Dans le domaine de l'Optimisation Combinatoire, la résolution de manière optimale de problèmes de grande taille par le biais d'algorithmes Branch-and-Bound requiert un nombre très élevé de ressources de calcul. De nos jours, de telles ressources sont accessibles grâce aux grilles de calcul, composées de grappes de clusters réparties sur différents sites géographiques. Ces environnements parallèles posent de nombreux défis scientifiques, notamment en termes de passage à l'échelle, de la prise en compte de l'hétérogénéité des ressources ainsi qu'en termes de tolérance aux pannes. La plupart des approaches existantes pour l'algorithme Branch-and-Bound parallèle sont basées sur une architecture de type Maître-Esclave, où un processus maître répartit les tâches à accomplir auprès de processus esclaves en charge de les traiter. L'utilisation d'une telle entité centrale constitue un obstacle majeur en ce qui concerne le passage à l'échelle. Dans cette thèse, nous proposons de relever ces défis ainsi que de surmonter cet obstacle grâce à une approche innovante et complètement distribuée, basée sur une architecture Pair-à-Pair (P2P). Celle-ci repose sur un seul type de processus (le pair), qui a pour mission d'explorer son propre ensemble de tâches, de le partager avec d'autres pairs et de diffuser l'information globale. Nous définissons des mécanismes adaptés en lien avec l'algorithme Branch-and-Bound, qui traitent de la répartition de la charge, de la diffusion de la meilleure solution trouvée et de la détection de la terminaison des calculs. En plus de multiples expérimentations sur le problème d'ordonnancement du Flow-Shop sur la grille de calcul Grid'5000, nous proposons une preuve formelle de la correction de notre approche. Par ailleurs, nous traitons une problématique souvent ignorés dans les travaux relatifs au calcul P2P, qui est l'importance de la topologie du réseau P2P. Généralement, une topologie très simple est utilisée. Les résultats obtenus montrent que notre approche permet le déploiement de réseaux de calculs à de très grandes échelles, constitués potentiellement de centaines de milliers de coeurs de calcul. Notre dernière contribution consiste en une approche Pair-à-Pair tolérante aux pannes afin de prendre en compte la nature généralement très volatile des ressources de calcul. Les résultats obtenus prouvent la robustesse de l'approche dans des environnements à la fois réalistes et sujets à de nombreux dysfonctionnements. / In the field of Combinatorial Optimization, the resolution to optimality of large instances of optimization problems through the use of Branch-and-Bound algorithms require a huge amount of computational resources. Nowadays, such resources are available from computing grids, which are sets of computing nodes geographically distributed over multiple sites. These parallel environments introduces multiples challenges related to the scalability, the heterogeneity of resources and the fault tolerance. Most of the existing approaches for the Branch-and-Bound algorithm are based on the Master-Slave paradigm where a central entity shares work units among slave entities in charge of processing them. Such an architecture represents an obstacle to scalability. In this thesis, we propose to face the challenges of grid environments and overcome this limitation by proposing an innovative and fully distributed approach based on the Peer-to-Peer paradigm. This architecture is based on a unique type of entity, a peer which is in charge of exploring its own local work pool and broadcasts global information to the network. We provide mechanisms to deal with the main tasks of the Branch-and-Bound algorithm : the load balancing, the diffusion of the best solution and the detection of the termination. Along with extensive experiments conducted on the Flow-Shop Scheduling Problem using the Grid'5000 Experimental Grid, we propose a formal proof of the correctness of our approach.In addition to this, we tackle a central issue when designing a Peer-to-Peer application : the impact of the P2P network topology on the performance of our approach. This aspect is often ignored in most of existing works, where only a predefined organization is chosen for the peers. The obtained results showed that the approach allows to deploy computing networks at extreme scales, involving hundreds of thousands of computing cores. Our final contribution consists in a Fault-Tolerant approach to deal with the dynamicity of the network (the volatility of computational resources). Results indicate that it faces efficiently various real-case and failure-intensive situations.

Differential pairs may gradually replace single trace as the media transmitting high-speed signal on high-speed digital circuit. This dissertation investigates the impact on electromagnetic radiation from high-speed circuit board by the distance between differential traces and edge effect .At the same time, we use the result of measurement and simulation to make sure the measurement method correct .The result shows that,the shorter the distance is,the lower the EMI of differential pairs have .The edge effect will has the ability of destroying the suppression of EMI. Based on the consideration of measuring correctly, we use a solid kind of measurement method to search some non-ideal effects before studying EMI from differential pairs .These effect may exist on real measurement or ideal simulation. We hope to understand the environment of measurement as clearly as possible. In addition, we address one simple and fast method to investigate radiation mechanism that resulted from edge effect of differential pairs.By this method to calculate radiation, we will understand more and more the radiation mechanism.

