There any many different aspects in natural languages and their related dynamics that have been studied. In the case of languages, some quantitative analyses have been done by using stochastic models. Furthermore, natural languages can be understood as complex systems. Thus, there is a possibility to use set of tools development to analyse complex networks, which are computationally represented by graphs, also to analyse natural languages. Furthermore, these tools can be used to represent and analyse some related dynamics taking place on the networks. Observe that knowledge is intrinsically related to language, because language is the vehicle used by humans beings to transmit dicoveries, and the language itself is also a type of knowledge. This thesis is divided into two types of analyses: (i) texts and (II) dynamical aspects. In the first part, we proposed networks representations of text in different scales analyses, starting from the analysis of writing style considering word adjacency networks (co-occurence) to understand local patterns of words, to a mesoscopic representation, which is created from chunks of text and grasps information of the unfolding of the story. In the second part, we considered the structure and dynamics related to knowledge and language, in this case, starting from the larger scale, in which we studied the connectivity between applied and theoretical physics. In the following, we simulated the knowledge acquisition by researchers in a multi-agent dynamics and an intelligent machine that solves problems, which is represented by a network. At the smallest considered scale, we simulate the transmission of networks. This transmission considers the data as a series of organized symbols that is obtained from a dynamics. In order to improve the speed of transmission, the series can be compacted. For that, we considered the information theory and Huffman code. The proposed network-based approaches were found to be suitable to deal with the employed analysis for all of the tested scales. / Existem diversos aspectos das linguagens naturais e de dinâmicas relacionadas que estão sendo estudadas. No caso das línguas, algumas análises quantitativas foram feitas usando modelos estocásticos. Ademais, linguagens naturais podem ser entendidas como sistemas complexos. Para analisar linguagens naturais, existe a possibilidade de utilizar o conjunto de ferramentas que já foram desenvolvidas para analisar redes complexas, que são representadas computacionalmente. Além disso, tais ferramentas podem ser utilizadas para representar e analisar algumas dinâmicas relacionadas a redes complexas. Observe que o conhecimento está intrinsecamente relacionado à linguagem, pois a linguagem é o veículo usado para transmitir novas descobertas, sendo que a própria linguagem também é um tipo de conhecimento. Esta tese é dividida em dois tipos de análise : (i) textos e (ii) aspectos dinâmicos. Na primeira parte foram propostas representações de redes de texto em diferentes escalas de análise. A partir da análise do estilo de escrita, considerando redes de adjacência de palavras (co-ocorrência) para entender padrões locais de palavras, até uma representação mesoscópica, que é criada a partir de pedaços de texto e que representa informações do texto de acordo com o desenrolar da história. Na segunda parte, foram consideradas a estrutura e dinâmica relacionadas ao conhecimento e à linguagem. Neste caso, partiu-se da escala maior, com a qual estudamos a conectividade entre física aplicada e física teórica. A seguir, simulou-se a aquisição de conhecimento por pesquisadores em uma dinâmica multi-agente e uma máquina inteligente que resolve problemas, que é representada por uma rede. Como a menor escala considerada, foi simulada a transmissão de redes. Essa transmissão considera os dados como uma série de símbolos organizados que são obtidos a partir de uma dinâmica. Para melhorar a velocidade de transmissão, a série pode ser compactada. Para tanto, foi utilizada a teoria da informação e o código de Huffman. As propostas de abordagens baseadas em rede foram consideradas adequadas para lidar com a análise empregada, em todas as escalas testadas.

<p>Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.</p>

Complex network theory provides an elegant and powerful framework to statistically investigate the topology of local and long range dynamical interrelationships, i.e., teleconnections, in the climate system. Employing a refined methodology relying on linear and nonlinear measures of time series analysis, the intricate correlation structure within a multivariate climatological data set is cast into network form. Within this graph theoretical framework, vertices are identified with grid points taken from the data set representing a region on the the Earth's surface, and edges correspond to strong statistical interrelationships between the dynamics on pairs of grid points. The resulting climate networks are neither perfectly regular nor completely random, but display the intriguing and nontrivial characteristics of complexity commonly found in real world networks such as the internet, citation and acquaintance networks, food webs and cortical networks in the mammalian brain. Among other interesting properties, climate networks exhibit the "small-world" effect and possess a broad degree distribution with dominating super-nodes as well as a pronounced community structure. We have performed an extensive and detailed graph theoretical analysis of climate networks on the global topological scale focussing on the flow and centrality measure betweenness which is locally defined at each vertex, but includes global topological information by relying on the distribution of shortest paths between all pairs of vertices in the network. The betweenness centrality field reveals a rich internal structure in complex climate networks constructed from reanalysis and atmosphere-ocean coupled general circulation model (AOGCM) surface air temperature data. Our novel approach uncovers an elaborately woven meta-network of highly localized channels of strong dynamical information flow, that we relate to global surface ocean currents and dub the backbone of the climate network in analogy to the homonymous data highways of the internet. This finding points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). Carefully comparing the backbone structures detected in climate networks constructed using linear Pearson correlation and nonlinear mutual information, we argue that the high sensitivity of betweenness with respect to small changes in network structure may allow to detect the footprints of strongly nonlinear physical interactions in the climate system. The results presented in this thesis are thoroughly founded and substantiated using a hierarchy of statistical significance tests on the level of time series and networks, i.e., by tests based on time series surrogates as well as network surrogates. This is particularly relevant when working with real world data. Specifically, we developed new types of network surrogates to include the additional constraints imposed by the spatial embedding of vertices in a climate network. Our methodology is of potential interest for a broad audience within the physics community and various applied fields, because it is universal in the sense of being valid for any spatially extended dynamical system. It can help to understand the localized flow of dynamical information in any such system by combining multivariate time series analysis, a complex network approach and the information flow measure betweenness centrality. Possible fields of application include fluid dynamics (turbulence), plasma physics and biological physics (population models, neural networks, cell models). Furthermore, the climate network approach is equally relevant for experimental data as well as model simulations and hence introduces a novel perspective on model evaluation and data driven model building. Our work is timely in the context of the current debate on climate change within the scientific community, since it allows to assess from a new perspective the regional vulnerability and stability of the climate system while relying on global and not only on regional knowledge. The methodology developed in this thesis hence has the potential to substantially contribute to the understanding of the local effect of extreme events and tipping points in the earth system within a holistic global framework. / Die Theorie komplexer Netzwerke bietet einen eleganten Rahmen zur statistischen Untersuchung der Topologie lokaler und langreichweitiger dynamischer Zusammenhänge (Telekonnektionen) im Klimasystem. Unter Verwendung einer verfeinerten, auf linearen und nichtlinearen Korrelationsmaßen der Zeitreihenanalyse beruhenden Netzwerkkonstruktionsmethode, bilden wir die komplexe Korrelationsstruktur eines multivariaten klimatologischen Datensatzes auf ein Netzwerk ab. Dabei identifizieren wir die Knoten des Netzwerkes mit den Gitterpunkten des zugrundeliegenden Datensatzes, während wir Paare von besonders stark korrelierten Knoten als Kanten auffassen. Die resultierenden Klimanetzwerke zeigen weder die perfekte Regularität eines Kristallgitters, noch eine vollkommen zufällige Topologie. Vielmehr weisen sie faszinierende und nichttriviale Eigenschaften auf, die charakteristisch für natürlich gewachsene Netzwerke wie z.B. das Internet, Zitations- und Bekanntschaftsnetzwerke, Nahrungsnetze und kortikale Netzwerke im Säugetiergehirn sind. Besonders erwähnenswert ist, dass in Klimanetzwerken das Kleine-Welt-Phänomen auftritt. Desweiteren besitzen sie eine breite Gradverteilung, werden von Superknoten mit sehr vielen Nachbarn dominiert, und bilden schließlich regional wohldefinierte Untergruppen von intern dicht vernetzten Knoten aus. Im Rahmen dieser Arbeit wurde eine detaillierte, graphentheoretische Analyse von Klimanetzwerken auf der globalen topologischen Skala durchgeführt, wobei wir uns auf das Netzwerkfluss- und Zentralitätsmaß Betweenness konzentrierten. Betweenness ist zwar lokal an jedem Knoten definiert, enthält aber trotzdem Informationen über die globale Netzwerktopologie. Dies beruht darauf, dass die Verteilung kürzester Pfade zwischen allen möglichen Paaren von Knoten in die Berechnung des Maßes eingeht. Das Betweennessfeld zeigt reichhaltige und zuvor verborgene Strukturen in aus Reanalyse- und Modelldaten der erdoberflächennahen Lufttemperatur gewonnenen Klimanetzen. Das durch unseren neuartigen Ansatz enthüllte Metanetzwerk, bestehend aus hochlokalisierten Kanälen stark gebündelten Informationsflusses, bringen wir mit der Oberflächenzirkulation des Weltozeans in Verbindung. In Analogie mit den gleichnamigen Datenautobahnen des Internets nennen wir dieses Metanetzwerk den Backbone des Klimanetzwerks. Unsere Ergebnisse deuten insgesamt darauf hin, dass Meeresoberflächenströmungen einen wichtigen Beitrag zur Kopplung und Stabilisierung des globalen Oberflächenlufttemperaturfeldes leisten. Wir zeigen weiterhin, dass die hohe Sensitivität des Betweennessmaßes hinsichtlich kleiner Änderungen der Netzwerktopologie die Detektion stark nichtlinearer physikalischer Wechselwirkungen im Klimasystem ermöglichen könnte. Die in dieser Arbeit vorgestellten Ergebnisse wurden mithilfe statistischer Signifikanztests auf der Zeitreihen- und Netzwerkebene gründlich auf ihre Robustheit geprüft. In Anbetracht fehlerbehafteter Daten und komplexer statistischer Zusammenhänge zwischen verschiedenen Netzwerkmaßen ist diese Vorgehensweise besonders wichtig. Weiterhin ist die Entwicklung neuer, allgemein anwendbarer Surrogate für räumlich eingebettete Netzwerke hervorzuheben, die die Berücksichtigung spezieller Klimanetzwerkeigenschaften wie z.B. der Wahrscheinlichkeitsverteilung der Kantenlängen erlauben. Unsere Methode ist universell, weil sie zum Verständnis des lokalisierten Informationsflusses in allen räumlich ausgedehnten, dynamischen Systemen beitragen kann. Deshalb ist sie innerhalb der Physik und anderer angewandter Wissenschaften von potentiell breitem Interesse. Mögliche Anwendungen könnten sich z.B. in der Fluiddynamik (Turbulenz), der Plasmaphysik und der Biophysik (Populationsmodelle, neuronale Netzwerke und Zellmodelle) finden. Darüber hinaus ist der Netzwerkansatz für experimentelle Daten sowie Modellsimulationen gültig, und eröffnet folglich neue Perspektiven für Modellevaluation und datengetriebene Modellierung. Im Rahmen der aktuellen Klimawandeldebatte stellen Klimanetzwerke einen neuartigen Satz von Analysemethoden zur Verfügung, der die Evaluation der lokalen Vulnerabilität und Stabilität des Klimasystems unter Berücksichtigung globaler Randbedingungen ermöglicht. Die in dieser Arbeit entwickelten und untersuchten Methoden könnten folglich in der Zukunft, innerhalb eines holistisch-globalen Ansatzes, zum Verständnis der lokalen Auswirkungen von Extremereignissen und Kipppunkten im Erdsystem beitragen.

Complex networks are employed as a mathematical description of complex systems in many different fields, ranging from biology to sociology, economy and ecology. Dynamical processes in these systems often display phase transitions, where the dynamics of the system changes qualitatively. In combination with these phase transitions certain components of the system might irretrievably go extinct. In this case, we talk about absorbing transitions. Developing mathematical tools, which allow for an analysis and prediction of the observed phase transitions is crucial for the investigation of complex networks. In this thesis, we investigate absorbing transitions in dynamical networks, where a certain amount of diversity is lost. In some real-world examples, e.g. in the evolution of human societies or of ecological systems, it is desirable to maintain a high degree of diversity, whereas in others, e.g. in epidemic spreading, the diversity of diseases is worthwhile to confine. An understanding of the underlying mechanisms for emergence and persistence of diversity in complex systems is therefore essential. Within the scope of two different network models, we develop an analytical approach, which can be used to estimate the prerequisites for diversity. In the first part, we study a model for opinion formation in human societies. In this model, regimes of low diversity and regimes of high diversity are separated by a fragmentation transition, where the network breaks into disconnected components, corresponding to different opinions. We propose an approach for the estimation of the fragmentation point. The approach is based on a linear stability analysis of the fragmented state close to the phase transition and yields much more accurate results compared to conventional methods. In the second part, we study a model for the formation of complex food webs. We calculate and analyze coexistence conditions for several types of species in ecological communities. To this aim, we employ an approach which involves an iterative stability analysis of the equilibrium with respect to the arrival of a new species. The proposed formalism allows for a direct calculation of coexistence ranges and thus facilitates a systematic analysis of persistence conditions for food webs. In summary, we present a general mathematical framework for the calculation of absorbing phase transitions in complex networks, which is based on concepts from percolation theory. While the specific implementation of the formalism differs from model to model, the basic principle remains applicable to a wide range of different models.

Complex systems can often be modelled as networks, in which their basic units are represented by abstract nodes and the interactions among them by abstract links. This network of interactions is the key to understanding emergent collective phenomena in such systems. In most cases, it is an adaptive network, which is defined by a feedback loop between the local dynamics of the individual units and the dynamical changes of the network structure itself. This feedback loop gives rise to many novel phenomena. Adaptive networks are a promising concept for the investigation of collective phenomena in different systems. However, they also present a challenge to existing modelling approaches and analytical descriptions due to the tight coupling between local and topological degrees of freedom. In this thesis, I present a simple rule-based framework for the investigation of adaptive networks, using which a wide range of collective phenomena can be modelled and analysed from a common perspective. In this framework, a microscopic model is defined by the local interaction rules of small network motifs, which can be implemented in stochastic simulations straightforwardly. Moreover, an approximate emergent-level description in terms of macroscopic variables can be derived from the microscopic rules, which we use to analyse the system\'s collective and long-term behaviour by applying tools from dynamical systems theory. We discuss three adaptive-network models for different collective phenomena within our common framework. First, we propose a novel approach to collective motion in insect swarms, in which we consider the insects\' adaptive interaction network instead of explicitly tracking their positions and velocities. We capture the experimentally observed onset of collective motion qualitatively in terms of a bifurcation in this non-spatial model. We find that three-body interactions are an essential ingredient for collective motion to emerge. Moreover, we show what minimal microscopic interaction rules determine whether the transition to collective motion is continuous or discontinuous. Second, we consider a model of opinion formation in groups of individuals, where we focus on the effect of directed links in adaptive networks. Extending the adaptive voter model to directed networks, we find a novel fragmentation mechanism, by which the network breaks into distinct components of opposing agents. This fragmentation is mediated by the formation of self-stabilizing structures in the network, which do not occur in the undirected case. We find that they are related to degree correlations stemming from the interplay of link directionality and adaptive topological change. Third, we discuss a model for the evolution of cooperation among self-interested agents, in which the adaptive nature of their interaction network gives rise to a novel dynamical mechanism promoting cooperation. We show that even full cooperation can be achieved asymptotically if the networks\' adaptive response to the agents\' dynamics is sufficiently fast.

A large number of complex systems can be modelled as networks of interacting units. From a mathematical point of view the topology of such systems can be represented as graphs of which the nodes represent individual elements of the system and the edges interactions or relations between them. In recent years networks have become a principal tool for analyzing complex systems in many different fields. This thesis introduces an information theoretic approach for finding characteristic connectivity patterns of networks, also called network motifs. Network motifs are sometimes also referred to as basic building blocks of complex networks. Many real world networks contain a statistically surprising number of certain subgraph patterns called network motifs. In biological and technological networks motifs are thought to contribute to the overall function of the network by performing modular tasks such as information processing. Therefore, methods for identifying network motifs are of great scientific interest. In the prevalent approach to motif analysis network motifs are defined to be subgraphs that occur significantly more often in a network when compared to a null model that preserves certain features of the network. However, defining appropriate null models and sampling these has proven to be challenging. This thesis introduces an alternative approach to motif analysis which looks at motifs as regularities of a network that can be exploited to obtain a more efficient representation of the network. The approach is based on finding a subgraph cover that represents the network using minimal total information. Here, a subgraph cover is a set of subgraphs such that every edge of the graph is contained in at least one subgraph in the cover while the total information of a subgraph cover is the information required to specify the connectivity patterns occurring in the cover together with their position in the graph. The thesis also studies the connection between motif analysis and random graph models for networks. Developing random graph models that incorporate high densities of triangles and other motifs has long been a goal of network research. In recent years, two such model have been proposed . However, their applications have remained limited because of the lack of a method for fitting such models to networks. In this thesis, we address this problem by showing that these models can be formulated as ensembles of subgraph covers and that the total information optimal subgraph covers can be used to match networks with such models. Moreover, these models can be solved analytically for many of their properties allowing for more accurate modelling of networks in general. Finally, the thesis also analyzes the problem of finding a total information optimal subgraph cover with respect to its computational complexity. The problem turns out to be NP-hard hence, we propose a greedy heuristic for it. Empirical results for several real world networks from different fields are presented. In order to test the presented algorithm we also consider some synthetic networks with predetermined motif structure.

ARAÚJO, Eduardo Barbosa. Scientific Collaboration Networks from Lattes Database: Topology, Dynamics and Gender Statistics. 2016. 88 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2016-07-19T15:58:54Z No. of bitstreams: 1 2016_tese_ebaraujo.pdf: 3600069 bytes, checksum: a78e83ffda97c499e589b405da4da3c8 (MD5) / Approved for entry into archive by Edvander Pires (edvanderpires@gmail.com) on 2016-07-19T15:59:07Z (GMT) No. of bitstreams: 1 2016_tese_ebaraujo.pdf: 3600069 bytes, checksum: a78e83ffda97c499e589b405da4da3c8 (MD5) / Made available in DSpace on 2016-07-19T15:59:07Z (GMT). No. of bitstreams: 1 2016_tese_ebaraujo.pdf: 3600069 bytes, checksum: a78e83ffda97c499e589b405da4da3c8 (MD5) Previous issue date: 2016 / Understanding the dynamics of research production and collaboration may reveal better strategies for scientific careers, academic institutions and funding agencies. Here we propose the use of a large and multidisciplinary database of scientific curricula in Brazil, namely, the Lattes Platform, to study patterns of scientific production and collaboration. Detailed information about publications and researchers is available in this database. Individual curricula are submitted by the researchers themselves so that co-authorship is unambiguous. Researchers can be evaluated by scientific productivity, geographical location and field of expertise. Our results show that the collaboration network is growing exponentially for the last three decades, with a distribution of number of collaborators per researcher that approaches a power-law as the network gets older. Moreover, both the distributions of number of collaborators and production per researcher obey power-law behaviors, regardless of the geographical location or field, suggesting that the same universal mechanism might be responsible for network growth and productivity. We also show that the collaboration network under investigation displays a typical assortative mixing behavior, where teeming researchers (i.e., with high degree) tend to collaborate with others alike. Moreover, we discover that on average men prefer collaborating with other men than with women, while women are more egalitarian. This is consistently observed over all fields and