Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

Modelling and quantifying brain connectivity and dynamics with applications in aging and ADHD

Human brain is a complex organ and made up of integrative networks encompassing a large number of regions. These regions communicate with each other to share information involved in complex cognitive processes. Functional connectivity (FC) represents the level of synchronization between different brain regions/networks. Studying functional interactions of the brain creates a platform for understanding functional architecture of the brain as an integrative network and has implications for understanding human cognition. Furthermore, there is evidence that FC patterns are sensitive to different diseases. In addition, age is a significant determinant of intra-/inter-individual variability in the FC patterns. Therefore, key aims for the studies included in this thesis were to apply and develop novel resting-state FC methodologies, with applications in healthy aging and ADHD. Indeed, measures of the brain’s FC may serve as a useful tool to diagnose and predict the course of disease, and useful in developing individualized therapies. Age- or disease-related alterations in the FC could reflect a multitude of factors, including changes in structural connectivity. However, we still have limited knowledge of the emergence of brain dynamics from the underlying anatomy. The interplay between the brain’s structure and dynamics underlies all brain functions. Therefore, in the last study we focused on the systematic modeling of the brain network dynamics. Large-scale computational models are uniquely suited to address difficult questions related to the role of brain’s structural network in shaping functional interactions. In addition, computational modeling of the brain enables us to test different hypotheses without any experimental complication while it provides us with a platform for improving our understanding of different brain mechanisms. A new macroscopic computational model of the brain oscillations for resting-state fMRI was introduced in this thesis, which outperforms previous model in the same class. Then, the effects of malfunctions in different brain regions were simulated and subsequently predicted perturbation patterns were recruited for local vulnerability mapping as well as quantification of hazard rates induced after perturbing any brain regio

Module hierarchy and centralisation in the anatomy and dynamics of human cortex

Systems neuroscience has recently unveiled numerous fundamental features of the macroscopic architecture of the human brain, the connectome, and we are beginning to understand how characteristics of brain dynamics emerge from the underlying anatomical connectivity. The current work utilises complex network analysis on a high-resolution structural connectivity of the human cortex to identify generic organisation principles, such as centralised, modular and hierarchical properties, as well as specific areas that are pivotal in shaping cortical dynamics and function. After confirming its small-world and modular architecture, we characterise the cortex’ multilevel modular hierarchy, which appears to be reasonably centralised towards the brain’s strong global structural core. The potential functional importance of the core and hub regions is assessed by various complex network metrics, such as integration measures, network vulnerability and motif spectrum analysis. Dynamics facilitated by the large-scale cortical topology is explored by simulating coupled oscillators on the anatomical connectivity. The results indicate that cortical connectivity appears to favour high dynamical complexity over high synchronizability. Taking the ability to entrain other brain regions as a proxy for the threat posed by a potential epileptic focus in a given region, we also show that epileptic foci in topologically more central areas should pose a higher epileptic threat than foci in more peripheral areas. To assess the influence of macroscopic brain anatomy in shaping global resting state dynamics on slower time scales, we compare empirically obtained functional connectivity data with data from simulating dynamics on the structural connectivity. Despite considerable micro-scale variability between the two functional connectivities, our simulations are able to approximate the profile of the empirical functional connectivity. Our results outline the combined characteristics a hierarchically modular and reasonably centralised macroscopic architecture of the human cerebral cortex, which, through these topological attributes, appears to facilitate highly complex dynamics and fundamentally shape brain function

Network science for social and technological systems

This thesis contains a collection of research outcomes from the field of complex networks. The results presented here have been divided in two parts, one devoted to theoretical methods and the other to data-driven applications. Although many of the results, especially in the first part, are general enough for describing many complex systems, a special focus on social systems has been used throughout the thesis. The first part contains ideas that explore the interplay of topology and dynamics in complex systems, divided in three chapters dedicated to opinion dynamics, modular networks and weighted networks respectively. Regarding opinion dynamics, we study the emergence of self-organised leadership and herding behaviour in the voter model. Regarding modular networks, we present a generative model for networks with community structure and arbitrary bridgeness distribution. We also show how bridgeness interplays with functional behaviour in different dynamical systems. We use such interplay to define the concept of dynamical centrality, and show its applications to network dismantling under limited topological information. Finally, we demonstrate how topological uncertainty in link weights induces fluctuations on the critical threshold for multiple dynamical processes on networks. We also discuss the role of degree heterogeneity in this propagation, finding non-trivial dependencies for scale-free networks. The second part contains two applications of network analysis to real-world systems. The first application is a data study on the rail network of London and its surrounding area. We show how topological resilience measures are strongly correlated to the performance of train operators in the network. The second application contains a network-based model of armed conflict prediction at city level of analysis. We use several centrality measures as features for machine learning models, showing how network information generates very significant improvements in out-of-sample prediction performance

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