A probabilistic model for the evaluation of module extraction algorithms in complex biological networks

This thesis presents CiGRAM, a model of complex networks ith known modular structure that is capable of generating realistic graph topology. Much of the recent focus on module detection has been geared towards developing new algorithms capable of detecting biologically significant clusters. However, evaluating clusterings detected by different methods shows that there is little topological agreement or consensus in terms of meta-data despite most methods discovering modules with significant ontology. In this thesis an approach to modelling complex networks with ground-truth modular structure is presented. This approach is capable of generating graphs with heterogeneous degree distributions, high clustering coefficients and assortative degree correlations observed in real data but often ignored in existing benchmarks. Moreover, the model for modular structure concludes that non-modular random graphs are indistinguishable from modules. This model can be tuned to fit many empirical biological and non-biological datasets through fitting target graph summary statistics. The ground-truth structure allows the evaluation of module extraction algorithms in a domain specific context. Furthermore, it was found that degree assortativity appears to negatively impact several module extraction methods such as the popular infomap and modularity maximisation methods. Results presented disagree with other benchmark models highlighting the potential for future research into improving existing methods in ways that challenge assumptions about the detectability of modules

A probabilistic model for the evaluation of module extraction algorithms in complex biological networks

This thesis presents CiGRAM, a model of complex networks ith known modular structure that is capable of generating realistic graph topology. Much of the recent focus on module detection has been geared towards developing new algorithms capable of detecting biologically significant clusters. However, evaluating clusterings detected by different methods shows that there is little topological agreement or consensus in terms of meta-data despite most methods discovering modules with significant ontology. In this thesis an approach to modelling complex networks with ground-truth modular structure is presented. This approach is capable of generating graphs with heterogeneous degree distributions, high clustering coefficients and assortative degree correlations observed in real data but often ignored in existing benchmarks. Moreover, the model for modular structure concludes that non-modular random graphs are indistinguishable from modules. This model can be tuned to fit many empirical biological and non-biological datasets through fitting target graph summary statistics. The ground-truth structure allows the evaluation of module extraction algorithms in a domain specific context. Furthermore, it was found that degree assortativity appears to negatively impact several module extraction methods such as the popular infomap and modularity maximisation methods. Results presented disagree with other benchmark models highlighting the potential for future research into improving existing methods in ways that challenge assumptions about the detectability of modules

The modular structure of brain functional connectivity networks: a graph theoretical approach

Complex networks theory offers a framework for the analysis of brain functional connectivity as measured by magnetic resonance imaging. Within this approach the brain is represented as a graph comprising nodes connected by links, with nodes corresponding to brain regions and the links to measures of inter-regional interaction. A number of graph theoretical methods have been proposed to analyze the modular structure of these networks. The most widely used metric is Newman's Modularity, which identifies modules within which links are more abundant than expected on the basis of a random network. However, Modularity is limited in its ability to detect relatively small communities, a problem known as ``resolution limit''. As a consequence, unambiguously identifiable modules, like complete sub-graphs, may be unduly merged into larger communities when they are too small compared to the size of the network. This limit, first demonstrated for Newman's Modularity, is quite general and affects, to a different extent, all methods that seek to identify the community structure of a network through the optimization of a global quality function. Hence, the resolution limit may represent a critical shortcoming for the study of brain networks, and is likely to have affected many of the studies reported in the literature. This work pioneers the use of Surprise and Asymptotical Surprise, two quality functions rooted in probability theory that aims at overcoming the resolution limit for both binary and weighted networks. Hereby, heuristics for their optimization are developed and tested, showing that the resulting optimal partitioning can highlight anatomically and functionally plausible modules from brain connectivity datasets, on binary and weighted networks. This novel approach is applied to the partitioning of two different human brain networks that have been extensively characterized in the literature, to address the resolution-limit issue in the study of the brain modular structure. Surprise maximization in human resting state networks revealed the presence of a rich structure of modules with heterogeneous size distribution undetectable by current methods. Moreover, Surprise led to different, more accurate classification of the network's connector hubs, the elements that integrate the brain modules into a cohesive structure. In synthetic networks, Asymptotical Surprise showed high sensitivity and specificity in the detection of ground-truth structures, particularly in the presence of noise and variability such as those observed in experimental functional MRI data. Finally, the methodological advances hereby introduced are shown to be a helpful tool to better discern differences between the modular organization of functional connectivity of healthy subjects and schizophrenic patients. Importantly, these differences may point to new clinical hypotheses on the etiology of schizophrenia, and they would have gone unnoticed with resolution-limited methods. This may call for a revisitation of some of the current models of the modular organization of the healthy and diseased brain

