Clustering applications dealing with perception based or biased data lead to models with non-disjunct clusters. There, objects to be clustered are allowed to belong to several clusters at the same time which results in a fuzzy clustering. It can be shown that this is equivalent to searching all maximal cliques in dynamic graphs like G_t=(V,E_t), where E_(t-1) in E_t, t=1,... ,T; E_0=(). In this article algorithms are provided to track all maximal cliques in a fully dynamic graph. It is naturally to raise the question about the maximum clique, having all maximal cliques. Therefore this article discusses potentials and drawbacks for this problem as well. (author's abstract) / Series: Working Papers on Information Systems, Information Business and Operations

Graphs are a commonly used abstraction for diverse kinds of interactions, e.g., on Twitter and Facebook. Different kinds of topological properties of such graphs are computed for gaining insights into their structure. Computing properties of large real networks is computationally very challenging. Further, most real world networks are dynamic, i.e., they change over time. Therefore there is a need for efficient dynamic algorithms that offer good space-time trade-offs. In this thesis we study the problem of computing the reachability set size of a vertex, which is a fundamental problem, with applications in databases and social networks. We develop the first Giraph based algorithms for different dynamic versions of these problems, which scale to graphs with millions of edges. / Master of Science

In the development of multicellular organisms, tissue development and homeostasis require coordinated cellular motion. For example, in conditions such as wound healing, immune and epithelial cells need to proliferate and migrate. Deregulation of key signalling pathways in pathological conditions causes alterations in cellular motion properties that are critical for disease development and progression, in cancer it leads to invasion and metastasis. Consequently there is strong interest in identifying factors, including drugs that affect the motion and interactions of cells in disease using experimental models suitable for high-content screening. There are two main modes of cell migration; individual and collective migration. Currently analysis tools for robust, sensitive and comprehensive motion characterisation in varying experimental conditions for large extended timelapse acquisitions that jointly considers both modes are limited. We have developed a systematic motion analysis framework, Motion Sensing Superpixels (MOSES) to quantitatively capture cellular motion in timelapse microscopy videos suitable for high-content screening. MOSES builds upon established computer vision approaches to deliver a minimal parameter, robust algorithm that can i) extract reliable phenomena-relevant motion metrics, ii) discover spatiotemporal salient motion patterns and iii) facilitate unbiased analysis with little prior knowledge through unique motion 'signatures'. The framework was validated by application to numerous datasets including YouTube videos, zebrafish immunosurveillance and Drosophila embryo development. We demonstrate two extended applications; the analysis of interactions between two epithelial populations in 2D culture using cell lines of the squamous and columnar epithelia from human normal esophagus, Barrett's esophagus and esophageal adenocarcinoma and the automatic monitoring of 3D organoid culture growth captured through label-free phase contrast microscopy. MOSES found unique boundary formation between squamous and columnar cells and could measure subtle changes in boundary formation due to external stimuli. MOSES automatically segments the motion and shape of multiple organoids even if present in the same field of view. Automated analysis of intestinal organoid branching following treatment agrees with independent RNA-seq results.

Agglomerative Clustering techniques work by recursively merging graph vertices into communities, to maximize a clustering quality metric. The metric of Modularity coined by Newman and Girvan, measures the cluster quality based on the premise that, a cluster has collections of vertices more strongly connected internally than would occur from random chance. Various fast and efficient algorithms for community detection based on modularity maximization have been developed for static graphs. However, since many (contemporary) networks are not static but rather evolve over time, the static approaches are rendered inappropriate for clustering of dynamic graphs. Modularity optimization in changing graphs is a relatively new field that entails the need to develop efficient algorithms for detection and maintenance of a community structure while minimizing the “Size of change” and computational effort. The objective of this work was to develop an efficient dynamic agglomerative clustering algorithm that attempts to maximize modularity while minimizing the “size of change” in the transitioning community structure. First we briefly discuss the previous memoryless dynamic reagglomeration approach with localized vertex freeing and illustrate its performance and limitations. Then we describe the new backtracking algorithm followed by its performance results and observations. In experimental analysis of both typical and pathological cases, we evaluate and justify various backtracking and agglomeration strategies in context of the graph structure and incoming stream topologies. Evaluation of the algorithm on social network datasets, including Facebook (SNAP) and PGP Giant Component networks shows significantly improved performance over its conventional static counterpart in terms of execution time, Modularity and Size of Change.

