Browsing NUI Galway Theses by Subject "Mathematics"
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Algorithms for Nilpotent Linear Groups
(20110304)In this thesis, we develop practical algorithms for irreducibility and primitivity testing of finite nilpotent linear groups defined over various fields of characteristic zero, including number fields and rational function ... 
Automorphisms of Pairwise Combinatorial Designs
(20120214)In this thesis, we investigate group actions on certain families of pairwise combinatorial designs, in particular Hadamard matrices and symmetric 2(4t1, 2t1, t1) designs. A Hadamard matrix H is called cocyclic if a ... 
Behavioural fluency: An investigation of instructional approaches to build fluency with academic skills and associated outcomes
(20140711)This thesis investigates the efficacy of instructional approaches designed to build fluency with mathematics skills, specifically, frequencybuilding, Precision Teaching (PT) and the Morningside Mathematics Fluency curricula. ... 
Classification Problems for Finite Linear Groups
(20130308)This thesis is concerned with classification problems for finite linear groups. Our main concern is with groups of prime degree, and groups defined over finite fields and fields of zero characteristic. We use the computational ... 
Completions of partial matrices
(20150323)A partial matrix over a field is a matrix whose entries are either elements of the field or independent indeterminates. A completion of a partial matrix is any matrix that results from assigning a field element to each ... 
Computational homology of ntypes
(20140110)An ntype X is a CWspace with homotopy groups \pi_iX=0 for all i>n. Up to homotopy equivalence such a space can be specified algebraically by means of a simplicial group whose Moore complex is trivial in degrees >= n. For ... 
Dihedral codes
(2009)In this thesis we give new constructions of a number of extremal type II codes. Algebraic proofs are provided that the constructions do in fact yield the codes. The codes are constructed using group rings of which the ... 
Edgeminimal graphs of exponent 2
(20171121)A simple undirected finite graph G has the me_2property if every pair of distinct vertices of G is connected by a path of length 2, but this property does not survive the deletion of an edge. If u and v are adjacent ... 
Extensions and Applications of Survival Trees in Medical Data
(20120917)Survival trees are a nonparametric modeling strategy that can be included in the area of statistical modeling. These type of models can be used as an alternative to Cox proportional hazards models for the analysis of ... 
Features and purposes of mathematical proofs in the view of novice students: observations from proof validation and evaluation performances
(20101222)This thesis describes a comprehensive exploratory study of the approaches taken by novice students to the validation and evaluation of mathematical proofs. A theoretical framework based on sociocultural learning theories ... 
Integration of Genetic Biomarkers in Prognostic Models for Breast Cancer Survival
(20140108)The main aim of my PhD is to create a prognostic model for invasive breast cancer patients for disease recurrence and death. The data were collected retrospectively and are comprised of 647 invasive breast cancer patients ... 
Investigation of T cell receptor and immunoglobulin repertoire through next generation sequencing data
(20170808)The diversity of the immunological repertoire has long been a subject of research focus, providing important insights into the adaptive immune system. Rapid developments in next generation sequencing technologies ... 
Machine learning and highperformance computing: Infrastructure and algorithms for the genomescale study of genetic and epigenetic regulatory mechanisms with applications in neuroscience
(20140630)The advent of nextgeneration sequencing (NGS) has fundamentally changed modern genomics research. These sequencers generate terabytes of data and necessitate the use, not only of highperformance compute (HPC) clusters ... 
Mathematical Analysis of Some Models for Drug Delivery
(20120827)This thesis is concerned with the mathematical modelling of controlled drug release from a number of delivery systems. There are two major strands to the work: (i) modelling release from affinitybased systems, and, (ii) ... 
Mathematical models of centromere associating proteins
(20140711)This thesis describes the development and analysis of new mathematical models of Centromere Protein A (CENPA) incorporation in mammalian centromeres, intermolecular autophosphorylation and Aurora B kinase activity in ... 
Meseanchymal stem cell mediated sodium iodide symporter gene therapy of breast cancer
(20140507)Introduction: The Sodium Iodide Symporter (NIS) facilitates iodide accumulation in the thyroid and radioiodide imaging and treatment of thyroid disease. Studies have suggested that elevated levels of NIS expression in ... 
On the collection of topologies, generalised metrics and continuity spaces
(20130927)This articlebased thesis comprises a collection of four papers, each of which constitutes a chapter written in manuscript form. The elemental theme behind the first three chapters is the study of several collections of ... 
On the table of marks of a direct product of finite groups
(20160210)The table of marks was first introduced by William Burnside in his book "Theory of groups of finite order" in 1955. The table of marks counts the number of fixed points one subgroup has in the action of the cosets of ... 
Parabolic and equalrank subroot systems with applications to symmetric spaces and flag manifolds
(20160620)Using the algebraic structure of subroot systems in the root system of a complex simple Lie algebra g, we prove a generalization for compact homogeneous spaces with positive Euler characteristic of the 'strange formula' ... 
Preconditioning techniques for singularly perturbed differential equations
(20150923)This thesis considers computer methods for solving singularly perturbed differential equations. Standard algorithms are very inefficient when applied to these problems, although the exact reasons for this have not ...