[pt] Esta tese aborda diversos problemas que podem ser tratados mediante modelos de dinâmica de opiniões, segundo os quais os indivíduos, conectados de acordo com redes complexas, interagem mediante regras que moldam as preferências e o posicionamento desses indivíduos com relação a uma determinada questão. A metodologia utilizada para investigar os padrões emergentes dessas interações consiste na utilização de diversas técnicas da física estatística. A tese está organizada em torno de quatro problemas distintos, com uma questão particular a ser respondida em cada caso, buscando sempre a validação empírica dos resultados teóricos e computacionais. No primeiro trabalho, é respondida a seguinte questão básica sobre propriedades da rede que podem ter impacto sobre os processos de propagação: quais são os valores típicos das distâncias, coeficiente de aglomeração e outras grandezas estruturais da rede, quando considerado o ensemble de redes aleatórias com uma assortatividade fixa? No segundo trabalho, investigamos os padrões que surgem na avaliação de filmes, considerando como fonte o IMDb (Internet Movie Database). Encontramos que a distribuição de votos apresenta um comportamento livre de escala com um expoente muito próximo de 3/2. Curiosamente, esse padrão é robusto, independente de atributos dos filmes como nota média, idade ou gênero. A análise empírica aponta para um mecanismo de propagação de adoções simples, que gera uma dinâmica de avalanches de campo médio. No terceiro trabalho, abordamos o problema de múltiplas escolhas por meio de um modelo que inclui a possibilidade de indecisão e onde as escolhas dos indivíduos evoluem segundo uma regra de pluralidade. Mostramos que essa dinâmica em redes com a propriedade de mundo pequeno produz diferentes estados estacionários realísticos, que dependem do número de alternativas e da distribuição de graus: consenso, distribuição de adoções larga similar à reais e situações onde a indecisão predomina, quando o número de alternativas é suficientemente grande. Por último, investigamos o surgimento de posições extremas na sociedade, mediante pesquisas em uma ampla gama de questões. O aumento de atitudes extremas tem como precursor uma relação não linear entre a fração de extremistas e a de moderados. Propomos um modelo, com regras de ativação baseadas na teimosia dos indivíduos, que permite interpretar o início da não linearidade em termos de uma transição abrupta do tipo percolação de inicialização onde acontecem cascatas de extremismo. Como conclusão geral, destacamos que esta tese ilustra como os modelos de opinião, aliados às enormes bases de dados, fornecem resultados com poder de interpretação e predição dos padrões empíricos. / [en] This thesis addresses several problems that can be treated through models of opinion dynamics, according to which individuals, connected according to complex networks, interact through rules that shape their preferences and opinions in relation to a particular issue. The methodology used to investigate the patterns that emerge from those interactions relies on the use of various techniques of statistical physics. The thesis is organized around four distinct problems, with a particular question to be answered in each case, always looking for empirical validation of the theoretical and computational results. In the first work, it is answered the following basic question about network properties that can have impact on the spreading processes: what are the typical values of the distances, clustering coefficient and other structural quantities, when considering the ensemble of random networks with fix assortativity? In the second study, we investigated the patterns that emerge in the ratings of films, considering as source IMDb (Internet Movie Database). We found that the distribution of votes has a scale-free behavior with a exponent close to 3/2. Interestingly, this pattern is robust, independently of movie attributes such as average note, age or gender. The empirical analysis points to a simple mechanism of adoption propagation, that generates mean-field avalanches. In the third study, we discuss the problem of multiple choices by means of a model which includes the possibility of indecision and where the choices of individuals evolve according to a plurality rule. We show that this dynamics on top of networks with the small-world property produces different stationary states that depend on the number of alternatives and on the degree distribution: consensus, wide adoption distributions similar to actual ones and situations where indecision prevails when the number of alternatives is large enough. Finally, we investigate the appearance of extreme positions in society, through the polls on a wide variety of questions. The increase of extreme opinions has as precursor a non-linear relationship between the fraction of extremists and that of moderates. We propose a model with activation rules, based on the stubbornness of the individuals, which enables interpreting the beginning of the non-linearity in terms of an abrupt transition of the class of bootstrap percolation, where activation cascades occur. As a general conclusion, we emphasize that this thesis illustrates how opinion models, combined with huge databases, provide results with power of interpretation and prediction of empirical patterns.

