Avec l’avènement du numérique, il est désormais possible aux chercheurs d’amasser des grandes quantités de données et les plateformes de réseaux sociaux en ligne ne font pas exception à cela. Les sociologues, comme d’autres, se sont emparés de ces nouvelles ressources afin de poursuivre leurs enquêtes sur les modalités de l’interaction entre individus et leur impact sur la structuration de la sociabilité. Suivant cette voie, ce travail de thèse vise à l’analyse d’un grand nombre de comptes Facebook, aussi bien au travers des outils classiques de l’analyse de données que de la théorie des graphes, à laquelle des contributions méthodologiques sont apportées. Deux facteurs principaux encouragent l’étude de l’activité et de la sociabilité en ligne. D’une part, le temps important dédié à cette plateforme par de nombreux internautes justifie l’intérêt porté par les sociologues aux échanges qui s’y construisent. Par ailleurs, et contrairement à ce que l’on peut observer sur d’autre sites de réseaux sociaux en ligne, les liens entre individus sur Facebook sont proches de ceux hors-lignes. Dans un premier temps, la thèse s’évertue à démêler les multiples facettes de ce à quoi ”être sur Facebook” correspond. Distribués autour de pratiques normatives fabulées, les usages de nos enquêtés fluctuent au gré de leur appropriation ou non des composantes de l’importante variété de moyens de communication proposés par la plateforme. Ces usages, comme on le verra, sont ainsi différemment adoptés selon les catégories socioprofessionnelles et influent par ailleurs sur les modalités d’échanges et d’interactions des enquêtés avec leurs amis en ligne. Ces modalités sont également explorées dans ce travail, tout comme le rôle du conjoint et sa place dans la structure relationnelle. La seconde partie de la thèse se propose de construire une typologie de ces structures relationnelles dites égocentrées, c’est-à-dire depuis le point de vue de l’enquêté. Cette typologie des réseaux de sociabilité en ligne se base sur l’énumération de leurs sous-graphes induits, les graphlets, initialement développée par des chercheurs en bioinformatique. Cette approche offre une vision méso (entre micro et macro) des réseaux, propice à souligner des phénomènes inédits de sociologie des réseaux. A fort potentiel pluri-disciplinaire, la méthodologie graphlets elle même est également discutée et explorée. / With the digital advent, it is now possible for researchers to collect important amounts of data and online social network platforms are surely part of it. Sociologists, among others, seized those new resources to investigate over interaction modalities between individuals as well as their impact on the structure of sociability. Following this lead, this thesis work aims at analyzing a large number of Facebook accounts, through data analysis and graph theory classical tools, and to bring methodological contributions. Two main factors encourage to study Facebook social activities. On one hand, the importance of time spent on this platform by many Internet users justifies by itself the sociologists interest. On the other, and contrarily to what we observe on other social network websites, ties between individuals are similar to the ones that appear offline. First, the thesis proposes to detangle the multiple meanings that are behind the fact of ”being on Facebook”. The uses of our surveyed are not compacted in fantasized normative practices but vary depending on how they appropriate the different composers of the platform tools. These uses, as we will see it, do not concern all the socioprofessional categories in the same way and they also influence how the respondents interact with their online friends. The manuscript also explores these interactions, as well as the lover role into the relational structure. Second part of the thesis builds a typology of these relational structures. They are said as egocentred, which means that they are taken from the perspective of the respondent. This typology of social networks is based on their graphlet counts, that are the number of times each type of subnetwork appear in them. This approach offers a meso perspective (between micro and macro), that is propitious to underline some new social phenomena. With a high pluri-disciplinary potential, the graphlet methodology is also discussed and explored itself.

Le projet scientifique dans lequel s’inscrit ma thèse a pour objectif l’élaboration d’algorithmes distribués et efficaces pour les réseaux informatiques. Ce projet vise une catégorie particulière des algorithmes distribués, dits auto-stabilisants. Il s’agit d’algorithmes ayant pour propriété de retrouver un comportement correct suite à une panne dans le réseau et ce, sans aucune intervention humaine. Le travail effectué en collaboration avec mes directeurs de thèse s’est concentré, plus précisément, autour des problèmes de couplage, de cliques et des paradigmes de publications-souscriptions dans ce domaine de l’informatique théorique. Dans un premier temps on a traité le problème du couplage maximal dans sa version anonyme, en fournissant un algorithme auto-stabilisant probabiliste et efficace. Ces travaux sont parus dans le journal PPL. De plus, on s’est intéressé au problème du couplage dans sa version maximum identifiée. Son travail améliore le dernier algorithme présent dans la littérature pour l’approximation de ce type de couplage au 2/3 de la solution optimale. Ces travaux sont parus dans une conférence internationale OPODIS. Par ailleurs, j'ai eu l’opportunité de collaborer en Allemagne avec Prof. Volker Turau au sein du groupe de télématique de l’Université technique de Hambourg. Le cadre de cette collaboration a été les algorithmes auto-stabilisants pour les paradigmes de publication-souscription. Cela a abouti à un algorithme efficace pour la version en canal de ce problème, introduisant la notion de raccourci pour le routage de messages dans ces paradigmes. Les résultats ont fait l’objet d’un Brief Announcement et d’un papier, publiés dans des conférences internationales, SSS et NetSyS. J'ai aussi bénéficié d’une collaboration avec Mr. Gerry Siegemund qui a été accueilli au laboratoire d’Informatique de l’École Polytechnique. Il a été question de trouver un algorithme efficace et auto-stabilisant pour la partition d’un réseau en cliques. Cette collaboration a eu pour résultat un algorithme pour le problème améliorant le dernier en date. Ce résultat est en cours de rédaction pour soumission à une conférence internationale. / The main focus of my thesis is the design of an efficient kind of distributed algorithms, known as: Self-stabilizing. These algorithms have the property to recover from faults in the environment they're executed in, and this without any human intervention. Recovering here, means converging toward a pre-defined, correct configuration. In this setting, I was mainly interested by the problems of matching in graphs, clique partitions and publication subscription paradigms. For the maximal version of the matching problem in anonymous graphs, we achieved a more efficient randomized, self-stabilizing algorithm. This work is published in a journal version in PPL. The maximum version of the same problem, but in an identified setting, led to the design of an efficient self-stabilizing algorithm that approximates the optimal solution up to the 2/3. This result was published at OPODIS. During a research visit at TUHH, Hamburg, Germany. Together with Pr. Volker Turau we tackled the problem of self-stabilizing publish/subscribe paradigms. This led to an algorithm introducing the new notion of short-cuts in this type of structures and was published under a brief announcement and a regular paper at SSS and NetSyS. In collaboration with Mr. Siegemund, then a visiting researcher at LIX, École Polytechnique, we worked on an efficient self-stabilizing algorithm for clique partitions. This work is still in progress and in preparation for an eventual publication.

