Graph-Theoretical Tools for the Analysis of Complex Networks

We are currently experiencing an explosive growth in data collection technology that threatens to dwarf the commensurate gains in computational power predicted by Moore’s Law. At the same time, researchers across numerous domain sciences are finding success using network models to represent their data. Graph algorithms are then applied to study the topological structure and tease out latent relationships between variables. Unfortunately, the problems of interest, such as finding dense subgraphs, are often the most difficult to solve from a computational point of view. Together, these issues motivate the need for novel algorithmic techniques in the study of graphs derived from large, complex, data sources. This dissertation describes the development and application of graph theoretic tools for the study of complex networks. Algorithms are presented that leverage efficient, exact solutions to difficult combinatorial problems for epigenetic biomarker detection and disease subtyping based on gene expression signatures. Extensive testing on publicly available data is presented supporting the efficacy of these approaches. To address efficient algorithm design, a study of the two core tenets of fixed parameter tractability (branching and kernelization) is considered in the context of a parallel implementation of vertex cover. Results of testing on a wide variety of graphs derived from both real and synthetic data are presented. It is shown that the relative success of kernelization versus branching is found to be largely dependent on the degree distribution of the graph. Throughout, an emphasis is placed upon the practicality of resulting implementations to advance the limits of effective computation

Essays in economic prehistory

This thesis consists of three papers that explore early human organization. In the first paper I argue that the economic and social structure of early humans would have resulted in an especially difficult consanguinity problem. In particular, adverse selection in the exogamous marriage market would have resulted in high levels of consanguinity and resulting fitness depression. A partial solution to this problem was the evolution of aversion to endogamy, known as the Westermarck effect, and was essential for the survival of our species. The second paper (joint with Haiyun Chen) develops a model that explains linguistic diversity as the cumulative result of strategic incentives faced by linguistic groups. In this model, autonomous groups interact periodically in games that represent either cooperation, competition, or a lack of interaction. Common language facilitates cooperation such as trade, whereas language unique to one group affords that group an advantage in competitive interactions. The relative frequency of cooperation and conflict in a region provides incentives for each group to modify their own language, and therefore leads to changes in linguistic diversity over time. Our model predicts that higher frequency of conflict relative to cooperation will increase a region\u27s linguistic diversity. The third paper (joint with Gregory K. Dow and Clyde G. Reed) investigates the incidence of early warfare among foragers and farmers in prehistory. Our focus is specifically on conflict over land. Food is produced using inputs of labor and land, and the probability of victory in a conflict depends on relative group sizes. The group sizes are determined by individual migration and Malthusian population dynamics. Both factors result in larger populations at better sites, which deters attack. There are two necessary conditions for warfare: high enough individual mobility costs and large enough shocks to the relative productivities of the sites. Together, these conditions are sufficient. In particular, technological or environmental shocks that alter the productivities of sites can trigger warfare, but only if individual agents do not change sites in response. These results are consistent with evidence from archaeology and anthropology