Criminal networks exploit vulnerabilities in the global financial system, using it as a conduit to launder criminal proceeds. Law enforcement agencies, financial institutions, and regulatory organizations often scrutinize voluminous financial records for suspicious activities and criminal conduct as part of anti-money laundering investigations. However, such studies are narrowly focused on incidents and triggered by tip-offs rather than data mining insights. This research models cross-border financial flows using a network theoretic approach and proposes a symmetric-key encryption algorithm to preserve information privacy in multi-dimensional data sets. The newly developed tools will enable regulatory organizations, financial institutions, and law enforcement agencies to identify suspicious activity and criminal conduct in cross-border financial transactions. Anti-money laundering, which comprises laws, regulations, and procedures to combat money laundering, requires financial institutions to verify and identify their customers in various circumstances and monitor suspicious activity transactions. Instituting anti-money laundering laws and regulations in a country carries the benefit of creating a data-rich environment, thereby facilitating non-classical analytical strategies and tools. Graph theory offers an elegant way of representing cross-border payments/receipts between resident and non-resident parties (nodes), with links representing the parties' transactions. The network representations provide potent data mining tools, facilitating a better understanding of transactional patterns that may constitute suspicious transactions and criminal conduct. Using network science to analyze large and complex data sets to detect anomalies in the data set is fast becoming more important and exciting than merely learning about its structure. This research leverages advanced technology to construct and visualize the cross-border financial flows' network structure, using a directed and dual-weighted bipartite graph. Furthermore, the develops a centrality measure for the proposed cross-border financial flows network using a method based on matrix multiplication to answer the question, "Which resident/non-resident nodes are the most important in the cross-border financial flows network?" The answer to this question provides data mining insights about the network structure. The proposed network structure, centrality measure, and characterization using degree distributions can enable financial institutions and regulatory organizations to identify dominant nodes in complex multi-dimensional data sets. Most importantly, the results showed that the research provides transaction monitoring capabilities that allow the setting of customer segmentation criteria, complementing the built-in transaction-specific triggers methods for detecting suspicious activity transactions. / Thesis (PhD)--University of Pretoria, 2021. / Banking Sector Education and Training Authority (BANKSETA) / UP Postgraduate Bursary / Industrial and Systems Engineering / PhD / Unrestricted

This work proposes a three-state microscopic opinion formation model based on the stochastic dynamics of the three-state majority-vote model. In order to mimic the heterogeneous compositions of societies, the agent-based model considers two different types of individuals: noise agents and contrarians. We propose an extension of the model for the simulation of the dynamics of financial markets. Agents are represented as nodes in a network of interactions and they can assume any of three distinct possible states (e.g. buy, sell or remain inactive, in a financial context). The time evolution of the state of an agent is dictated by probabilistic dynamics that include both local and global influences. A noise agent is subject to local interactions, tending to assume the majority state of its nearest neighbors with probability 1-q (dissenting from it with a probability given by the noise parameter q). A contrarian is subject to a global interaction with the society as a whole, tending to assume the state of the global minority of said society with probability 1 -q (dissenting from it with probability q). The stochastic dynamics are simulated on complex networks of different topologies, including square lattices, Barabási-Albert networks, Erdös-Rényi random graphs and small-world networks built according to a link rewiring scheme. We perform Monte Carlo simulations to study the second-order phase transition of the system on small-world networks. We perform finite-size scaling analysis and calculate the phase diagram of the system, as well as the standard critical exponents for different values of the rewiring probability. We conclude that the rewiring of the lattice drives the system to different universality classes than that of the three-state majority-vote model on a two dimensional square lattice. The model’s extension for financial markets exhibits the typical qualitative and quantitative features of real financial time series, including heavy-tailed return distributions, volatility clustering and long-term memory for the absolute values of the returns. The histograms of returns are fitted by means of coupled exponential distributions, quantitatively revealing transitions between leptokurtic, mesokurtic and platykurtic regimes in terms of a nonlinear statistical coupling and a shape parameter which describe the complexity of the system.