essentially independent on the number of collaborators of the researcher. The solely exception is for engineering, where clearly this gender bias is less pronounced, when the number of collaborators increases. We also find that the distribution of number of collaborators follows a power-law, with a cut-off that is gender dependent. This reflects the fact that on average men produce more papers andhave more collaborators than women. We also find that both genders display the same tendency towards interdisciplinary collaborations, except for Exact and Earth Sciences, where women having many collaborators are more open to interdisciplinary research. / Compreender a dinâmica de produção e colaboração em pesquisa pode revelar melhores estratégias para carreiras científicas, instituições acadêmicas e agências de fomento. Neste trabalho nós propomos o uso de uma grande e multidisciplinar base de currículos científicos brasileira, a Plataforma Lattes, para o estudo de padrões em pesquisa científica e colaborações. Esta base de dados inclui informações detalhadas acerca de publicações e pesquisadores. Currículos individuais são enviados pelos próprios pesquisadores de forma que a identificação de coautoria não é ambígua. Pesquisadores podem ser classificados por produção científica, localização geográfica e áreas de pesquisa. Nossos resultados mostram que a rede de colaborações científicas tem crescido exponencialmente nas últimas três décadas, com a distribuição do número de colaboradores por pesquisador se aproximando de uma lei de potência à medida que a rede evolui. Além disso, ambas a distribuição do número de colaboradores e a produção por pesquisador seguem o comportamento de leis de potência, independentemente da região ou áreas, sugerindo que um mesmo mecanismo universal pode ser responsável pelo crescimento da rede e pela produtividade dos pesquisadores. Também mostramos que as redes de colaboração investigadas apresentam um típico comportamento assortativo, no qual pesquisadores de alto nível (com muitos colaboradores) tendem a colaborador com outros semelhantes. Em seguida, mostramos que homens preferem colaborar com outros homens enquanto mulheres são mais igualitárias ao estabelecer suas colaborações. Isso é consistentemente observado em todas as áreas e é essencialmente independente do número de colaborações do pesquisador. A única exceção sendo a área de Engenharia, na qual este viés é claramente menos pronunciado para pesquisadores com muitas colaborações. Também mostramos que o número de colaborações segue o comportamento de leis de potência, com um cutoff dependente do gênero. Isso se reflete no fato de que em média mulheres produzem menos artigos e têm menos colaborações que homens. Também mostramos que ambos os gêneros exibem a mesma tendência quanto a colaborações interdisciplinares, exceto em Ciências Exatas e da Terra, nas quais mulheres tendo mais colaboradores são mais propensas a pesquisas interdisciplinares.

Nesta tese investigam-se três pontos ligados a fragilidades topológicas de grafos e suas aplicações a redes complexas reais e, em especial, a redes de relacionamentos criminais. Na primeira etapa, apresenta-se in abstracto um método inédito e eficiente de fragmentação de redes complexas por módulos. O procedimento identifica em primeiro lugar comunidades topológicas por meio da qual a rede pode ser representada usando algoritmos heurísticos de extração de comunidades. Então, somente os nós que participam de ligaçõees inter-comunitaárias são removidos em ordem decrescente de sua centralidade de intermediação. Ilustra-se o método pela aplicação a uma variedade de redes reais nas áreas social, de infraestrutura, e biológica. Mostra-se que a abordagem por módulos supera ataques direcionados a vértices baseados somente no ordenamento de índices de centralidade, com ganhos de eficiência fortemente relacionados à modularidade da rede.No segundo momento, introduzem-se os conceitos de robustez e fragilidade de redes generalizadas para avaliar o quanto um determinado sistema se comporta frente a ataques incompletos. Ainda, avalia-se o desempenho (relação entre robustez e custo computacional) de diversos ataques sequenciais e simultâneos a redes modulares por meio de uma medida empírica que chamamos de performance. Mostra-se por meio de redes artificiais de referência e de redes reais que para sistemas altamente modulares a estratégia de fragmentação por módulos apresenta um desempenho até 10 vezes superior aos demais ataques. Na última etapa, explora-se com maior profundidade a natureza subjacente de redes reais de relacionamentos criminais. Apresenta-se uma rede única e sem precedentes construída pela Polícia Federal Brasileira consistindo de mais de 35.000 relacionamentos entre 24.000 indivíduos. Os dados foram coletados entre abril e agosto de 2013 e consistem em informações fornecidas diretamente pelos investigadores responsáveis de cada caso. O sistema apresenta características típicas de redes sociais, porém é bem mais “escuro"que o comportamento típico, com baixos níveis tanto de densidade de arestas quanto de eficiência de rede. Além do mais, o sistema é extremamente modular o que implica ser possível desmantelar toda a rede de crimes federais brasileiros com a remoção de aproximadamente 2% dos indivíduos escolhidos conforme a prescrição do método modular. Também, a rede