Department of Mathematical Sciences
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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 ... -
An error correction neural network for stock market prediction
(Stellenbosch : Stellenbosch University, 2019-04)ENGLISH ABSTRACT : Predicting stock market has long been an intriguing topic for research in different fields. Numerous techniques have been conducted to forecast stock market movement. This study begins with a review ... -
Mathematical models of Ebola virus disease with socio-economic dynamics
(Stellenbosch : Stellenbosch University, 2019-04)ENGLISH ABSTRACT : West Africa hosted the deadliest Ebola virus disease epidemic from 2013 to 2016 and one of the common characteristics of the affected countries is their status of being developing countries. Poor ... -
Investigating diffusion on networks with long-range interactions: application to object clustering using the generalised heat kernel invariants
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : Diffusion on networks is widely used to model dynamical processes on networks such as propagation of information through a social network for marketing purposes [79], spread of epidemics within a social ... -
Forecasting stock returns: A comparison of five models
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : Forecasting the movement of stock returns prices has been of interest to researches for many decades. Due to the complex and chaotic nature of the stock market, it has been difficult for researches to ... -
A stage structured model for HIV/AIDS in the presence of vertical transmission: The case of Ghana
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT :Vertical transmission remains a global problem with respect to HIV infection dynamics. It refers to the transmission of HIV from the mother to child during pregnancy, delivery and breastfeeding soon after ... -
On the definable generalized Bohr compactification of SL(2,Qp)
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : This paper provides an overview of existing knowledge regarding the socalled definable generalized Bohr compactification of the group SL(2, Qp) of 2 × 2 matrices with determinant 1 and entries in Qp. ... -
Modelling the role of correctional services on gangs : insights through a mathematical model
(Royal Society, 2017)Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing ... -
A categorical approach to lattice-like structures
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : This thesis is a first step in a categorical approach to lattice-like structures. Its central notion, that of a majority category, relates to the category of lattices, in a similar way as Mal’tsev ... -
Host-seeking efficiency can explain population dynamics of the tsetse fly Glossina morsitans morsitans in response to host density decline
(Public Library of Science, 2017)Females of all blood-feeding arthropod vectors must find and feed on a host in order to produce offspring. For tsetse—vectors of the trypanosomes that cause human and animal African trypanosomiasis—the problem is more ... -
On the inducibility of rooted trees
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : The density of appearances of a fixed tree in a larger tree is examined for rooted trees without vertices of outdegree 1 (also known as topological trees). Given a topological tree S with k leaves and ... -
Analysis of tree spectra
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : We study the set of eigenvalues (spectrum) of the adjacency matrix, Laplacian matrix and the distance matrix of trees. In particular, we focus on the distribution of eigenvalues in the spectra of large ... -
Modelling the potential role of media campaigns in ebola transmission dynamics
(Hindawi Publishing Corporation, 2017)A six-compartment mathematical model is formulated to investigate the role of media campaigns in Ebola transmission dynamics. The model includes tweets or messages sent by individuals in different compartments. The media ... -
Paths vs. stars in the local prole of trees
(Electronic Journal of Combinatorics, 2017)The aim of this paper is to provide an affirmative answer to a recent question by Bubeck and Linial on the local profile of trees. -
Internode morphometrics and allometry of Tonkin Cane Pseudosasa amabilis
(John Wiley & Sons Ltd, 2017-10)Pseudosasa amabilis (McClure) (Poales: Gramineae) is a typical bamboo species naturally distributed in large area of south China and famous for its culm strength. Although bamboos were found to share the same development ... -
Protection number in plane trees
(University of Belgrade - School of Electrical Engineering, 2017-10)The protection number of a plane tree is the minimal distance of the root to a leaf; this definition carries over to an arbitrary node in a plane tree by considering the maximal subtree having this node as a root. We ... -
Is invasion success of Australian trees mediated by their native biogeography, phylogenetic history, or both?
(Oxford University Press on behalf of the Annals of Botany Company, 2017)For a plant species to become invasive it has to progress along the introduction-naturalization-invasion (INI) continuum which reflects the joint direction of niche breadth. Identification of traits that correlate with and ... -
Combining uncertainties in a court of law using Bayesian networks
(Obiter Law Journal: Nelson Mandela Metropolitan University (NMMU), Faculty of Law, 2017)People generally have difficulty dealing with the counter-intuitive notion of probability, and therefore they often misunderstand aspects of uncertainty. This is particularly significant in a court of law when for example ... -
Investigating tumour micro environment dynamics based on cytokine-mediated innate-adaptive immunity
(Stellenbosch : Stellenbosch University, 2018-03)ENGLISH ABSTRACT : Cancer is a leading cause of death worldwide, yet much is still unknown about its mechanism of establishment, recurrence cycle and destruction. It is known that the successive alterations that occur ...
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