Systems such as the power grid, world wide web (WWW), and internet are categorized as complex systems because of the presence of a large number of interacting elements. For example, the WWW is estimated to have a billion webpages and understanding the dynamics of such a large number of individual agents (whose individual interactions might not be fully known) is a challenging task. Complex network representations of these systems have proved to be of great utility. Statistical physics is the study of emergence of macroscopic properties of systems from the characteristics of the interactions between individual molecules. Hence, statistical physics of complex networks has been an effective approach to study these systems. In this dissertation, I have used statistical physics to study two distinct phenomena in complex systems: i) Cascading failures and ii) Shortest paths in complex networks. Understanding cascading failures is considered to be one of the “holy grails“ in the study of complex systems such as the power grid, transportation networks, and economic systems. Studying failures of these systems as percolation on complex networks has proved to be insightful. Previously, cascading failures have been studied extensively using two different models: k-core percolation and interdependent networks. The first part of this work combines the two models into a general model, solves it analytically, and validates the theoretical predictions through extensive computer simulations. The phase diagram of the percolation transition has been systematically studied as one varies the average local k-core threshold and the coupling between networks. The phase diagram of the combined processes is very rich and includes novel features that do not appear in the models which study each of the processes separately. For example, the phase diagram consists of first- and second-order transition regions separated by two tricritical lines that merge together and enclose a two-stage transition region. In the two-stage transition, the size of the giant component undergoes a first-order jump at a certain occupation probability followed by a continuous second-order transition at a smaller occupation probability. Furthermore, at certain fixed interdependencies, the percolation transition cycles from first-order to second-order to two-stage to first-order as the k-core threshold is increased. We setup the analytical equations describing the phase boundaries of the two-stage transition region and we derive the critical exponents for each type of transition. Understanding the shortest paths between individual elements in systems like communication networks and social media networks is important in the study of information cascades in these systems. Often, large heterogeneity can be present in the connections between nodes in these networks. Certain sets of nodes can be more highly connected among themselves than with the nodes from other sets. These sets of nodes are often referred to as ’communities’. The second part of this work studies the effect of the presence of communities on the distribution of shortest paths in a network using a modular Erdős-Rényi network model. In this model, the number of communities and the degree of modularity of the network can be tuned using the parameters of the model. We find that the model reaches a percolation threshold while tuning the degree of modularity of the network and the distribution of the shortest paths in the network can be used as an indicator of how the communities are connected.

First and foremost, I would like to extend my deepest gratitude to my advisor, Professor Narsingh Deo, for his excellent guidance and encouragement, and also for introducing me to this wonderful science of complex networks. Without his support this dissertation would not have been possible. I would also like to thank the members of my research committee, professors Charles Hughes, Ratan Guha, Mainak Chatterjee and Yue Zhao for their advice and guidance during the entire process. I am indebted to the faculty and the staff of the Department of Electrical Engineering and Computer Science for providing me the resources and environment to perform this research. I am grateful to my colleagues in the Parallel and Quantum computing lab for the stimulating discussions and support. I would also like to thank Dr. Hemant Balakrishnan and Dr. Sanjeeb Nanda for their valuable suggestions and guidance. My heartfelt thanks to my parents, Vasudevan and Raji, who have always been supportive of my decisions and encouraged me with their best wishes. I would also like to thank my sister Gomathy, for her words of care and affection during tough times. Special thanks to my friends in Orlando for being there when I needed them

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We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. Correspondences between relations and graphs are given and a brief introduction to graph theory is followed by a more detailed study of cohesiveness and centrality. We show how graph degeneracy is equivalent to the concept of k-cores, which give a measure of the cohesiveness or interconnectedness of a subgraph. We then further extend this to d-cores of directed graphs. After a brief introduction to topology, focusing on topological spaces from distances, we present a historical discussion on the early developments of algebraic topology. This is followed by a more formal introduction to simplicial homology where we define the homology groups. In the context of algebraic topology, the d-cores of a digraph give rise to a partially ordered set of subgraphs, leading to a set of filtrations that is two-dimensional in nature. Directed clique complexes of digraphs are defined in order to encode the directionality of complete subdigraphs. Finally, we apply these methods to the neuronal network of C.elegans. Persistent homology with respect to directed core filtrations as well as robustness of homology to targeted edge percolations in different directed cores is analyzed. Much importance is placed on intuition and on unifying methods of such dispersed disciplines as sociology and network neuroscience, by rooting them in pure mathematics. / Vi presenterar en rigorös men lättillgänglig introduktion till de abstrakta strukturer på ändliga mängder som är grundläggande för en formell studie av komplexa nätverk. Detta inkluderar en grundlig redogörelse av binära relationer och distansrum, deras egenskaper samt likheter. Korrespondenser mellan olika typer av relationer och grafer förklaras och en kort introduktion till grafteori följs av en mer detaljerad studie av sammanhållning och centralitet. Vi visar hur begreppet 'degeneracy' är ekvivalent med begreppet k-kärnor (eng: k-cores), vilket ger ett mått på sammanhållningen hos en delgraf. Vi utökar sedan detta till konceptet d-kärnor (eng: d-cores) för riktade grafer. Efter en kort introduktion till topologi med fokus på topologiska rum från distansrum, så presenterar vi en historisk diskussion kring den tidiga utvecklingen av algebraisk topologi. Detta följs av en mer formell introduktion till homologi, där vi bl.a. definierar homologigrupperna. Vi definierar sedan så kallade riktade klick-komplex som simplistiska komplex (eng: simplicial complexes) från riktade grafer, där d-kärnorna av en riktad graf då ger upphov till filtrerade komplex i två parametrar. Persistent homologi med avseende på dessa riktade kärnfiltreringar såväl som robusthet mot kantpercolationer i olika kärnor analyseras sedan för det neurala nätverket hos C.Elegans. Stor vikt läggs vid intuition och förståelse, samt vid att förena metodiker för så spridda discipliner som sociologi och neurovetenskap.

