Philosophiae Doctor - PhD / Adaptive networks are complex networks with nontrivial topological features and connection patterns between their elements which are neither purely regular nor purely random. Their applications are in sociology, biology, physics, genetics, epidemiology, chemistry, ecology, materials science, the traditional Internet and the emerging Internet of-Things. For example, their applications in sociology include social networks such as Facebook which have recently raised the interest of the research community. These networks may hide patterns which, when revealed, can be of great interest in many practical applications. While the current adaptive network models remain mostly theoretical and conceptual, however, there is currently no unified modelling framework for implementing the development, comparison, communication and validation of agent-based adaptive network models through using proper empirical data and computation models from different research fields. In this thesis, a unified framework has been developed that combines agent- based adaptive network models and adaptive control structures. In this framework, the control parameters of adaptive network models are included as a part of the state- topology coevolution and are automatically adjusted according to the observations obtained from the system being studied. This allows the automatic generation of enhanced adaptive networks by systematically adjusting both the network topology and the control parameters at the same time to accurately reflect the real-world complex system. We develop three different applications within the general framework for agent- based adaptive network modelling and simulation of real-world complex systems in different research fields. First, a unified framework which combines adaptive net- work models and adaptive control structures is proposed for modelling and simulation of fractured-rock aquifer systems. Moreover, we use this unified modelling framework to develop an automatic modelling tool, Fracture3D, for automatically building enhanced fracture adaptive network models of fractured-rock aquifer systems, in which the fracture statistics and the structural properties can both follow the observed statistics from natural fracture networks. We show that the coupling between the fracture adaptive network models and the adaptive control structures with iterative parameter identification can drive the network topology towards a desired state by dynamically updating the geometrical states of fractures with a proper adaptive control structure. Second, we develop a unified framework which combines adaptive network models and multiple model adaptive control structures for modelling and simulation of social network systems. By using such a unified modelling framework, an automatic modelling tool, SMRI, is developed for automatically building the enhanced social adaptive network models through using mobile-phone-centric multimodal data with suitable computational models of behavioural state update and social interaction update. We show that the coupling between the social adaptive network models and the multiple model adaptive control structures can drive the community structure of a social adaptive network models towards a desired state through using the suitable computational models of behavioural state update and social interaction update predetermined by the multiple model adaptive control structure. Third, we develop a unified framework which combines adaptive network models and support vector machine based adaptive control structures for modelling and simulation of multicast congestion in mobile ad hoc network systems. Moreover, a multicast congestion detection scheme, WMCD, has been developed for the unified modelling framework, in which the incipient congestions of group members can be predicted by using support vector machine-based prediction models and current traffic states. We show that the network’s throughput capacity is efficiently improved through using the unified modelling framework, which dynamically adjusting the group structures according to the updated congestion states of group members generated by the WMCD scheme in order to relieve the high load.

The dynamics on networks and the dynamics of networks are usually entangled with each other in many highly connected systems, where the former means the evolution of state and the latter means the adaptation of structure. In this thesis, we will study the coupled dynamics through analytical and computational approaches, where the adaptive networks are driven by learning of various complexities. Firstly, we investigate information diffusion on networks through an adaptive voter model, where two opinions are competing for the dominance. Two types of dynamics facilitate the agreement between neighbours: one is pairwise imitation and the other is link rewiring. As the rewiring strength increases, the network of voters will transform from consensus to fragmentation. By exploring various strategies for structure adaptation and state evolution, our results suggest that network configuration is highly influenced by range-based rewiring and biased imitation. In particular, some approximation techniques are proposed to capture the dynamics analytically through moment-closure differential equations. Secondly, we study an evolutionary model under the framework of natural selection. In a structured community made up of cooperators and cheaters (or defectors), a new-born player will adopt a strategy and reorganise its neighbourhood based on social inheritance. Starting from a cooperative population, an invading cheater may spread in the population occasionally leading to the collapse of cooperation. Such a collapse unfolds rapidly with the change of external conditions, bearing the traits of a critical transition. In order to detect the risk of invasions, some indicators based on population composition and network structure are proposed to signal the fragility of communities. Through the analyses of consistency and accuracy, our results suggest possible avenues for detecting the loss of cooperation in evolving networks. Lastly, we incorporate distributed learning into adaptive agents coordination, which emerges as a consequence of rational individual behaviours. A generic framework of work-learn-adapt (WLA) is proposed to foster the success of agents organisation. To gain higher organisation performance, the division of labour is achieved by a series of events of state evolution and structure adaptation. Importantly, agents are able to adjust their states and structures through quantitative information obtained from distributed learning. The adaptive networks driven by explicit learning pave the way for a better understanding of intelligent organisations in real world.

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Reviewing inter-state warfare literature, I observe a correlation between the growth of international institutions, economic interchange, and levels of democracy, and corresponding decreases in incidents of international war. Conversely, internal conflicts comprise most conflicts in the post-1945 world, compared to inter-state conflicts. Within the larger intra-state literature, I note an underlying lineage to concepts evolving from Kant’s writings, specifically Kantian democratic peace theory (DPT) literature posited by Russett and ONeal (2001), and the informal social-juridical relationship within Metaphysics of Morals. From that pedigree, could a deeper understanding of internal political risks gained through application of Kantian DPT, interpolating Putnam’s (2002) Social Capital Theory (SCT) hold potential to provide researchers and policy makers insight into propensity for descent into conflict early enough to implement corrective actions? This investigation initially questions existence of intra-state processes performing similar ameliorating or exacerbating functions observed at inter-state level. Assessing that intra-state dynamics exhibit an elevated dependence on social factors necessitates adjustments to DPT to accommodate the adaptable nature of social constructs, leading to the designation of my theory as Kantian Adaptable Networks Theory (KANT). To test hypotheses, I start with DPT, incorporate elements of SCT, and identify a hybrid combination presenting greater explanatory power than either DPT or SCT factors alone. Fund for Peace’s Fragile State Indices (FSI) for 2005-2013 provides the dataset to conduct regression analysis to determine significance of DPT and/or SCT elements in static and time-series. Initial results indicate DPT/SCT provides explanatory value at the intra-state level with the Group Grievance factor generally presenting the most significant effect on probability of conflict. To assess resilience to intra-state conflict, I then explore brittleness of social-contract dynamics through the lens of Clausewitz’ center of gravity theory. In my exploration of applicability of KANT at the case level, I analyze FSI data for Syria and Kenya to determine resilience to shocks and ratcheted pressures, and explanation for differing outcomes. Based on the results of quantitative and case analysis, I present policy prescription considerations. Finally, I discuss additional avenues for follow-on research of issues and opportunities identified during the course of the investigation.

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.

This master thesis is the result of a collaborative work between EMBRAER and the Escola Politécnica da USP for the study of structural health monitoring (SHM) techniques using sensors applied to aircraft structures. The goal was to develop classification techniques to discriminate between different events arising in the aircraft structure during tests; in the short term, improving the current SHM system used by EMBRAER, based on acoustic emission and, in the long term, fostering the development of a fully distributed system. As a result of studying classification methods for immediate use, we developed two techniques: the Spectral Similarity and a Support Vector Machines (SVM) classifier. Both are unsupervised solutions, due to the unlabeled nature of the data provided. The two solutions were delivered as a final product to EMBRAER for prompt use in the existing SHM system. By studying distributed solutions for future implementations, we developed a detection algorithm based on adaptive techniques. The main result was a special initialization for a maximum likelihood (ML) detector that yields an exponential decay rate in the error probability to a nonzero steady state, using adaptive diffusion estimation in a distributed sensor network. The nodes that compose the network must decide, locally, between two concurrent hypotheses concerning the environment state where they are inserted, using local measurements and shared estimates coming from their neighbors. The exponential performance does not depend on the adaptation step size value, provided it is sufficiently small. The results concerning this distributed detector were published in the journal IEEE Signal Processing Letters. / Esta dissertação de mestrado é o resultado de um trabalho colaborativo entre a EMBRAER e a Escola Politécnica da USP no estudo de técnicas de monitoramento do estado de saúde de estruturas (Structural Health Monitoring - SHM) utilizando sensores em estruturas aeronáuticas. O objetivo foi desenvolver técnicas de classificação para discriminar entre diferentes eventos que surgem em estruturas aeronáuticas durante testes; para o curto prazo, aperfeiçoando o atual sistema de SHM utilizado pela EMBRAER, baseado em emissão acústica e, no longo prazo, fomentando o desenvolvimento de um sistema completamente distribuído. Como resultado do estudo de métodos de classificação para uso imediato, desenvolvemos duas técnicas: a Similaridade Espectral e um classificador que utiliza Support Vector Machines (SMV). Ambas as técnicas são soluções não-supervisionadas, devido a natureza não rotulada dos dados fornecidos. As duas soluções foram entregues como um produto final para a EMBRAER para pronta utilização em seu atual sistema de SHM. Ao estudar soluções completamente distribuídas para futuras implementações, desenvolvemos um algoritmo de detecção baseado em técnicas adaptativas. O principal resultado foi uma inicialização especial para um detector de máxima verossimilhança (maximum likelihood - ML) que possui uma taxa de decaimento exponencial na probabilidade de erro até um valor não nulo em regime estacionário, utilizando estimação adaptativa em uma rede distribuída. Os nós que compõem a rede devem decidir, localmente, entre duas hipóteses concorrentes com relação ao estado do ambiente onde eles estão inseridos, utilizando medidas locais e estimativas compartilhadas vindas de nós vizinhos. O desempenho exponencial não depende do valor do passo de adaptação, se este for suficientemente pequeno. Os resultas referentes a este detector distribuído foram publicados na revista internacional IEEE Signal Processing Letters.