é controlável no sentido da teoria matemática de controle, significando que com acesso a aproximadamente 20% dos nós é possível, em tese, levar qualquer variável dinâmica de um estado inicial a um estado final arbitrário em um tempo finito. Exibi-se tambám uma análise topológica e de fragilidades de uma segunda rede criminal relacionada a investigações da Polícia Federal. Trata-se de um fórum online destinado à prática de crimes cibernéticos na chamada camada profunda da internet (deep web). (Continuação ) Após a coleta dos dados foi possível construir uma rede de relacionamentos com quase 10.000 indivíduos. Comparou-se, entãoo, a estratégia usada de fato pela Polícia Federal durante a Operação Darknet com a previsão teórica de ataques topológicos à rede criminal e mostrou-se que ataques dirigidos por grau teriam fragmentado o sistema de maneira quase 15 vezes mais eficiente. Por outro lado, esta rede não é modular apesar de novamente apresentar uma arquitetura mais “escura" que o usual. Por termo, demonstra-se que os ataques por arestas estão diretamente relacionados ao aprisionamento enquanto que a ressocialização e/ou morte dos indivíduos é melhor interpretada como a remoção por vértices. Destarte, comprovou-se que de um ponto de vista topológico a ressocialização é de fato mais eficiente em reduzir a criminalidade do que o aprisionamento. Contudo, na rede de crimes federais estudada essa diferenca é muito pequena, de tal modo que ambas as políticas poderiam, em tese, ser aplicadas a fim de se combater eficientemente o sistema criminoso. / In this thesis we investigate three points connected to topological fragilities of graphs and their applications to real complex networks and, in particular, to networks of criminal relationships. In the first step, we present an unprecedented and efficient method of fragmentation of complex networks by modules. Firstly, the procedure identifies topological communities through which the network can be represented using heuristic communities extraction algorithms. After that, only the nodes that bridge communities are removed in descending order of their betweenness centrality . We illustrate the method by the applying it to a variety of real networks in the social, infrastructure, and biological fields. We show that the modular approach outperforms attacks traditional attacks based only on the ordering of centrality indexes, with efficiency gains strongly related to the modularity of the network. In the second moment, we introduce the concepts of generalized robustness and fragility of networks to evaluate how much a certain system behaves in the face of incomplete attacks. Also, we evaluate the relation between robustness and computational cost of several sequential and simultaneous attacks to modular networks by means of an empirical measure that we call performance. In this sense, we show through artificial and real networks that for highly modular systems the strategy of fragmentation by modules presents a performance up to 10 times superior to traditional attacks. In the last step, we explore in more depth the underlying nature of real networks of criminal relationships. We present a unique and unprecedented network built by the Brazilian Federal Police consisting of more than 35,000 relationships among 24,000 individuals. The data were collected between April and August 2013 and consist of information provided directly by the investigators responsible for each case. The system has typical characteristics of social networks, but is much "darker"than traditional social networks, with low levels of edge density and network efficiency. Moreover, the network is extremely modular which implies that it is possible to dismantle all the network of Brazilian federal crimes with the removal of approximately 2% of the individuals chosen according to the modular method. Also the network is controllable in the sense of the mathematical control theory, meaning that with access only to 20% of nodes it is possible, In theory, to take any dynamic variable from an initial state to an arbitrary final state in a finite time. We also show a topological analysis of a second criminal network related to Federal Police investigations. This is an online forum for cybercrime in the so-called deep web. After the data collection, it was possible to build a network of relationships with almost 10,000 individuals. We then compared the strategy actually used by the Federal Police during Operation Darknet with the theoretical prediction of topological attacks on the criminal network and showed that degree-based attacks would have fragmented the system almost 15 times more efficiently. On the other hand, this network is not modular despite presenting a "darker"architecture than usual. As a last result, this particular system is not controllable in practical terms. We finish the study by showing that edge attacks are directly related to the imprisonment whereas the resocialization and/or death of the individuals is better interpreted as the removal of vertices. Thus, we prove that from a topological point of view resocialization is in fact more efficient in reducing crime rates than imprisonment. However, in the network of federal crimes studied here this difference is very small, so that both policies could in theory be applied in order to combat effectively the criminal system.

