A shuman beings, we are continuously struggling to comprehend the mechanism of dierent natural systems. Many times, we face a complex system where the emergent properties of the system at a global level can not be explained by a simple aggregation of the system's components at the micro-level. To better understand the macroscopic system eects, we try to model microscopic events and their interactions. In order to do so, we rely on specialized tools to connect local mechanisms with global phenomena. One such tool is network theory. Networks provide a powerful way of modeling and analyzing complex systems based on interacting elements. The interaction pattern links the elements of the system together and provides a structure that controls how information permeates throughout the system. For example, the passing of information about job opportunities in a society depends on how social ties are organized. The interaction pattern, therefore, often is essential for reconstructing and understanding the global-scale properties of the system. In this thesis, I describe tools and models of network theory that we use and develop to analyze the organization of social or transportation systems. More specifically, we explore complex networks by asking two general questions: First, which mechanistic theoretical models can better explain network formation or spreading processes on networks? And second, what are the signi cant functional units of real networks? For modeling, for example, we introduce a simple agent-based model that considers interacting agents in dynamic networks that in the quest for information generate groups. With the model, we found that the network and the agents' perception are interchangeable; the global network structure and the local information pathways are so entangled that one can be recovered from the other one. For investigating signi cant functional units of a system, we detect, model, and analyze signi cant communities of the network. Previously introduced methods of significance analysis suer from oversimpli ed sampling schemes. We have remedied their shortcomings by proposing two dierent approaches: rst by introducing link prediction and second by using more data when they are available. With link prediction, we can detect statistically signi cant communities in large sparse networks. We test this method on real networks, the sparse network of the European Court of Justice case law, for example, to detect signi cant and insigni cant areas of law. In the presence of large data, on the other hand, we can investigate how underlying assumptions of each method aect the results of the signi cance analysis. We used this approach to investigate dierent methods for detecting signi cant communities of time-evolving networks. We found that, when we highlight and summarize important structural changes in a network, the methods that maintain more dependencies in signi cance analysis can predict structural changes earlier. In summary, we have tried to model the systems with as simple rules as possible to better understand the global properties of the system. We always found that maintaing information about the network structure is essential for explaining important phenomena on the global scale. We conclude that the interaction pattern between interconnected units, the network, is crucial for understanding the global behavior of complex systems because it keeps the system integrated. And remember, everything is connected, albeit not always directly.

L'acide rétinoïque (AR) est un morphogène dérivé de la vitamine A, qui intervient dans le contrôle de l'organogenèse, de la prolifération et de la différenciation cellulaires chez les Chordés. Dans ce contexte, nous avons étudié les régulations spatio-temporelles de la voie de signalisation de l’AR au cours du développement de l’amphioxus, en mettant l'accent sur l’espèce européenne Branchiostoma lanceolatum.Nous avons tout d'abord inhibé ou activé la voie de signalisation de l’AR lors du développement embryonnaire en traitant des embryons d’amphioxus à des doses variables de composés pharmacologiques interférant avec le métabolisme des rétinoïdes. Grâce à l’utilisation d’outils mathématiques spécifiques, nous avons établi un schéma détaillé des effets des traitements effectués sur le développement du système nerveux central (SNC) et du pharynx chez l’amphioxus en nous basant sur l’expression de gènes marqueurs de tissus spécifiques. À l’issue de cette première analyse, nous avons par la suite étudié les effets d’une perturbation de la signalisation de l’AR à des points clés du développement chez l’amphioxus lors de la régionalisation du SNC et du pharynx. Nous avons ainsi montré que la voie de signalisation de l’AR intervient dans la régionalisation de l’axe antéro-postérieur via le contrôle des gènes hox dès le stade gastrula et jusqu’aux stades larvaires. En outre, nous avons réalisé l'étude préliminaire du gène homologue chez l’amphioxus du gène aldh1a2 des Vertébrés, et avons démontré que la régulation du niveau de synthèse de l’AR au cour du développement est conservée entre l’amphioxus et les Vertébrés. Finalement, nous avons montré que la voie de l’AR participe également à la morphogenèse caudale chez l’amphioxus, et que le mécanisme impliqué semble différent de celui proposé chez les Vertébrés où l’AR contrôle la structuration de la nageoire caudale par le ciblage des tissus mésenchymateux. / Retinoic acid (RA) is an endogenous vitamin A-derived morphogen. In this context, we studied the spatiotemporal roles of RA signaling in amphioxus development, focusing on the European amphioxus species: Branchiostoma lanceolatum. We first created excess and insufficiency models of RA signaling by exposing amphioxus embryos to series of doses of different pharmacological compounds targeting either the RA receptors or the RA metabolism machinery. By introducing the important mathematical concept of a Cartesian coordinate system founded by René Descartes, we created detailed diagrams of the concentration-dependent defects caused by RA signaling in the central nervous system (CNS) and pharynx of amphioxus by evaluating the statistical significances of tissue-specific marker gene expression in labeled embryos. This analysis yielded a very detailed description of the sensitivities of the developing amphioxus CNS and pharynx to altered RA signaling levels. Following this initial challenge, we correlated the effects of altered RA signaling levels with key amphioxus developmental stages characterized by structural transitions in CNS and pharynx. We show that hox-mediated RA signaling in axial patterning is active beyond the gastrula stage and might be maintained until at least early larval stage, with possible roles in more regionalized axis formation and organ induction. In addition, we carried out a preliminary study on a RA synthesizing gene in amphioxus, called aldh1a, a possible homolog of the vertebrate aldh1a2 gene, demonstrating that the feedback between RA signaling and RA synthesizing levels has emerged before the split of the cephalochordate and vertebrate lineages. Moreover, we are able to show that RA signaling also participates in tail fin morphogenesis in amphioxus by a mechanism that is probably not comparable to that in vertebrates, where RA modulates caudal fin patterning through targeting mesenchymal derivatives.

DNA microarrays are a relatively new technology for assessing the expression levels of thousands of genes simultaneously. Researchers hope to find genes that are differentially expressed by hybridizing cDNA from known treatment sources with various genes spotted on the microarrays. The large number of tests involved in analyzing microarrays has raised new questions in multiple testing. Several approaches for identifying differentially expressed genes have been proposed. This paper considers two: (1) a mixed models approach, and (2) the Signiffcance Analysis of Microarrays.

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