Mathematics and Statistics
Recent Deposits

Contemporary wave–ice interaction models
Sea ice is an important indicator and agent of changes in the global climate system. The ice is affected by waves that travel into the Marginal Ice Zone (MIZ) and cause floes to raft, deform and, potentially, fracture. The ... 
Semiparametric dispersal kernels in stochastic spatiotemporal epidemic models
The dispersal kernel plays a fundamental role in stochastic spatiotemporal epidemic models. By quantifying the rate at which an infectious source infects a susceptible individual in terms of their separation distance, the ... 
Modelling strategies to improve genetic evaluation for the New Zealand sheep industry
The question of how best to optimise the accuracy of genetic evaluation for livestock populations has been given new life by the advent of genomics. Therefore we will investigate methods of evaluating and/or improving the ... 
Mass loss due to gravitational waves with a cosmological constant
The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the 1960s. Recent findings from looking at distant supernovae ... 
The structure of GCR and CCR groupoid C*algebras
We remove the assumptions of amenability in two theorems of Clark about C*algebras of locally compact groupoids. The first result is that if the groupoid C*algebra is GCR, or equivalently then the groupoid's orbits are ... 
Inverse problems in evolutionary biology
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 ... 
Modeling Continuous Time Series With Many Zeros
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 ... 
Analogues of Leavitt path algebras for higherrank graphs
Directed graphs and their higherrank 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 ... 
C*algebras generated by semigroups of partial isometries
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 ... 
The behaviour of sea ice in ocean waves
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 iceinfested seas. In turn it ... 
Towards a Fast Bayesian Climate Reconstruction
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 ... 
The Numerical Initial Boundary Value Problem for the Generalised Conformal Field Equations in General Relativity
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 ... 
Studies of spacetimes with spatial topologies S3 and S1 X S2
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 ... 
Equilibrium States on Toeplitz Algebras
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 ... 
KMS states of graph algebras with a generalised gauge dynamics
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 ... 
Flat Embeddings of Genetic and Distance Data
The idea of displaying data in the plane is very attractive in many different fields of research. This thesis will focus on distancebased phylogenetics and multidimensional scaling (MDS). Both types of method can be viewed ... 
Features of written proofs from New Zealand IMO students
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 ... 
Effect of chemokine superdiffusion on leucocyte chemotaxis
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, ... 
Statistical Methods for the Analysis of Copy Number Variation
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 ... 
Grünwaldtype approximations and boundary conditions for onesided fractional derivative operators
The focus of this thesis is twofold. The first part investigates higher order numerical schemes for onedimensional fractionalinspace partial differential equations in 𝐿₁(ℝ). The approximations for the (space) fractional ...