Orientador: David Corrêa Martins Júnior / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Neurociência e Cognição, 2016. / A biologia sistêmica é um campo de pesquisa interdisciplinar que estuda as complexas interações que ocorrem entre os componentes biológicos de um organismo vivo com o objetivo de entender o seu comportamento, o qual emerge a partir dessas interações. Essas interações compõem uma rede altamente complexa, cujos interagentes podem ser de diversas naturezas. Nesse contexto, as doenças complexas são caracterizadas justamente por serem poligênicas e multifatoriais, ou seja, a gênese e o desenvolvimento dessas doenças são uma consequência da interação conjunta de diversos fatores, incluindo não apenas genes, proteínas e outras moléculas, como também fatores epigenéticos e ambientais. No entanto, diferentes métodos de priorização gênica apresentam resultados (listas de genes) com baixa convergência. Assim, a comparação desses métodos é uma questão crucial. Os objetivos principais da presente dissertação foram a realização de uma extensa revisão da literatura em relação às técnicas de priorização de genes associados a doenças complexas e a comparação de algumas dessas técnicas. Foram selecionadas duas ferramentas: o WGCNA (Weighted Gene Correlation Network Analysis) e o NERI (Network-Medicine Relative Importance), ambos métodos que baseiam-se em teoria de redes complexas e co-expressão para priorização gênica, sendo que o NERI tem o diferencial de modelar as hipóteses da Network Medicine para priorização com base na integração de dados de expressão, de redes de interação proteína-proteína (PPI) e de estudos de associação. Para comparação dos resultados, foram utilizados três bancos de dados de expressão gênica relacionados a esquizofrenia. Como previsto, devido ao diferencial de integração de dados proposto pelo NERI, tal técnica resultou em listas de genes com replicação superior à obtida pelo WGCNA para os três bancos de dados em questão. Além disso a interseção entre as listas de genes priorizados de cada metodologia foi baixa, com poucos genes sendo compartilhados pelos resultados dos dois métodos. Ambas metodologias selecionaram genes com relevância biológica relacionada a esquizofrenia, incluindo grupos de genes relacionados a atividade do sistema imune (infecções, estresse), atividade do Sistema Nervoso Central (atividade sináptica, crescimento axonal) e também de embriogênese. Baseando-se nesses resultados, conclui-se que a análise de redes e a integração de dados biológicos são fundamentais para uma ferramenta apresentar resultados promissores, sobretudo no âmbito da descoberta de novos genes e suas redes de interação biológica que seriam possivelmente desconhecidas se fosse realizada apenas a análise individual de cada tipo de dado biológico disponível. / Systems Biology is an interdisciplinary research field which studies the complex interactions that occur between biological compounds of a living organism in order to understand their behavior, which emerges from these interactions. Such interactions compose a highly complex network, whose elements can be of several types. In this context, complex diseases are characterized precisely by being of polygenic and multifactorial nature, i.e., the genesis and development of these diseases are a result of the joint interaction of several factors, including not only genes, proteins and other molecules, but also epigenetic and environmental factors. However, many methods for gene prioritization present results (list of genes) with small convergence. Thus, the comparison involving those methods is a crucial issue. The main objectives of this master thesis was to perform an extensive literature review related to gene prioritization techniques associated to complex diseases and the comparison of part of these techniques. Two techniques were selected: WGCNA (Weighted Gene Correlation Network Analysis) and NERI (Network-Medicine Relative Importance), both methods based on complex networks theory and co-expression for gene prioritization, but NERI having the differential of modeling the Network Medicine hypotheses for prioritization based on integration of expression, protein-protein interaction (PPI) network and association studies. For comparison of the results, three gene expression databases related to schizophrenia were adopted. As predicted, due to the data integration proposed by NERI, such technique resulted in genes lists with superior replication for the three databases mentioned. Additionally, the intersection between the results of the genes lists prioritized by the two methodologies was small, with few genes being found in both lists. Both methods selected biologically relevant to schizophrenia, including groups of genes related to imune system activity (infections, stress), Central Nervous System activity (synaptic activity, axonal growth) and embryogenesis. From these results, it follows that network analysis and biological data integration are fundamental for a gene prioritization method to present promising results, mainly for discovery of new genes and their biological interaction networks that would possibly be unknown if only an individual analysis of each biological data available were performed.

Nesta tese investigam-se três pontos ligados a fragilidades topológicas de grafos e suas aplicações a redes complexas reais e, em especial, a redes de relacionamentos criminais. Na primeira etapa, apresenta-se in abstracto um método inédito e eficiente de fragmentação de redes complexas por módulos. O procedimento identifica em primeiro lugar comunidades topológicas por meio da qual a rede pode ser representada usando algoritmos heurísticos de extração de comunidades. Então, somente os nós que participam de ligaçõees inter-comunitaárias são removidos em ordem decrescente de sua centralidade de intermediação. Ilustra-se o método pela aplicação a uma variedade de redes reais nas áreas social, de infraestrutura, e biológica. Mostra-se que a abordagem por módulos supera ataques direcionados a vértices baseados somente no ordenamento de índices de centralidade, com ganhos de eficiência fortemente relacionados à modularidade da rede.No segundo momento, introduzem-se os conceitos de robustez e fragilidade de redes generalizadas para avaliar o quanto um determinado sistema se comporta frente a ataques incompletos. Ainda, avalia-se o desempenho (relação entre robustez e custo computacional) de diversos ataques sequenciais e simultâneos a redes modulares