Masters Degrees (Mathematical Sciences)
Recent Submissions
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Algebraic points in tame expansions of fields
(Stellenbosch : Stellenbosch University, 2021-12)ENGLISH ABSTRACT: We investigate the behaviour of algebraic points in several expansions of the real, complex and p-adic fields. We build off the work of Eleftheriou, Günaydin and Hieronymi in [17] and [18] to prove a ... -
A deep learning approach to landmark detection in tsetse fly wing images
(Stellenbosch : Stellenbosch University, 2021-12)ENGLISH ABSTRACT: Single-wing images were captured from 14,354 pairs of field-collected tsetse wings of species Glossina pallidipes and G. m. morsitans, and analysed together with relevant biological recordings. To answer ... -
Towards a nuanced view of diagnostic test properties: an application to transfusion transmitted risk estimation
(Stellenbosch : Stellenbosch University, 2021-03)ENGLISH ABSTRACT: Laboratory screening (rather than pathogen inactivation) is likely to remain, for the foreseeable future, the primary means of ensuring the safety of blood products from transfusion transmissible viruses ... -
An axiomatic approach to the ordinal number system
(Stellenbosch : Stellenbosch University, 2021-03)ENGLISH ABSTRACT: Ordinal numbers are transfinite generalisations of natural numbers, and are usually defined and studied concretely as special types of sets. In this thesis we explore an abstract approach to developing ... -
The geometry of the moduli space of biquadratic field extensions
(Stellenbosch : Stellenbosch University, 2020-12)ENGLISH ABSTRACT: Mathematicians are always interested in understanding mathematical objects from different angles, This makes the task of classifying mathematical objects useful, as it permits one to study a mathematical ... -
Investigating correlation among geometrical parameters of isotropic and anisotropic fibrous porous media
(Stellenbosch : Stellenbosch University, 2020-12)ENGLISH ABSTRACT: In this study four main geometrical models available in the literature that approximate the micro-structure of metal foams (i.e. the cubic unit cell model, the tetrakaidecahedron model, the dodecahedron ... -
Formalizing auctions
(Stellenbosch : Stellenbosch University, 2020-12)ENGLISH ABSTRACT: Auctions have proven to be an efficient economical instrument over the years. Since the advent of internet-based commerce, some of their many forms have become important. To avoid problems related to ... -
Defining and assessing the spectrum of tuberculosis (TB) disease: application to diagnosis and prognosis
(Stellenbosch : Stellenbosch University, 2020-12)ENGLISH ABSTRACT: Although Tuberculosis (TB) has been a topic of investigation for centuries, a satisfactory method of identifying patients with clinically active TB is yet to be discovered. This has two important negative ... -
Calibrating a stochastic SIR-model to simulated data using different calibration methods : a tutorial & comparison of methods
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: Mathematical models have helped researchers identify and quantify trends in observed data, which is especially useful in the field of epidemiology. Fitting models to data enhances the credibility of ... -
Comparison of old and new algorithms for s,t -network reliability
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: Network reliability is the probability of an operative path connecting the source s with the terminal t. s, t-network reliability problems have been proven to be #P-complete. In this thesis we present ... -
Predicting water quality variables
(Stellenbosch : Stellenbosch University., 2020-03)ENGLISH ABSTRACT: Water is an important substance for all of life, and can be used in domestic, agricultural and industrial activities. Water quality determines the usefulness of water for particular purposes, ... -
Comparison of approaches for spatial interpolation of weather data on a specific date
(Stellenbosch : Stellenbosch University, 2020-03)ENGLISH ABSTRACT: This study compares four approaches to spatial interpolation of minimum and maximum temperature, and rainfall weather variables using data from 92 weather stations in the region of KwaZulu-Natal in South ... -
Stability of ecological communities with antagonistic interactions
(Stellenbosch : Stellenbosch University, 2020-03)ENGLISH ABSTRACT: Stability of large ecological systems has been a focus of theoretical ecology for more than 40 years. Here I review the stability criteria for large communities with antagonistic interactions. I show ... -
Modelling the impact of different health care systems and dropouts on the dynamics of HIV/AIDS
(Stellenbosch : Stellenbosch University, 2020-03)ENGLISH ABSTRACT: Side effects from antiretroviral drugs (ARVs) over time, present a major challenge to individuals on treatment and is a major cause of dropouts from treatment programs. The provision of treatment for ... -
Complex life cycle and biphasic range expansion in plants.
(Stellenbosch : Stellenbosch University, 2020-03)ENGLISH ABSTRACT: The rate of the spread of populations into new habitat has been extensively studied. In particular, the long-term spread rate of plant populations has been analytically formulated in terms of the ... -
Explicit bound on Siegel zeros of imaginary quadratic fields
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: Please refer to full text for abstract. -
On a generalisation of k-Dyck paths
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: (Refer to full text abstract for symbols that did not transfer correctly). We consider a family of non-negative lattice paths consisting of the step set f(1; 1); (1;k)g called k-Dyck paths, which are ... -
Intracellular and immune-response delays effects on the interation between tumor cells, oncolytic viruses and the immune system
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: Lately, oncolytic viruses have been used to mitigate cancer as they lyse tumor cells whilst leaving normal cells largely unharmed (as opposed to many other forms of cancer treatment). The oncolytic ... -
Euler Classes and Frobenius Algebras
(Stellenbosch : Stellenbosch University, 2019-04)ENGLISH ABSTRACT : This thesis investigates the relationship between the handle element of the De Rham cohomology algebra of a compact oriented smooth manifold, thought of as a Frobenius algebra, and the Euler class of ... -
A duality theoretic perspective on recognisable languages
(Stellenbosch : Stellenbosch University, 2019-04)ENGLISH ABSTRACT : A connection between recognisable languages and profinite identities is established through the composition of two famous theorems: Eilenberg’s theorem and Reiterman’s theorem. In this work, we present ...
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