Inference, simulation, modeling, and analysis of complex networks, with special emphasis on complex networks in systems biology

Across diverse fields ranging from physics to biology, sociology, and economics, the technological advances of the past decade have engendered an unprecedented explosion of data on highly complex systems with thousands, if not millions of interacting components. These systems exist at many scales of size and complexity, and it is becoming ever-more apparent that they are, in fact, universal, arising in every field of study. Moreover, they share fundamental properties---chief among these, that the individual interactions of their constituent parts may be well-understood, but the characteristic behaviour produced by the confluence of these interactions---by these complex networks---is unpredictable; in a nutshell, the whole is more than the sum of its parts.;There is, perhaps, no better illustration of this concept than the discoveries being made regarding complex networks in the biological sciences. In particular, though the sequencing of the human genome in 2003 was a remarkable feat, scientists understand that the "cellular-level blueprints" for the human being are cellular-level parts lists, but they say nothing (explicitly) about cellular-level processes. The challenge of modern molecular biology is to understand these processes in terms of the networks of parts---in terms of the interactions among proteins, enzymes, genes, and metabolites---as it is these processes that ultimately differentiate animate from inanimate, giving rise to life! It is the goal of systems biology---an umbrella field encapsulating everything from molecular biology to epidemiology in social systems---to understand processes in terms of fundamental networks of core biological parts, be they proteins or people.;By virtue of the fact that there are literally countless complex systems, not to mention tools and techniques used to infer, simulate, analyze, and model these systems, it is impossible to give a truly comprehensive account of the history and study of complex systems. The author's own publications have contributed network inference, simulation, modeling, and analysis methods to the much larger body of work in systems biology, and indeed, in network science. The aim of this thesis is therefore twofold: to present this original work in the historical context of network science, but also to provide sufficient review and reference regarding complex systems (with an emphasis on complex networks in systems biology) and tools and techniques for their inference, simulation, analysis, and modeling, such that the reader will be comfortable in seeking out further information on the subject.;The review-like Chapters 1, 2, and 4 are intended to convey the co-evolution of network science and the slow but noticeable breakdown of boundaries between disciplines in academia as research and comparison of diverse systems has brought to light the shared properties of these systems. It is the author's hope that theses chapters impart some sense of the remarkable and rapid progress in complex systems research that has led to this unprecedented academic synergy.;Chapters 3 and 5 detail the author's original work in the context of complex systems research. Chapter 3 presents the methods and results of a two-stage modeling process that generates candidate gene-regulatory networks of the bacterium B.subtilis from experimentally obtained, yet mathematically underdetermined microchip array data. These networks are then analyzed from a graph theoretical perspective, and their biological viability is critiqued by comparing the networks' graph theoretical properties to those of other biological systems. The results of topological perturbation analyses revealing commonalities in behavior at multiple levels of complexity are also presented, and are shown to be an invaluable means by which to ascertain the level of complexity to which the network inference process is robust to noise.;Chapter 5 outlines a learning algorithm for the development of a realistic, evolving social network (a city) into which a disease is introduced. The results of simulations in populations spanning two orders of magnitude are compared to prevaccine era measles data for England and Wales and demonstrate that the simulations are able to capture the quantitative and qualitative features of epidemics in populations as small as 10,000 people. The work presented in Chapter 5 validates the utility of network simulation in concurrently probing contact network dynamics and disease dynamics.