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Human mobility is a complex phenomenon emerging from the nexus between social, demographic, economic, political and environmental systems. In this thesis we develop novel mathematical models for the study of complex systems, to improve our understanding of mobility patterns and enhance our ability to predict local and global flows for real-world applications.The first and second chapters introduce the concept of human mobility from the point of view of complex systems science, showing the relation between human movements and their predominant drivers. In the second chapter in particular, we will illustrate the state of the art and a summary of our scientific contributions. The rest of the thesis is divided into three parts: structure, causes and effects.The third chapter is about the structure of a complex system: it represents our methodological contribution to Network Science, and in particular to the problem of network reconstruction and topological analysis. We propose a novel methodological framework for the definition of the topological descriptors of a complex network, when the underlying structure is uncertain. The most used topological descriptors are redefined – even at the level of a single node – as probability distributions, thus eluding the reconstruction phase. With this work we have provided a new approach to study the topological characteristics of complex networks from a probabilistic perspective. The forth chapter deals with the effects of human mobility: it represents our scientific contribution to the debate about the COVID-19 pandemic and its consequences. We present a complex-causal analysis to investigate the relationship between environmental conditions and human activity, considered as the components of a complex socio-environmental system. In particular, we derive the network of relations between different flavors of human mobility data and other social and environmental variables. Moreover, we studied the effects of the restrictions imposed on human mobility – and human activities in general – on the environmental system. Our results highlight a statistically significant qualitative improvement in the environmental variable of interest, but this improvement was not caused solely by the restrictions due to COVID-19 pandemic, such as the lockdown.The fifth and sixth chapters deal with the modelling of causes of human mobility: the former is a concise chapter that illustrate the phenomenon of human displacements caused by environmental disasters. Specifically, we analysed data from different sources to understand the factors involved in shaping mobility patterns after tropical cyclones. The latter presents the Feature-Enriched Radiation Model (FERM), our generalization of the Radiation Model which is a state-of-the-art mathematical model for human mobility. While the original Radiation Model considers only the population as a proxy for mobility drivers, the FERM can handle any type of exogenous information that is used to define the attractiveness of different geographical locations. The model exploits this information to divert the mobility flows towards the most attractive locations, balancing the role of the population distribution. The mobility patterns at different scales can be reshaped, following the exogenous drivers encoded in the features, without neglecting the global configuration of the system.

The changing topology of a network is driven by the need to maintain or optimize network function. As this function is often related to moving quantities such as traffic, information, etc., efficiently through the network, the structure of the network and the dynamics on the network directly depend on the other. To model this interplay of network structure and dynamics we use the dynamics on the network, or the dynamical processes the network models, to influence the dynamics of the network structure, i.e., to determine where and when to modify the network structure. We model the dynamics on the network using Jackson network dynamics and the dynamics of the network structure using minimal specialization, a variant of the more general network growth model known as specialization. The resulting model, which we refer to as the integrated specialization model, coevolves both the structure and the dynamics of the network. We show this model produces networks with real-world properties, such as right-skewed degree distributions, sparsity, the small-world property, and non-trivial equitable partitions. Additionally, when compared to other growth models, the integrated specialization model creates networks with small diameter, minimizing distances across the network. Along with producing these structural features, this model also sequentially removes the network's largest bottlenecks. The result are networks that have both dynamic and structural features that allow quantities to more efficiently move through the network.