The classical field theory of Schwinger pair creation can be described using an effective Schrodinger equation with an inverted harmonic oscillator Hamiltonian. It is a well known fact that the inverted harmonic oscillator admits a canonical transformation to a Q.P type Berry-Keating Hamiltonian. In this thesis we demonstrate that the classical field theory of Schwinger pair creation has a hidden scale invariance described by the quantum mechanics of an attractive inverse square potential in the canonically rotated (Q,P) coordinates of the inverted harmonic oscillator. The quantum mechanics of the inverse square potential is well known because of the problem of fall to the center and the associated ambiguities in the boundary condition. It is also well known as a description of the physics of pair creation in the presence of an event horizon and black hole decay. We use point particle effective field theory (PPEFT) to derive the boundary condition which describes pair creation. This leads to the addition of an inevitable Dirac delta function with imaginary coupling to the inverse square potential, describing the physics of the source. This non-hermitian physics leads to the Klein paradox. The conservation loss is due to the charged pairs being produced during tunneling. / Thesis / Master of Science (MSc)

La quantité de données numériques produites par les utilisateurs, comme les photos, les vidéos et les documents numériques, a énormément augmenté durant cette dernière décennie. Ces données possèdent une grande valeur et nécessitent d'être sauvegardées en sécurité. D'une part, les solutions basées sur les DVDs et les disques durs externes, bien que très communes, ne fournissent pas un niveau suffisant de fiabilité. D'autre part les solutions basées sur de serveurs centralisées sont très coûteuses. Pour ces raisons, la communauté de recherche a manifesté un grand intérêt pour l'utilisation des systèmes pair-à-pair pour la sauvegarde de donnés. Les systèmes pair-à-pair représentent une solution intéressante grâce à leur capacité de passage à l'échelle. En effet, la capacité du service augmente avec la demande. La conception d'un réseau de sauvegarde de fichiers pair-à-pair est une tâche très complexe et présente un nombre considérable de défis. Les pairs peuvent avoir une durée de connexion limitée et peuvent quitter le système à un taux qui est considérablement plus élevé que dans le cas des systèmes de stockage centralisés. Notre intérêt se concentre sur la manière de fournir efficacement du stockage de données suffisamment fiable en appliquant des schémas de redondance appropriés et en adoptant des bons mécanismes pour maintenir une telle redondance. Cet effort n'est pas négligeable, dans la mesure où la maintenance du stockage de données dans un tel système exige des ressources importantes en termes de capacité de stockage et de largeur de bande passante. Notre contribution se porte sur deux aspects. Premièrement, nous proposons et étudions des codes correcteurs pour la redondance capables de combiner l'efficacité en bande passante de la réplication à l'efficacité en stockage des codes correcteurs classiques. En particulier, nous présentons et analysons deux nouvelles classes de codes: Regenerating Codes et Hierarchical Codes. Deuxièmement, nous proposons un système de réparation, nommé "adaptive proactive repair scheme", qui combine l'adaptabilité des systèmes réactifs avec l'utilisation régulière de la bande passante des systèmes proactifs, en généralisant les deux approches existantes.

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Cette thèse porte sur l'étude de certains aspects du principe d'incertitude en analyse harmonique.Historiquement le principe d'incertitude fut énoncé en 1927 par Heisenberg qui a montré unepropriété fondamentale de la mécanique quantique qui dit qu'il est impossible de mesurer, avecprécision, à la fois la position et la vitesse d'une particule. Le but de cette thèse est d'étendre certainsrésultats concernant les paires annihilantes à deux contextes.Dans la première partie nous étendons le principe d’incertitude local et les principes d'incertitudede Benedicks-Amrein-Berthier, de Shubin-Vakilian-Wolff et de Logvinenko-Sereda pour latransformée de Fourier-Bessel. Ces principes font qu’on ne peut pas localiser aussi précisémentqu’on le veut une fonction et sa transformée de Fourier-Bessel.Dans la deuxième partie, nous abordons les principes d'incertitude dans le cadre discret fini, dontl'intérêt a été renouvelé par la théorie de "l'échantillonnage comprimée" qui est plus connue sous levocable anglo-saxon du "compresseve sensing". Le thème général de ce travail est l'étude desprincipes d'incertitude qualitatifs et quantitatifs pour la transformée de Fourier discrète/ discrète à fenêtre. / In this thesis we are interested in Uncertainty Principles. Published by Heisenberg in 1927, the uncertainty principle was a key discovery in the early development of quantum theory. It implies that it is impossible to simultaneously measure the present position and momentum of a particle. The aim of this thesis is to extend some results about annihilating pairs in two contexts. In the first part we extend the local uncertainty principle, the Benedicks-Amrein-Berthier uncertainty principle, the Shubin-Vakilian-Wolff uncertainty principle and the Logvinenko-Sereda uncertainty principle for the Fourier-Bessel transform. This uncertainty principles state that a function and its Fourier- Bessel transform cannot be simultaneously well concentrated. The aim of the second part is to deal with uncertainty principles in finite the dimensional settings witch is linked to the theory of compresseve sensing. Our result extends previously known qualitative uncertainty principles into more quantitative for the discrete Fourier transform/ short time Fourier transform.