Cette thèse porte sur la rapidité du temps de mélange de chaînes de Markov sur des graphes. La contribution principale concerne les graphes avec des dynamiques locales sur les arêtes, la topologie du graphe évoluant au fur et à mesure que les arêtes glissent les unes le long des autres. Nous proposons une classification des différents modèles existants de graphes dynamiques, tout en illustrant l’importance des transitions le long d’une structure mouvante pour améliorer la vitesse de convergence. Cette étude est complétée par la preuve, pour l’une de ces dynamiques, d’un temps de mélange rapide. Nous définissons notamment l’expansion partielle d’un graphe. Celle-ci permet de suivre l’avancement de la dynamique, partant d’un état de faible expansion, jusqu’à obtention d’une bonne expansion à l’équilibre. La fin de cette thèse porte sur une amélioration de l’algorithme de simulation parfaite de Propp et Wilson. Nous introduisant un oracle pour les transitions, inspiré de l’échantillonnage préférentiel, qui permet de réduire la complexité de l’algorithme. Nous fournissons une preuve de correction, ainsi qu’une étude de l’impact de cette méthode sur la vitesse d’échantillonnage d’ensembles indépendants pour certains graphes. / This thesis focuses on the rapid mixing of graph-related Markov chains. The main contribution concerns graphs with local edge dynamics, in which the topology of a graph evolves as edges slide along one another. We propose a classification of existing models of dynamic graphs, and illustrate how evolving along a changing structure improves the convergence rate. This is complemented by a proof of the rapid mixing time for one such dynamic. As part of this proof, we introduce the partial expansion of a graph. This notion allows us to track the progression of the dynamic, from a state with poor expansion to good expansion at equilibrium. The end of the thesis proposes an improvement of the Propp and Wilson perfect sampling technique. We introduce oracle sampling, a method inspired by importance sampling that reduces the overall complexity of the Propp and Wilson algorithm. We provide a proof of correctness, and study the performance of this method when sampling independent sets from certain graphs.

Cette thèse porte sur l’étude de la complexité de l’exploration de graphes dynamiquespar agent mobile. Une entité mobile (appelée agent) se déplaçant dans un graphe dynamiquedoit traverser/visiter au moins une fois chacun de ses sommets. (Le tempsde traversée d’une arête est unitaire.) Ce problème fondamental en algorithmique paragents mobiles a été très étudié dans les graphes statiques depuis l’article originel deClaude Shannon. Concernant les graphes dynamiques, seul le cas des graphes dynamiquespériodiques a été étudié. Nous étudions ce problème dans deux familles degraphes dynamiques, les graphes dynamiques périodiquement variables (PV-graphes)et les graphes dynamiques T-intervalle-connexes. Les résultats obtenus dans cette thèseaméliorent des résultats existants et donnent des bornes optimales sur le problèmeétudié. / In this thesis, we study the complexity of the problem of exploration by a mobileagent in dynamic graphs. A mobile entity (called agent) moving in a dynamic graph hasto traverse/visit each of its vertices at least once. This fundamental problem in computatingby mobile agents has been well-studied in static graphs since the original paper ofClaude Shannon. However, for highly dynamic graphs, only the case of periodic dynamicgraphs has been studied. We study this problem in two families of dynamic graphs,periodically-varying graphs (PV-graphs) and T-interval-connected dynamic graphs. Theobtained results improve the existing results and give optimal bounds on the studiedproblems.