Image representation plays an important role in image processing applications, which usually. contain a huge amount of data. An image is a two-dimensional array of points, and each point contains information (eg: color). A 1024 by 1024 pixel image occupies 1 mega byte of space in the main memory. In actual circumstances 2 to 3 mega bytes of space are needed to facilitate the various image processing tasks. Large amounts of secondary memory are also required to hold various data sets. In this thesis, two different operations on the quadtree are presented. There are, in general, two types of data compression techniques in image processing. One approach is based on elimination of redundant data from the original picture. Other techniques rely on higher levels of processing such as interpretations, generations, inductions and deduction procedures (1, 2). One of the popular techniques of data representation that has received a considerable amount of attention in recent years is the quadtree data structure. This has led to the development of various techniques for performing conversions and operations on the quadtree. Klinger and Dyer (3) provide a good bibliography of the history of quadtrees. Their paper reports experiments on the degree of compaction of picture representation which may be achieved with tree encoding. Their experiments show that tree encoding can produce memory savings. Pavlidis [15] reports on the approximation of pictures by quadtrees. Horowitz and Pavidis [16] show how to segment a picture using traversal of a quadtree. They segment the picture by polygonal boundaries. Tanimoto [17] discusses distortions which may occur in quadtrees for pictures. Tanimoto [18, p. 27] observes that quadtree representation is particularly convenient for scaling a picture by powers of two. Quadtrees are also useful in graphics and animation applications [19, 20] which are oriented toward construction of images from polygons and superpositiofis of images. Encoded pictures are useful for display, especially if encoding lends itself to processing.

In this thesis a heuristic method for factoring semiprimes by multiagent depth-limited search of PG2N graphs is presented. An analysis of PG2N graph connectivity is used to generate heuristics for multiagent search. Further analysis is presented including the requirements on choosing prime numbers to generate 'hard' semiprimes; the lack of connectivity in PG1N graphs; the counts of spanning trees in PG2N graphs; the upper bound of a PG2N graph diameter and a conjecture on the frequency distribution of prime numbers on Hamming distance. We further demonstrated the feasibility of the HD2 breadth first search of PG2N graphs for factoring small semiprimes. We presented the performance of different multiagent search heuristics in PG2N graphs showing that the heuristic of most connected seedpick outperforms least connected or random connected seedpick heuristics on small PG2N graphs of size N

In this thesis, available tools for call graph generation, processing and visualization are analyzed. Based on this analysis, a call-graph processing tool is designed. The tool is then implemented and tested on call graphs generated from various real-world programs, including the Linux Kernel.

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Convolutional Neural Networks (CNNs) have dominated the task of imageclassification since 2012. Some key components of their success are that the underlying architecture integrates a set inductive biases such as translational invariance and the training computation can be significantly reduced by employing weight sharing. CNNs are powerful tools for generating new representations of images tailored to a particular task such as classification. However, because each image is passed through the network independent of other images, CNNs are not able to effectively aggregate information between examples. In this thesis, we explore the idea of using Graph Neural Networks (GNNs) in conjunction with CNNs to produce an architecture that has both the representational capacity of a CNN and the ability to aggregate information between examples. Graph Neural Networks apply the concept of convolutions directly on graphs. A result of this is that GNNs are able to learn from the connections between nodes. However, when working with image datasets, there is no obvious choice on how to construct a graph. There are certain heuristics such as ensuring homophily that have empirically been shown to increase the performance of GNNs. In this thesis, we apply different schemes of constructing a graph from image data for the downstream task of image classification and experiment with settings such as using multiple feature spaces and enforcing a bipartite graph structure. We also propose a model that allows for end to end training using CNNs and GNNs with proxies and attention that improves classification accuracy in comparison to a regular CNN. / Computer and Information Science