The influence of topology and information diffusion on networked game dynamics

This thesis studies the influence of topology and information diffusion on the strategic interactions of agents in a population. It shows that there exists a reciprocal relationship between the topology, information diffusion and the strategic interactions of a population of players. In order to evaluate the influence of topology and information flow on networked game dynamics, strategic games are simulated on populations of players where the players are distributed in a non-homogeneous spatial arrangement. The initial component of this research consists of a study of evolution of the coordination of strategic players, where the topology or the structure of the population is shown to be critical in defining the coordination among the players. Next, the effect of network topology on the evolutionary stability of strategies is studied in detail. Based on the results obtained, it is shown that network topology plays a key role in determining the evolutionary stability of a particular strategy in a population of players. Then, the effect of network topology on the optimum placement of strategies is studied. Using genetic optimisation, it is shown that the placement of strategies in a spatially distributed population of players is crucial in maximising the collective payoff of the population. Exploring further the effect of network topology and information diffusion on networked games, the non-optimal or bounded rationality of players is modelled using topological and directed information flow of the network. Based on the topologically distributed bounded rationality model, it is shown that the scale-free and small-world networks emerge in randomly connected populations of sub-optimal players. Thus, the topological and information theoretic interpretations of bounded rationality suggest the topology, information diffusion and the strategic interactions of socio-economical structures are cyclically interdependent

The influence of topology and information diffusion on networked game dynamics

This thesis studies the influence of topology and information diffusion on the strategic interactions of agents in a population. It shows that there exists a reciprocal relationship between the topology, information diffusion and the strategic interactions of a population of players. In order to evaluate the influence of topology and information flow on networked game dynamics, strategic games are simulated on populations of players where the players are distributed in a non-homogeneous spatial arrangement. The initial component of this research consists of a study of evolution of the coordination of strategic players, where the topology or the structure of the population is shown to be critical in defining the coordination among the players. Next, the effect of network topology on the evolutionary stability of strategies is studied in detail. Based on the results obtained, it is shown that network topology plays a key role in determining the evolutionary stability of a particular strategy in a population of players. Then, the effect of network topology on the optimum placement of strategies is studied. Using genetic optimisation, it is shown that the placement of strategies in a spatially distributed population of players is crucial in maximising the collective payoff of the population. Exploring further the effect of network topology and information diffusion on networked games, the non-optimal or bounded rationality of players is modelled using topological and directed information flow of the network. Based on the topologically distributed bounded rationality model, it is shown that the scale-free and small-world networks emerge in randomly connected populations of sub-optimal players. Thus, the topological and information theoretic interpretations of bounded rationality suggest the topology, information diffusion and the strategic interactions of socio-economical structures are cyclically interdependent

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page

AN EDGE-CENTRIC PERSPECTIVE FOR BRAIN NETWORK COMMUNITIES

Thesis (Ph.D.) - Indiana University, Department of Psychological and Brain Sciences and Program in Neuroscience, 2021The brain is a complex system organized on multiple scales and operating in both a local and distributed manner. Individual neurons and brain regions participate in specific functions, while at the same time existing in the context of a larger network, supporting a range of different functionalities. Building brain networks comprised of distinct neural elements (nodes) and their interrelationships (edges), allows us to model the brain from both local and global perspectives, and to deploy a wide array of computational network tools. A popular network analysis approach is community detection, which aims to subdivide a network’s nodes into clusters that can used to represent and evaluate network organization. Prevailing community detection approaches applied to brain networks are designed to find densely interconnected sets of nodes, leading to the notion that the brain is organized in an exclusively modular manner. Furthermore, many brain network analyses tend to focus on the nodes, evidenced by the search for modular groupings of neural elements that might serve a common function. In this thesis, we describe the application of community detection algorithms that are sensitive to alternative cluster configurations, enhancing our understanding of brain network organization. We apply a framework called the stochastic block model, which we use to uncover evidence of non-modular organization in human anatomical brain networks across the life span, and in the informatically-collated rat cerebral cortex. We also propose a framework to cluster functional brain network edges in human data, which naturally results in an overlapping organization at the level of nodes that bridges canonical functional systems. These alternative methods utilize the connection patterns of brain network edges in ways that prevailing approaches do not. Thus, we motivate an alternative outlook which focuses on the importance of information provided by the brain’s interconnections, or edges. We call this an edge-centric perspective. The edge-centric approaches developed here offer new ways to characterize distributed brain organization and contribute to a fundamental change in perspective in our thinking about the brain

