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                <title xml:lang="en">On the collective behaviors of bio-inspired distributed systems</title>
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              <p>In recent years there has been a surge of interest on behalf of the algorithmic community in applying its theoretical tools to the understanding of complex systems, in particular biological ones, such as insect colonies, flocks of birds, and networks of neurons. We contribute to the investigation of such systems in three different directions. First, we analyze computational dynamics for stochastic coordination tasks in multi-agent systems: in particular, we focus on the consensus problem in environments where communication is affected by some form of noise. In this setting, we analyze two known opinion dynamics, the Undecided-State and the 3-Majority dynamics, and prove that they exhibit a phase-transition at different noise thresholds. Below the threshold, the two dynamics quickly reach an almost-consensus metastable phase; above, no form of consensus is possible. Second, we study Lévy walks, i.e. special random walks known to model many movement patterns found in nature, characterized by a step-length density distribution proportional to a power-law. We analyze their parallel hitting time and show how to use them to design an almost optimal algorithm for the ANTS problem, a distributed search problem on Z^2 which captures some aspects of animal foraging theory. Third, we consider the Assembly Calculus, a recently proposed distributed computational model of the brain which consists of stylized spiking neurons and synapses, and we test experimentally its capabilities, largely unexplored. In particular, we implement known heuristics for the Blocks World planning task; we empirically prove that reasonably large and complex programs in the Assembly Calculus run correctly and reliably.</p>
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              <p>Récemment, la communauté algorithmique a manifesté un intérêt croissant pour l'utilisation de ses outils théoriques à la compréhension des systèmes complexes, notamment biologiques, tels que les colonies d'insectes, les volées d'oiseaux et les réseaux de neurones. Nous contribuons à l'étude de ces systèmes dans trois directions différentes. Premièrement, nous analysons des dynamiques computationnelles pour les tâches de coordination stochastique dans les systèmes multi-agents. En particulier, nous nous focalisons sur le problème du consensus dans des environnements où la communication est bruyante : nous analysons deux dynamiques d'opinion, les dynamiques Undecided-State et 3-Majority, et nous prouvons qu'elles présentent une transition de phase à des seuils de bruit différents. En dessous du seuil, ces dynamiques atteignent rapidement une phase métastable de quasi-consensus ; au-dessus, aucune forme de consensus n'est possible. Deuxièmement, nous étudions les Lévy walks, des marches aléatoires qui modélisent des schémas de mouvement trouvés dans la nature, dont la distribution de la longueur de pas suit une loi de puissance. Nous analysons leur temps d'arrêt (hitting time) parallèle et les utilisons pour concevoir un algorithme optimal pour l'ANTS problem, un problème de recherche distribuée sur Z^2 qui capture certains aspects de la théorie du butinage. Troisièmement, nous considérons l'Assembly Calculus, un modèle distribué du cerveau récemment proposé, qui consiste en des neurones et des synapses stylisés, et nous testons expérimentalement ses capacités, largement inexplorées, en mettant en œuvre des heuristiques connues pour la tâche de planification du monde des blocs. Nous montrons empiriquement que des programmes grands et complexes dans ce modèle s'exécutent correctement et de manière fiable.</p>
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