Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / No sÃculo XXI a humanidade produziu mais novos dados (informaÃÃes) do que em toda sua histÃria. Entender a natureza dos diversos sistemas que geram essa abundÃncia de dados se tornou um dos grandes desafios desse sÃculo. Uma forma de analisar formalmente esses grandes bancos de dados à empregando a teoria da informaÃÃo desenvolvida por Claude Shannon. Essa teoria permite, usando o princÃpio da mÃxima entropia, encontrar as distribuiÃÃes de probabilidades que melhor descrevem os comportamentos coletivos desses sistemas. Nessa dissertaÃÃo, discutimos a possibilidade de usar modelos tipo Ising para descrever observaÃÃes de sistemas reais. Devido a suas limitaÃÃes, empregar o modelo de Ising implica em supor que os elementos que constituem o sistema real sà podem estar em dois estados, por exemplo ativo ou inativo. AlÃm disso, o modelo de Ising da conta apenas de interaÃÃes entre pares de elementos e desconsidera a possibilidade de interaÃÃes entre grupos maiores de elementos. Como discutiremos, mesmo com essas limitaÃÃes tal modelo pode descrever bem resultados observados em alguns sistemas naturais, como por exemplo redes de neurÃnios. Especificamente, discutiremos resultados de trabalhos anteriores que mostram que usando apenas as mÃdias de atividade de cada neurÃnio e a correlaÃÃo entre os mesmo, usando a teoria de Shannon, observa-se que os estados visitados pela rede seguem à distribuiÃÃo de Ising. Para testar a aplicabilidade desse mÃtodo em diversos sistemas geramos dados sintÃticos, obtidos de modelos tipo Ising em trÃs situaÃÃes: ferromagnÃtico, anti-ferro e vidro de spins (spin glass). NÃs chamamos o sistema que gera os dados sintÃticos de sistema subjacente. Usamos mÃtodos de maximizaÃÃo de entropia para tentar construir sistemas modelos que consigam reproduzir as mÃdia e correlaÃÃes observadas nos dados sintÃticos. Dessa forma, verificamos em que situaÃÃes nossos mÃtodos conseguem de fato gerar um sistema modelo que reproduza o sistema subjacente que gerou os dados. Esses resultados podem estabelecer um limite de aplicabilidade para a tÃcnica discutida.

Recent experimental techniques in biology made possible the acquisition of overwhelming amounts of data concerning complex biological networks, such as neural networks, gene regulation networks and protein-protein interaction networks. These techniques are able to record states of individual components of such networks (neurons, genes, proteins) for a large number of configurations. However, the most biologically relevantinformation lies in their connectivity and in the way their components interact, information that these techniques aren't able to record directly. The aim of this thesis is to study statistical methods for inferring information about the connectivity of complex networks starting from experimental data. The subject is approached from a statistical physics point of view drawing from the arsenal of methods developed in the study of spin glasses. Spin-glasses are prototypes of networks of discrete variables interacting in a complex way and are widely used to model biological networks. After an introduction of the models used and a discussion on the biological motivation of the thesis, all known methods of network inference are introduced and analysed from the point of view of their performance. Then, in the third part of the thesis, a new method is proposed which relies in the remark that the interactions in biology are not necessarily symmetric (i.e. the interaction from node A to node B is not the same as the one from B to A). It is shown that this assumption leads to methods that are both exact and efficient. This means that the interactions can be computed exactly, given a sufficient amount of data, and in a reasonable amount of time. This is an important original contribution since no other method is known to be both exact and efficient.

Des techniques expérimentales récentes ont donné la possibilité d'acquérir un très grand nombre de données concernant des réseaux biologiques complexes, comme des réseaux de neurones, des réseaux de gènes et des réseaux d'interactions de protéines. Ces techniques sont capables d'enregistrer les états des composantes individuelles de ces réseaux (neurones, gènes, protéines) pour un grand nombre de configurations. Cependant, l'information la plus pertinente biologiquement se trouve dans la connectivité de ces systèmes et dans la façon précise avec laquelle ces composantes interagissent, information que les techniques expérimentales ne sont pas au point d'observer directement. Le bût de cette thèse est d'étudier les méthodes statistiques nécessaires pour inférer de l'information sur la connectivité des réseaux complexes en partant des données expérimentales. Ce sujet est traité par le point de vue de la physique statistique, en puisant de l'arsenal de méthodes théoriques qui ont été développées pour l'étude des verres de spins. Les verres de spins sont des exemples de réseaux à variables discrètes qui interagissent de façon complexe et sont souvent utilisés pour modéliser des réseaux biologiques. Après une introduction sur les modèles utilisés ainsi qu'une discussion sur la motivation biologique de cette thèse, toutes les méthodes d'inférence de réseaux connues sont présentées et analysées du point de vue de leur performance. Par la suite, dans la troisième partie de la thèse, un nouvelle méthode est proposée qui s'appuie sur la remarque que les interactions en biologie ne sont pas nécessairement symétriques (c'est-à-dire l'interaction entre les noeuds A et B n'est pas la même dans les deux directions). Il est démontré que cette assomption conduit à des méthodes qui sont capables de prédire les interactions de façon exacte, étant donné un nombre suffisant de données, tout en utilisant un temps de calcul polynomial. Ceci est un résultat original important car toutes les autres méthodes connues sont soit exactes et non-polynomiales soit inexactes et polynomiales. / Recent experimental techniques in biology made possible the acquisition of overwhelming amounts of data concerning complex biological networks, such as neural networks, gene regulation networks and protein-protein interaction networks. These techniques are able to record states of individual components of such networks (neurons, genes, proteins) for a large number of configurations. However, the most biologically relevantinformation lies in their connectivity and in the way their components interact, information that these techniques aren't able to record directly. The aim of this thesis is to study statistical methods for inferring information about the connectivity of complex networks starting from experimental data. The subject is approached from a statistical physics point of view drawing from the arsenal of methods developed in the study of spin glasses. Spin-glasses are prototypes of networks of discrete variables interacting in a complex way and are widely used to model biological networks. After an introduction of the models used and a discussion on the biological motivation of the thesis, all known methods of network inference are introduced and analysed from the point of view of their performance. Then, in the third part of the thesis, a new method is proposed which relies in the remark that the interactions in biology are not necessarily symmetric (i.e. the interaction from node A to node B is not the same as the one from B to A). It is shown that this assumption leads to methods that are both exact and efficient. This means that the interactions can be computed exactly, given a sufficient amount of data, and in a reasonable amount of time. This is an important original contribution since no other method is known to be both exact and efficient.