This dissertation covers the two major parts of my Ph.D. research: i) developing theoretical framework of complex networks; and ii) applying complex networks models to quantitatively analyze economics systems. In part I, we focus on developing theories of interdependent networks, which includes two chapters: 1) We develop a mathematical framework to study the percolation of interdependent networks under targeted-attack and find that when the highly connected nodes are protected and have lower probability to fail, in contrast to single scale-free (SF) networks where the percolation threshold pc\ = 0, coupled SF networks are significantly more vulnerable with pc\ significantly larger than zero. 2) We analytically demonstrate that clustering, which quantifies the propensity for two neighbors of the same vertex to also be neighbors of each other, significantly increases the vulnerability of the system. In part II, we apply the complex networks models to study economics systems, which also includes two chapters: 1) We study the US corporate governance network, in which nodes representing directors and links between two directors representing their service on common company boards, and propose a quantitative measure of information and influence transformation in the network. Thus we are able to identify the most influential directors in the network. 2) We propose a bipartite networks model to simulate the risk propagation process among commercial banks during financial crisis. With empirical bank's balance sheet data in 2007 as input to the model, we find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation during the financial crisis between 2008 and 2011. The results suggest that complex networks model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008 - 2011.

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Equilibration, thermalization and scrambling appear to be intimately related, however their exact relation is unknown. As presented in the introduction these fields are at their current stages still quite popular and new directions are appearing regularly. We first put the fields into focus in the introduction and then the following chapters present three manuscripts as my contributions to these fields during my Master of Science project. Further introductions and background are presented in the manuscripts and my contributions are summarized at the beginning of each chapter. / Thesis / Master of Science (MSc)

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by Hon-chor Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaf 56). / by Hon-chor Lee. / Introduction --- p.1 / Series expansion for the conductivity of a linear random resistor network / Chapter 1. --- Introduction --- p.4 / Chapter 2. --- Comparison of the EMA with symbolic simulations in 2D --- p.5 / Chapter 3. --- Comparison of the EMA with Bergman and Kantor's findings --- p.6 / Chapter 4. --- Conclusion --- p.7 / Current moments of linear random resistor network / Chapter 1. --- Introduction --- p.10 / Chapter 2. --- Review of the definition of current moment --- p.10 / Chapter 3. --- Tremblay et. al.'s findings and symbolic simulation of current moments --- p.11 / Chapter 4. --- Conclusion --- p.13 / Effective medium theory for strongly nonlinear composites: comparison with numerical simulations / Chapter 1. --- Introduction --- p.15 / Chapter 2. --- Variational principles --- p.16 / Chapter 3. --- Formalism of EMA --- p.17 / Chapter 4. --- Comparison with numerical simulations --- p.19 / Chapter 5. --- Discussion --- p.21 / Percolative conduction in two-component strongly nonlinear composites / Chapter 1. --- Introduction --- p.25 / Chapter 2. --- Spherical inclusions --- p.25 / Chapter 3. --- Effective medium approximation in the vicinity of the percolation threshold --- p.27 / Chapter 4. --- Acknowledgment --- p.29 / Percolation Effects in Two Component Strongly Nonlinear Composites: Universal Scaling Behaviours / Chapter 1. --- Introduction --- p.31 / Chapter 2. --- General Scaling Relations for Two-Component Composites --- p.33 / Chapter 3. --- Estimate of Critical Exponents --- p.35 / Chapter 4. --- Numerical Simulations --- p.38 / Chapter 5. --- Discussions and Conclusions --- p.40 / Chapter 6. --- Acknowledgment --- p.40 / Improved effective medium theory for strongly nonlinear composites / Chapter 1. --- Introduction --- p.46 / Chapter 2. --- Formalism of Improved EMA --- p.47 / Chapter 3. --- Comparisons with numerical simulations and HS bound --- p.50 / Chapter 4. --- Discussions --- p.51 / Conclusion --- p.54

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 80-87).

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 99-114).

Interactions are what gives us the knowledge of the world around us. Interactions on all levels may fundamentally be seen as an exchange of information and a possible response of the same. Whether it is an electron in an electrical field or a handsome dude in a bar responding to a flirtation---interactions make things happen. In this sense we can see that objects without the capability of interacting with each other also are invisible to each other. Chains of pairwise interacting entities can serve as mediators of indirect interactions between objects. Nonetheless, in the limit of no interactions, we get into a philosophical debate whether we actually may consider anything to exist since it can not be detected in any way. Interactions between matter tend to be organized and show a hierarchical structure in which smaller sub-systems can be seen as parts of a bigger system, which in turn might be a smaller part of an even bigger system. This is reflected by the fact that we have sciences that successfully study specific interactions between objects or matter---physics, chemistry, biology, ecology, sociology,... What happens in a situation where all length scales are important? How does the structure of the underlying network of interactions affect the dynamical properties of a system? What network structures do we find and how are they created? This thesis is a physicist's view of collective dynamics, from superconductors to social systems and navigation in city street networks.

The main aim of this work is to study percolation theory on regular two dimensional / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2002.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 53-54). Also available in electronic version.