Graphs are powerful data structures that are widely used to represent complex forms of information. One area in which graphs are successfully being used is within compiler engineering, where a program under compilation can be represented as a graph that changes as the program is being compiled. These graphs, known as Intermediate Representation graphs, can be visualized to aid compiler engineers in understanding and debugging the compiler. However, graphs that change over time need to be visualized so that the viewer’s internal understanding of the graph is maintained. Simultaneously, the graph layouts should be of high quality. These criteria can be conflicting, making the visualization of changing graphs difficult. In this thesis, a dynamic graph layout algorithm to visualize dynamic Intermediate Representation graphs used in the C2 compiler in the Java HotSpotTM Virtual Machine was developed and evaluated. Currently, these graphs are visualized with hierarchical layouts, using a static graph layout algorithm. Five metrics were developed and used to evaluate the layouts by the dynamic algorithm against the layouts by the static algorithm. Four of these were concerned with the layout quality, by measuring the number of edge crossings, number of reversed edges, average degree of the edge bends and the average edge length. The fifth metric was related to mental map preservation and measures the Euclidean distance of node displacement across two layouts. Two experiments were conducted to compare the algorithms. The first experiment measured the layouts drawn by the algorithms when there were a couple of nodes added to or removed from a graph iteratively. A total of 1061 layouts were measured. In 74% of these, the dynamic algorithm caused less node displacement. The second experiment aimed to evaluate the algorithms against what is possible to achieve in regards of minimum node displacement while maintaining a high quality. The results of both experiments indicate that the dynamic layout algorithm yields layouts with less node displacement. However, the layouts generally have more reversed edges, more bends in the edges and overall longer edges. These metrics worsened as more iterations of changes were applied. The findings suggest that the dynamic layout algorithm is better at preserving the mental map, but at the cost of the layout quality. / Grafer är kraftfulla datastrukturer som används för att representera komplexa former av information. Ett område där grafer framgångsrikt används är inom kompilatorutveckling, där ett program under kompilering kan representeras som en graf som förändras medan programmet kompileras. Sådana grafer, kända som mellanrepresentationsgrafer, kan visualiseras för att hjälpa kompilatoringenjörer att förstå och felsöka kompilatorn. Dock behöver grafer som ändras över tid visualiseras så att användarens interna förståelse av grafen bibehålls. Samtidigt bör grafens layout vara av hög kvalitet. Dessa kriterier kan vara motsägelsefulla och gör visualiseringen av föränderliga grafer svår. I denna avhandling utvecklades och utvärderades en dynamisk layoutalgoritm för att visualisera dynamiska mellanrepresentationsgrafer som används i C2-kompilatorn i Java HotSpotTM Virtual Machine. Idag visualiseras dessa grafer med hierarkiska layouter som ritas av en statisk layoutalgoritm. Fem mått utvecklades och användes för att jämföra layouterna ritade av den dynamiska algoritmen med layouterna ritade av den statiska algoritmen. Fyra av dessa var relaterade till layoutkvaliteten och mäter antalet korsningar mellan kanter, antalet omvända kanter, den genomsnittliga graden av kantböjningar och den genomsnittliga kantlängden. Det femte måttet är relaterat till bevarandet av den mentala kartan och mätte nodförskjutningen mellan två layouter. Två experiment genomfördes för att jämföra algoritmerna. Det första experimentet mätte layouterna som ritades av algoritmerna när ett par noder lades till eller togs bort från en graf iterativt. Totalt mättes 1061 layouter. I 74% av dessa orsakade den dynamiska algoritmen mindre nodförskjutning. Det andra experimentet syftade till att utvärdera algoritmerna med avseende på minimal nodförskjutning samtidigt som hög kvalitet bibehålls. Resultaten från båda experimenten indikerar att den dynamiska layoutalgoritmen ger layouter med mindre nodförskjutning. Layouterna har dock generellt sett fler omvända kanter, fler böjningar i kanterna och längre kanter. Dessa mått försämrades när fler iterationer av förändringar tillämpades. Resultaten tyder på att den dynamiska layoutalgoritmen är bättre på att bevara den mentala kartan, men på bekostnad av layoutkvaliteten.

Les réseaux ad hoc dynamiques qui évoluent de manière non planifiée et imprévisible sont souvent étudiés en faisant l’hypothèse d’une composition et d’une topologie qui évoluent peu et relativement lentement. Il est alors possible de proposer dans ce contexte faiblement mobile des mécanismes (comme par exemple du routage, des infrastructures PKI, etc.) qui permettent aux applications conçues pour les réseaux statiques de continuer à fonctionner. Les travaux présentés dans cette thèse sont au contraire centrés sur lesréseaux ad hoc fortement dynamiques (iMANets). Les nœuds qui les constituent sont extrêmement mobiles et volatils, ce qui engendre des modifications incessantes et rapides de topologie. Les contributions principales de cette thèse sont (i) la définition d’une algèbre nommée CiMAN (Calculus for highly Mobile Ad hoc Networks) qui permet de modéliser les processus communicants dans ces réseaux ad hoc fortement mobiles, (ii) l’utilisation de cette algèbre pour prouver la correction d’algorithmes dédiés à ces réseaux, et (iii) unmiddleware et des applications de référence adaptés à ce contexte. / Mobile ad hoc networks that evolve in an unplanned and unpredictable mannerare often studied assuming that their composition and their topology evolve relatively slowly. In this context of weak mobility, it is then possible to propose mechanisms (such asrouting, Public Key Infrastructure, etc.) which make the application designed for a static context still operational. At the opposite, the work presented in this thesis focuses on highlymobile ad hoc networks (iMANets). The nodes of these networks are extremely mobile,bringing ceaseless and fast changes in the network topology. The main contributions of this thesis are (i) the definition of an algebra called CiMAN (Calculus for highly Mobile Adhoc Networks) which makes it possible to model communicating processes in these highly mobile ad hoc networks, (ii) the use of this algebra to prove the correctness of algorithms dedicated to these networks, and (iii) a middleware and reference applications specifically designed for this context.