por meio de uma medida empírica que chamamos de performance. Mostra-se por meio de redes artificiais de referência e de redes reais que para sistemas altamente modulares a estratégia de fragmentação por módulos apresenta um desempenho até 10 vezes superior aos demais ataques. Na última etapa, explora-se com maior profundidade a natureza subjacente de redes reais de relacionamentos criminais. Apresenta-se uma rede única e sem precedentes construída pela Polícia Federal Brasileira consistindo de mais de 35.000 relacionamentos entre 24.000 indivíduos. Os dados foram coletados entre abril e agosto de 2013 e consistem em informações fornecidas diretamente pelos investigadores responsáveis de cada caso. O sistema apresenta características típicas de redes sociais, porém é bem mais “escuro"que o comportamento típico, com baixos níveis tanto de densidade de arestas quanto de eficiência de rede. Além do mais, o sistema é extremamente modular o que implica ser possível desmantelar toda a rede de crimes federais brasileiros com a remoção de aproximadamente 2% dos indivíduos escolhidos conforme a prescrição do método modular. Também, a rede é controlável no sentido da teoria matemática de controle, significando que com acesso a aproximadamente 20% dos nós é possível, em tese, levar qualquer variável dinâmica de um estado inicial a um estado final arbitrário em um tempo finito. Exibi-se tambám uma análise topológica e de fragilidades de uma segunda rede criminal relacionada a investigações da Polícia Federal. Trata-se de um fórum online destinado à prática de crimes cibernéticos na chamada camada profunda da internet (deep web). (Continuação ) Após a coleta dos dados foi possível construir uma rede de relacionamentos com quase 10.000 indivíduos. Comparou-se, entãoo, a estratégia usada de fato pela Polícia Federal durante a Operação Darknet com a previsão teórica de ataques topológicos à rede criminal e mostrou-se que ataques dirigidos por grau teriam fragmentado o sistema de maneira quase 15 vezes mais eficiente. Por outro lado, esta rede não é modular apesar de novamente apresentar uma arquitetura mais “escura" que o usual. Por termo, demonstra-se que os ataques por arestas estão diretamente relacionados ao aprisionamento enquanto que a ressocialização e/ou morte dos indivíduos é melhor interpretada como a remoção por vértices. Destarte, comprovou-se que de um ponto de vista topológico a ressocialização é de fato mais eficiente em reduzir a criminalidade do que o aprisionamento. Contudo, na rede de crimes federais estudada essa diferenca é muito pequena, de tal modo que ambas as políticas poderiam, em tese, ser aplicadas a fim de se combater eficientemente o sistema criminoso. / In this thesis we investigate three points connected to topological fragilities of graphs and their applications to real complex networks and, in particular, to networks of criminal relationships. In the first step, we present an unprecedented and efficient method of fragmentation of complex networks by modules. Firstly, the procedure identifies topological communities through which the network can be represented using heuristic communities extraction algorithms. After that, only the nodes that bridge communities are removed in descending order of their betweenness centrality . We illustrate the method by the applying it to a variety of real networks in the social, infrastructure, and biological fields. We show that the modular approach outperforms attacks traditional attacks based only on the ordering of centrality indexes, with efficiency gains strongly related to the modularity of the network. In the second moment, we introduce the concepts of generalized robustness and fragility of networks to evaluate how much a certain system behaves in the face of incomplete attacks. Also, we evaluate the relation between robustness and computational cost of several sequential and simultaneous attacks to modular networks by means of an empirical measure that we call performance. In this sense, we show through artificial and real networks that for highly modular systems the strategy of fragmentation by modules presents a performance up to 10 times superior to traditional attacks. In the last step, we explore in more depth the underlying nature of real networks of criminal relationships. We present a unique and unprecedented network built by the Brazilian Federal Police consisting of more than 35,000 relationships among 24,000 individuals. The data were collected between April and August 2013 and consist of information provided directly by the investigators responsible for each case. The system has typical characteristics of social networks, but is much "darker"than traditional social networks, with low levels of edge density and network efficiency. Moreover, the network is extremely modular which implies that it is possible to dismantle all the network of Brazilian federal crimes with the removal of approximately 2% of the individuals chosen according to the modular method. Also the network is controllable in the sense of the mathematical control theory, meaning that with access only to 20% of nodes it is possible, In theory, to take any dynamic variable from an initial state to an arbitrary final state in a finite time. We also show a topological analysis of a second criminal network related to Federal Police investigations. This is an online forum for cybercrime in the so-called deep web. After the data collection, it was possible to build a network of relationships with almost 10,000 individuals. We then compared the strategy actually used by the Federal Police during Operation Darknet with the theoretical prediction of topological attacks on the criminal network and showed that degree-based attacks would have fragmented the system almost 15 times more efficiently. On the other hand, this network is not modular despite presenting a "darker"architecture than usual. As a last result, this particular system is not controllable in practical terms. We finish the study by showing that edge attacks are directly related to the imprisonment whereas the resocialization and/or death of the individuals is better interpreted as the removal of vertices. Thus, we prove that from a topological point of view resocialization is in fact more efficient in reducing crime rates than imprisonment. However, in the network of federal crimes studied here this difference is very small, so that both policies could in theory be applied in order to combat effectively the criminal system.