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Now showing items 1-10 of 12

#### Ordinal and convex assumptions in phylogenetic tree reconstruction

(University of Canterbury. School of Mathematics and Statistics, 2014)

Phylogenetics is a field primarily concerned with the reconstruction of the evolutionary history of present day species. Evolutionary history is often modeled by a phylogenetic tree, similar to a family tree. To recreate ...

#### Separability and complete reducibility of subgroups of the Weyl group of a simple algebraic group

(University of Canterbury. Mathematics and Statistics, 2012)

Let G be a reductive algebraic group defined over an algebraically closed field of characteristic p. A subgroup H of G is called G-complete reducible whenever H is contained in a parabolic subgroup P of G, it is contained ...

#### Embeddable Spherical Circle Planes

(University of Canterbury. Mathematics and Statistics, 2009)

Spherical circle planes are topological incidence geometries; one has a 2-
sphere P and a collection of 1-spheres in P such that any three points in P determine
exactly one of these 1-spheres (the ‘circles’ of the spherical ...

#### Modelling spiral waves in Xenopus laevis oocyte

(University of Canterbury. Mathematics and Statistics, 1997)

An investigation was made into the spiral waves solutions for the Atri et al model, a partial differential equation model for Ca²⁺ dynamics in the Xenopus laevis oocyte. Spiral wave solutions, both stable and unstable, ...

#### Evolution of Tandemly Repeated Sequences

(University of Canterbury. Mathematics & Statistics, 2009)

Despite being found in all presently sequenced genomes, the evolution of tandemly repeated sequences has only just begun to be understood. We can represent the duplication history of tandemly repeated sequences with ...

#### A modular system for constructing dynamical systems

(University of Canterbury. Mathematics, 1998)

This thesis discusses a method based on the dual principle of Rössler, and developed by Deng, for systematically constructing robust dynamical systems from lower dimensional subsystems. Systems built using this method may ...

#### Trees and terraces.

(University of Canterbury, 2016)

The reconstruction of evolutionary trees from data sets on overlapping sets of species
is a central problem in phylogenetics. Provided that the tree reconstructed for each subset
of species is rooted and that these trees ...

#### A study of Besov-Lipschitz and Triebel-Lizorkin spaces using non-smooth kernels

(University of Canterbury. Mathematics and Statistics, 2008)

We consider the problem of characterising Besov-Lipshitz and Triebel-Lizorkin
spaces using kernels with limited smoothness and decay. This extends the work of H.-Q.
Bui et al in [4] and [5] from kernels in S to more ...

#### Convergent variants of the Nelder-Mead algorithm.

(University of Canterbury. Mathematics and Statistics, 2000)

The Nelder-Mead algorithm for unconstrained optimisation has been used
extensively to solve parameter estimation and other problems since its inception
in 1965. Despite its age it is still the method of choice for ...

#### Neighbourhoods of Phylogenetic Trees: Exact and Asymptotic Counts

(University of Canterbury. Mathematics and Statistics, 2015)

A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for the reconstruction of trees, it is crucial to understand the ...