Com base em três modelos de mobilidade MapBasedMovement, RandomWayPoint e RandomWalk presentes no simulador The One, sugerimos e discutimos vários modelos es- tocásticos para mobilidade. Primeiramente, a dinâmica das unidades móveis é reduzida a um processo chamado grafo dinâmico, de forma que a configuração espacial das unidades móveis em cada instante de tempo está resumida em um grafo. Os vértices desse grafo são unidades móveis e não mudam conforme o tempo: consideramos um sistema fechado, as unidades não desaparecem e não aparecem novas. O elo entre duas unidades (vértices) em um instante de tempo significa um contato neste instante (a distância entre as unidades é menor que um raio de contato), assim o conjunto de elos muda durante a evolução do sistema. Em seguida, modelamos a evolução do grafo dinâmico como um conjunto de pro- cessos aleatórios binários de forma que cada componente do processo está associada com um par de unidades móveis indicando presença ou ausência de contato entre elas. Três componentes principais constroem o processo: (i) distribuição de tempo de intercontato, (ii) distribuição de tempo de contato, e (iii) independência/interação entre as unidades. Nesta Tese mostramos teoricamente e através de simulações como escolher todos os três componentes para três modelos de mobilidade mencionados acima na situação de baixa densidade de unidades móveis, chamado DTNs (Delay Tolerant Networks). Considerar a modelagem da mobilidade desse ponto de vista é novo e não existe na literatura, até onde sabemos. Existe uma discussão na literatura sobre o tempo de intercontato, mas não conhecemos os resultados e discussão sobre a distribuição do tempo de contato e a interdependência de processos de contatos. / Based on three mobility models MapBasedMovement, RandomWayPoint and Ran- domWalk present on The One Simulator we suggest and discuss various stochastic mo- dels for mobility. First the dynamics of mobile units is reduced to process called dynamic graph, so that the spatial configuration of mobile units in every moment of time is sum- med up in a graph. The vertices of this graph are mobile units and do not change with the time: consider a closed system, the units dont disappear and not appear new. The link between two units (vertices) in an instant of time means a contact right now (dis- tance between the units is less that the radius contact). So the set of links changes during the system evolution. As a second step, the evolution of dynamic graph model as a set of random processes. Each process component is associated with a pair of mobile units indicating presence or absence of contact between them. Three major components build process: (i) distribution of intercontact time , (ii) distribution of contact time, and (iii) Independence interaction between units. In this work we show theoretically and by si- mulation how to choose all three components for three mobility models mentioned above on the situation of low density of mobile units, called DTNs (Delay Tolerant Networks). Consider the mobility modeling from that point of view is new and does not exist in the literature for our knowledge. There is a discussion in the literature about the intercontact time, but we dont know the results and discussion on the distribution of contact time and the interdependence of contact process.

Nous étudions le problème de maintenir une distribution donnée de graphes aléatoires après une séquence arbitraire d’insertions et de suppressions de sommets. Dans l’objectif de modéliser l’évolution de réseaux logiques dynamiques,nous travaillons dans un modèle local où l’accès à la liste des sommets est restreint. À la place, nous faisons l’hypothèse d’un accès à une primitive globale qui retourne un sommet aléatoire, choisi uniformément dans l’ensemble total des sommets. Le problème de maintenance a été exploré sur plusieurs modèles simples de graphes aléatoires (graphes d’Erdos–Rényi, graphes basés sur le modèle par paires, graphes k-sortants uniformes). Pour chacun des modèles, un ou plusieurs algorithmes pour la tâche de maintenance ont été décris et analysés ; les plus élaborés de ces algorithmes sont asymptotiquement optimaux. Le problème de maintenance soulève plusieurs problèmes de simulation liés à notre contexte distribué. Nous nous sommes intéressé en particulier à la maintenabilité de distributions de graphes et à la simulabilité de familles de distributions de probabilité sur les entiers, dans le modèle d’aléa présenté.Une attention particulière a été portée sur la simulation efficace de lois spécifiques nous intéressant (certaines lois binomiales). Cette dernière a pu être obtenue en exploitant les propriétés d’un nouvel arbre de génération pour les permutations, que nous avons introduit. / We study the problem of maintaining a given distribution of randomgraphs under an arbitrary sequence of vertex insertions and deletions. Keeping inmind our objective to model the evolution of dynamic logical networks, we work ina local model where we do not have direct access to the list of all vertices. Instead,we assume access to a global primitive that returns a random vertex, chosen uniformlyfrom the whole vertex set. The maintenance problem has been explored onseveral simple random graph models (Erdos–Rényi random graphs, pairing modelbased random graphs, uniform k-out graphs). For each model, one or several updatealgorithms for the maintenance task have been described and analyzed ; the mostelaborate of them are asymptically optimal. The maintenance task rise several simulationissues linked to our distributed context. In particular, we have focused onmaintenability of random graph distributions and simulability of families of probabilitydistributions over integers in our local random model. Special attention hasbeen paid to efficient simulation of particular distributions we were interested in(certain binomial distributions). The latter has been obtained through the use ofproperties of a new generation tree for permutations, which has been introducedalong the way