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Final doctoral examination and defense of dissertation of Stephen Young

Title: Random Dot Product Graphs: A Flexible Model for Complex Networks

Time:	Tuesday, November 11th, 1:30pm
Location:	269 Skiles Building
Advisor:	Dr. Milena Mihail
Committee:	Dr. Prasad Tetali, School of Mathematics
	Dr. W. T. Trotter, School of Mathematics
	Dr. Xingxing Yu, School of Mathematics
	Dr. Joel Sokol, School of Industrial and Systems Engineering
Reader:	Dr. Linyuan Lu, University of South Carolina

Abstract:

At its heart, the study of complex networks is the quest for understanding the presence of structure where there is no a priori reason for such structure. This phenomena occurs in a wide range of contexts, from "optimized" networks such as the structure of the physical layer of the Internet and the power grid, to evolved networks such as gene-protein interaction networks and food webs, and from networks with "costly" edges such as sexual contact networks and collaboration networks to networks with "free" edges such as the LiveJournal friend network and the World Wide Web. Given that networks with such dissimilar sources exhibit similar behaviors, such as power-law degree distribution, clustering, and small diameter, it is natural to hope for a model of the various complex networks that would have explanatory power for all such networks. In many ways the Holy Grail of the study of complex networks is a flexible and robust model that encapsulates a large class (hopefully all) of complex networks and has the ability to be "fit" to various different networks, and further, that they should respect the semantic content of the underlying network in order that an understanding of the fitted model can be used to extract an understanding of the underlying network. The goal of this thesis is to prove a robust and flexible model that will hopefully be a stepping stone towards the eventual discovery of such a "Holy Grail" model.

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