Biological processes involve complex biochemical interactions among a large number of species like cells, RNA, proteins and metabolites. Learning these interactions is essential to interfering artificially with biological processes in order to, for example, improve crop yield, develop new therapies, and predict new cell or organism behaviors to genetic or environmental perturbations. For a biological process, two pieces of information are of most interest. For a particular species, the first step is to learn which other species are regulating it. This reveals topology and causality. The second step involves learning the precise mechanisms of how this regulation occurs. This step reveals the dynamics of the system. Applying this process to all species leads to the complete dynamical network. Systems biology is making considerable efforts to learn biological networks at low experimental costs. The main goal of this thesis is to develop advanced methods to build models for biological networks, taking the circadian system of Arabidopsis thaliana as a case study. A variety of network inference approaches have been proposed in the literature to study dynamic biological networks. However, many successful methods either require prior knowledge of the system or focus more on topology. This thesis presents novel methods that identify both network topology and dynamics, and do not depend on prior knowledge. Hence, the proposed methods are applicable to general biological networks. These methods are initially developed for linear systems, and, at the cost of higher computational complexity, can also be applied to nonlinear systems. Overall, we propose four methods with increasing computational complexity: one-to-one, combined group and element sparse Bayesian learning (GESBL), the kernel method and reversible jump Markov chain Monte Carlo method (RJMCMC). All methods are tested with challenging dynamical network simulations (including feedback, random networks, different levels of noise and number of samples), and realistic models of circadian system of Arabidopsis thaliana. These simulations show that, while the one-to-one method scales to the whole genome, the kernel method and RJMCMC method are superior for smaller networks. They are robust to tuning variables and able to provide stable performance. The simulations also imply the advantage of GESBL and RJMCMC over the state-of-the-art method. We envision that the estimated models can benefit a wide range of research. For example, they can locate biological compounds responsible for human disease through mathematical analysis and help predict the effectiveness of new treatments.

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A mesure que les réseaux s'étendent, ils deviennent de plus en plus susceptibles de défaillir. En effet, leurs nœuds peuvent être sujets à des attaques, pannes, corruptions de mémoire... Afin d'englober tous les types de fautes possibles, nous considérons le modèle le plus général possible : le modèle Byzantin, où les nœuds fautifs ont un comportement arbitraire (et donc, potentiellement malveillant). De telles fautes sont extrêmement dangereuses : un seul nœud Byzantin, s'il n'est pas neutralisé, peut déstabiliser l'intégralité du réseau.Nous considérons le problème d'échanger fiablement des informations dans un réseau multi-Sauts malgré la présence de telles fautes Byzantines. Des solutions existent mais nécessitent un réseau dense, avec un grand nombre de voisins par nœud. Dans cette thèse, nous proposons des solutions pour les réseaux faiblement connectés, tels que la grille, où chaque nœud a au plus 4 voisins. Dans une première partie, nous acceptons l'idée qu'une minorité de nœuds corrects échouent à communiquer fiablement. En contrepartie, nous proposons des solutions qui tolèrent un grand nombre de fautes Byzantines dans les réseaux faiblement connectés. Dans une seconde partie, nous proposons des algorithmes qui garantissent une communication fiable entre tous les nœuds corrects, pourvu que les nœuds Byzantins soient suffisamment distants. Enfin, nous généralisons des résultats existants à de nouveaux contextes : les réseaux dynamiques, et les réseaux de taille non-Bornée. / As modern networks grow larger and larger, they become more likely to fail. Indeed, their nodes can be subject to attacks, failures, memory corruptions... In order to encompass all possible types of failures, we consider the most general model of failure: the Byzantine model, where the failing nodes have an arbitrary (and thus, potentially malicious) behavior. Such failures are extremely dangerous, as one single Byzantine node, if not neutralized, can potentially lie to the entire network. We consider the problem of reliably exchanging information in a multihop network despite such Byzantine failures. Solutions exist but require a dense network, where each node has a large number of neighbors. In this thesis, we propose solutions for sparse networks, such as the grid, where each node has at most 4 neighbors. In a first part, we accept that some correct nodes fail to communicate reliably. In exchange, we propose quantitative solutions that tolerate a large number of Byzantine failures, and significantly outperform previous solutions in sparse networks. In a second part, we propose algorithms that ensure reliable communication between all correct nodes, provided that the Byzantine nodes are sufficiently distant from each other. At last, we generalize existing results to new contexts: dynamic networks, and networks with an unbounded diameter.