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Mathematics and Statistics
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(Thesis, Doctor of Philosophy, 2017)In this thesis, we explore three techniques which could be used to increase the efficiency of analyses in evolutionary genetics while still producing reasonably accurate results. The first of these methods improves the ... -
(Thesis, Master of Science, 2017)Earthquake activity is generally modeled using point processes as earthquake events usually occur at random times and locations. Recent studies have found it mathematically challenging and computationally complex to ...
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(Thesis, Doctor of Philosophy, 2017)Directed graphs and their higher-rank analogues provide an intuitive framework to study a class of C*-algebras which we call graph algebras. The theory of graph algebras has been developed by a number of researchers and ... -
(Thesis, Doctor of Philosophy, 2017)This thesis examines the C*-algebras associated to semigroups of partial isometries. There are many interesting examples of C*-algebras generated by families of partial isometries, for example the C*-algebras associated ... -
(Thesis, PhD, 1993)The entry of ocean waves from the open sea into pack ice is a feature of the marginal ice zone which has important consequences for navigation and the construction of offshore structures in ice-infested seas. In turn it ... -
(Thesis, Doctor of Philosophy, 2016)To understand global climate prior to the availability of widespread instrumental data, we need to reconstruct temperatures using natural proxies such as tree rings. For reconstructions of a temperature field with multiple ... -
(Thesis, Doctor of Philosophy, 2016)The purpose of this work is to develop for the first time a general framework for the Initial Boundary Value Problem (IBVP) of the Generalised Conformal Field Equations (GCFE). At present the only investigation toward ... -
(Thesis, Doctor of Philosophy, 2016)The purpose of this work is to introduce a new analytical and numerical approach to the treatment of the initial value problem for the vacuum Einstein field equations on spacetimes with spatial topologies S3 or S1 × S2 and ... -
(Thesis, Doctor of Philosophy, 2016)This thesis describes the equilibrium states (the KMS states) of dynamical systems arising from local homeomorphisms. It has two main components. First, we consider a local homeomorphism on a compact space and the ... -
(Thesis, Doctor of Philosophy, 2016)The goal of this thesis is to study the KMS states of graph algebras with a generalised gauge dynamics. We start by studying the KMS states of the Toeplitz algebra and graph algebra of a finite directed graph, each with ... -
(Thesis, Doctor of Philosophy, 2016)The idea of displaying data in the plane is very attractive in many different fields of research. This thesis will focus on distance-based phylogenetics and multidimensional scaling (MDS). Both types of method can be viewed ... -
(Thesis, Doctor of Philosophy, 2015)This research investigated the linguistic features of written mathematical proofs, and partial proofs, from a small group of secondary school mathematics students in New Zealand. The linguistic features included are ... -
(Thesis, Doctor of Philosophy, 2015)Chemotaxis is the major cytotaxic mechanism that leads the movement of phagocytes in the tissue towards the harmful agents. Loss of phagocytes ability to track and respond to danger signals can lead to chronic infections, ... -
(Thesis, Doctor of Philosophy, 2015)Copy number variation (CNV) is a type of genomic structural variation which has been associated with disease risk in humans and with trait variation in agricultural species. This type of variation has also been implicated ... -
Grünwald-type approximations and boundary conditions for one-sided fractional derivative operators (Thesis, Doctor of Philosophy, 2014)The focus of this thesis is two-fold. The first part investigates higher order numerical schemes for one-dimensional fractional-in-space partial differential equations in 𝐿₁(ℝ). The approximations for the (space) fractional ... -
(Thesis, Doctor of Philosophy, 2006)Biological management of populations plays an indispensable role in all areas of population biology. In deciding between possible management options, one of the most important pieces of information required by population ... -
(Thesis, Doctor of Philosophy, 2014)This research project develops a mathematical and numerical framework for representing static fluid interfaces as embedded manifolds. A variational principle is developed for the embedding function of a smooth manifold, ... -
(Thesis, Doctor of Philosophy, 2014)Molecular biology makes extensive use of methods that can accurately estimate the evolutionary relationships between species, particularly when the evolutionary history can be represented on an `evolutionary tree'. However, ... -
(Thesis, Master of Science, 2014)A Prüfer domain is defined as an integral domain for which each nonzero finitely generated ideal is invertible or, equivalently, projective. In general, if R is a domain, we have the following equivalent statements: (i) ... -
(Thesis, Doctor of Philosophy, 2013)The linearised general conformal field equations in their first and second order form are used to study the behaviour of the spin-2 zero-rest-mass equation on Minkowski background in the vicinity of space-like infinity.