Mathematical programming based approaches for classes of complex network problems : economical and sociological applications

The thesis deals with the theoretical and practical study of mathematical programming methodologies to the analysis complex networks and their application in economic and social problems. More specifically, it applies models and methods for solving linear and integer programming problems to network models exploiting the matrix structure of such models, resulting in efficient computational procedures and small processing time. As a consequence, it allows the study of larger and more complex networks models that arise in many economical and sociological applications. The main efforts have been addressed to the development of a rigorous mathematical programming based framework, which is able to capture many classes of complex network problems. Such a framework involves a general and flexible modeling approach, based on linear and integer programmin, as well as a collection of efficient probabilistic procedures to deal with these models. The computer implementation has been carried out by high level programming languages, such as Java, MatLab, R and AMPL. The final chapter of the thesis introduced an extension of the analyzed model to the case of microeconomic interaction, providing a fruitful mathematical linkage between its optimization-like properties and its multi-agents properties. The theoretical and practical use of optimization methods represents the trait-de-union of the different chapters. The overall structure of the thesis manuscript contains three parts: Part I: The fine-grained structure of complex networks: theories, models and methods; Chapter 1 and Chapter 2. Part II: Mathematical Programming based approaches for random models of network formation; Chapter 3, Chapter 4 and Chapter 5. Part III: Strategic models of network formation. Chapter 6. Results of this research have generated four working papers in quality scientific journals: one has been accepted and three are under review. Some results have been also presented in four international conferences.La tesis aborda el estudio teórico y práctico de las metodologías de programación matemática para el análisis de redes complejas y su aplicación a problemas económicos y sociales. Más específicamente, se aplica modelos y métodos para resolver problemas de programación lineal y de programación lineal entera explotando las estructuras matriciales de tales modelos, lo que resulta en procedimientos computacionales eficientes y bajo coste de procesamiento. Como consecuencia de ello, las metodologías propuestas permiten el estudio de modelos complejos de gran dimensión, para redes complejas que surgen en muchas aplicaciones económicas y sociológicas. Los principales esfuerzos se han dirigido al desarrollo de un marco teórico basado en la programación matemática, que es capaz de capturar muchas clases de problemas de redes complejas. Dicho marco teórico envuelve un sistema general y flexible de modelado y una colección de procedimientos probabilísticos para solucionar eficientemente dichos modelos, basados en la programación linear y entera. Las implementaciones informáticas se han llevado a cabo mediante lenguajes de programación de alto nivel, como Java, Matlab, R y AMPL. El último capítulo de la tesis introduce una extensión de los modelos analizados, para el caso de la interacción microeconómica, con el objetivo de establecer un nexo metodológico entre sus propiedades de optimización y sus propiedades multi-agentes. El uso teórico y práctico de los métodos de optimización representa el elemento de conjunción de los distintos capítulos. Parte I: The fine-grained structure of complex networks: theories, models and methods; - Capitulo 1 y Capitulo 2. Parte II: Mathematical Programming based approaches for random models of network formation; - Capitulo 3, Capitulo 4 y Capitulo 5. Parte III: Strategic models of network formation. - Capitulo 6. Los resultados de esta investigación han generado cuatro papers en revistas científicas indexadas: uno ha sido aceptado, tres están en revisión. Algunos resultados han sido también presentados en cuatro conferencias internacionale