Doctor of Philosophy (PhD). / The term `Lax pair' refers to linear systems (of various types) that are related to nonlinear equations through a compatibility condition. If a nonlinear equation possesses a Lax pair, then the Lax pair may be used to gather information about the behaviour of the solutions to the nonlinear equation. Conserved quantities, asymptotics and even explicit solutions to the nonlinear equation, amongst other information, can be calculated using a Lax pair. Importantly, the existence of a Lax pair is a signature of integrability of the associated nonlinear equation. While Lax pairs were originally devised in the context of continuous equations, Lax pairs for discrete integrable systems have risen to prominence over the last three decades or so and this thesis focuses entirely on discrete equations. Famous continuous systems such as the Korteweg de Vries equation and the Painleve equations all have integrable discrete analogues, which retrieve the original systems in the continuous limit. Links between the different types of integrable systems are well known, such as reductions from partial difference equations to ordinary difference equations. Infinite hierarchies of integrable equations can be constructed where each equation is related to adjacent members of the hierarchy and the order of the equations can be increased arbitrarily. After a literature review, the original material in this thesis is instigated by a completeness study that finds all possible Lax pairs of a certain type, including one for the lattice modified Korteweg de Vries equation. The lattice modified Korteweg de Vries equation is subsequently reduced to several q-discrete Painleve equations, and the reductions are used to form Lax pairs for those equations. The series of reductions suggests the presence of a hierarchy of equations, where each equation is obtained by applying a recursion relation to an earlier member of the hierarchy, this is confirmed using expansions within the Lax pairs for the q-Painleve equations. Lastly, some explorations are included into fake Lax pairs, as well as sets of equivalent nonlinear equations with similar Lax pairs.

Rapid MR imaging has facilitated the development of a variety of medical tools such as MR guided surgeries, drug delivery, stent placement, biopsies, and blood flow imaging. This rapid imaging is largely attributable to the development of parallel imaging techniques. In one such technique, single echo acquisition (SEA) imaging, scan time is reduced by substituting the lengthy phase encoding process with spatial information from an extensive receiver coil array. In order to easily construct and obtain images from this coil array, an ideal set of coil elements would be easily decoupled and tuned, possess high SNR and penetration depth, and would allow for operation in both transmit and receive mode. Several types of coils have been considered for use in massive coil arrays, including the planar pair coil, the loop coil and the stripline coil. This thesis investigates each of these coils for use in massive arrays for SEA imaging with enhanced penetration. This investigation includes: improving the currents on the planar pair coil, determining the feasibility of the loop coil and the stripline coil at the scale required for SEA, and comparing the salient properties of each coil type. This investigation revealed that the stripline coil appears to be the best coil element for SEA imaging with enhanced penetration.

Rapid MR imaging has facilitated the development of a variety of medical tools such as MR guided surgeries, drug delivery, stent placement, biopsies, and blood flow imaging. This rapid imaging is largely attributable to the development of parallel imaging techniques. In one such technique, single echo acquisition (SEA) imaging, scan time is reduced by substituting the lengthy phase encoding process with spatial information from an extensive receiver coil array. In order to easily construct and obtain images from this coil array, an ideal set of coil elements would be easily decoupled and tuned, possess high SNR and penetration depth, and would allow for operation in both transmit and receive mode. Several types of coils have been considered for use in massive coil arrays, including the planar pair coil, the loop coil and the stripline coil. This thesis investigates each of these coils for use in massive arrays for SEA imaging with enhanced penetration. This investigation includes: improving the currents on the planar pair coil, determining the feasibility of the loop coil and the stripline coil at the scale required for SEA, and comparing the salient properties of each coil type. This investigation revealed that the stripline coil appears to be the best coil element for SEA imaging with enhanced penetration.