This master thesis is the result of a collaborative work between EMBRAER and the Escola Politécnica da USP for the study of structural health monitoring (SHM) techniques using sensors applied to aircraft structures. The goal was to develop classification techniques to discriminate between different events arising in the aircraft structure during tests; in the short term, improving the current SHM system used by EMBRAER, based on acoustic emission and, in the long term, fostering the development of a fully distributed system. As a result of studying classification methods for immediate use, we developed two techniques: the Spectral Similarity and a Support Vector Machines (SVM) classifier. Both are unsupervised solutions, due to the unlabeled nature of the data provided. The two solutions were delivered as a final product to EMBRAER for prompt use in the existing SHM system. By studying distributed solutions for future implementations, we developed a detection algorithm based on adaptive techniques. The main result was a special initialization for a maximum likelihood (ML) detector that yields an exponential decay rate in the error probability to a nonzero steady state, using adaptive diffusion estimation in a distributed sensor network. The nodes that compose the network must decide, locally, between two concurrent hypotheses concerning the environment state where they are inserted, using local measurements and shared estimates coming from their neighbors. The exponential performance does not depend on the adaptation step size value, provided it is sufficiently small. The results concerning this distributed detector were published in the journal IEEE Signal Processing Letters. / Esta dissertação de mestrado é o resultado de um trabalho colaborativo entre a EMBRAER e a Escola Politécnica da USP no estudo de técnicas de monitoramento do estado de saúde de estruturas (Structural Health Monitoring - SHM) utilizando sensores em estruturas aeronáuticas. O objetivo foi desenvolver técnicas de classificação para discriminar entre diferentes eventos que surgem em estruturas aeronáuticas durante testes; para o curto prazo, aperfeiçoando o atual sistema de SHM utilizado pela EMBRAER, baseado em emissão acústica e, no longo prazo, fomentando o desenvolvimento de um sistema completamente distribuído. Como resultado do estudo de métodos de classificação para uso imediato, desenvolvemos duas técnicas: a Similaridade Espectral e um classificador que utiliza Support Vector Machines (SMV). Ambas as técnicas são soluções não-supervisionadas, devido a natureza não rotulada dos dados fornecidos. As duas soluções foram entregues como um produto final para a EMBRAER para pronta utilização em seu atual sistema de SHM. Ao estudar soluções completamente distribuídas para futuras implementações, desenvolvemos um algoritmo de detecção baseado em técnicas adaptativas. O principal resultado foi uma inicialização especial para um detector de máxima verossimilhança (maximum likelihood - ML) que possui uma taxa de decaimento exponencial na probabilidade de erro até um valor não nulo em regime estacionário, utilizando estimação adaptativa em uma rede distribuída. Os nós que compõem a rede devem decidir, localmente, entre duas hipóteses concorrentes com relação ao estado do ambiente onde eles estão inseridos, utilizando medidas locais e estimativas compartilhadas vindas de nós vizinhos. O desempenho exponencial não depende do valor do passo de adaptação, se este for suficientemente pequeno. Os resultas referentes a este detector distribuído foram publicados na revista internacional IEEE Signal Processing Letters.

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.

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.