Bayesian approach with standard Gaussian priors, for which the posterior-based reconstruction corresponds to a Tikhonov regulariser with a reproducing kernel Hilbert space norm penalty. We prove a semiparametric Bernstein–von Mises theorem for a large collection of linear functionals of the unknown, implying that semiparametric posterior estimation and uncertainty quantification are valid and optimal from a frequentist point of view. The general result is applied to three concrete examples that cover both the mildly and severely ill-posed cases: specifically, elliptic inverse problems, an elliptic boundary value problem, and the recovery of the initial condition of the heat equation. For the elliptic boundary value problem, we also obtain a nonparametric version of the theorem that entails the convergence of the posterior distribution to a prior-independent infinite-dimensional Gaussian probability measure with minimal covariance. As a consequence, it follows that the Tikhonov regulariser is an efficient estimator, and we derive frequentist guarantees for certain credible balls centred around it. Chapter 3 is concerned with statistical nonlinear inverse problems. We focus on the prototypical example of recovering the unknown conductivity function in an elliptic PDE in divergence form from discrete noisy point evaluations of the PDE solution. We study the statistical performance of Bayesian nonparametric procedures based on a flexible class of Gaussian (or hierarchical Gaussian) process priors, whose implementation is feasible by MCMC methods. We show that, as the number of measurements increases, the resulting posterior distributions concentrate around the true parameter generating the data, and derive a convergence rate, algebraic in inverse sample size, for the estimation error of the associated posterior means. Finally, in Chapter 4 we extend the posterior consistency analysis to dynamical models based on stochastic differential equations. We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and p-exponential priors, which are shown to converge to the truth at the minimax optimal rate over Sobolev smoothness classes in any dimension. Chapter 1 is dedicated to introducing the statistical models considered in Chapters 2 - 4, and to providing an overview of the theoretical results derived therein. The main theorems of Chapter 2 and Chapter 3 are illustrated via the results of simulations, and detailed comments are provided on the implementation.Richard Nickl’s ERC grant No. 647812; EPSRC grant EP/L016516/1 for the Cambridge Centre for Analysi

Entropies from coarse-graining: convex polytopes vs. ellipsoids

We examine the Boltzmann/Gibbs/Shannon $\mathcal{S}_{BGS}$ and the non-additive Havrda-Charv\'{a}t / Dar\'{o}czy/Cressie-Read/Tsallis \ $\mathcal{S}_q$ \ and the Kaniadakis $\kappa$-entropy \ $\mathcal{S}_\kappa$ \ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky's theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint.Comment: 63 pages. No figures. Standard LaTe

Evolution-Operator-Based Single-Step Method for Image Processing

This work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. From the point of image/signal processing, the LSEK gives rise to a family of lowpass filters. These filters contain controllable time delay and amplitude scaling. The new evolution operator-based method is constructed by pointwise adaptation of anisotropy to the coefficients of the LSEK. The Perona-Malik-type of anisotropic diffusion schemes is incorporated in the LSEK for image denoising. A forward-backward diffusion process is adopted to the LSEK for image deblurring or sharpening. A coupled PDE system is modified for image edge detection. The resulting image edge is utilized for image enhancement. Extensive computer experiments are carried out to demonstrate the performance of the proposed method. The major advantages of the proposed method are its single-step solution and readiness for multidimensional data analysis

Partielle Differentialgleichungen

The workshop dealt with partial differential equations in geometry and technical applications. The main topics were the combination of nonlinear partial differential equations and geometric problems, regularity of free boundaries, conformal invariance and the Willmore functional