Some topics in combinatorial phylogenetics

2010 Summer.Includes bibliographic references.Covers not scanned.Print version deaccessioned 2022.This thesis is in combinatorial phylogenetics and is focused on a study of Hadamard conjugation. It examines the question of whether the presence of an abelian permutation group acting regularly on the states is necessary for the application of this technique. New connections between phylogenetics and algebraic combinatorics are suggested, especially with (commutative) association schemes

Using network properties to predict disease dynamics on human contact networks

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations