Department of Mathematical Sciences
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On the minimal Hamming weight of a multi-base representation
(Elsevier, 2020)Given a finite set of bases b1, b2, ..., br (integers greater than 1), a multi-base representation of an integer n is a sum with summands dbα1 1 b α2 2 ··· bαr r , where the αj are nonnegative integers and the digits ... -
A wide class of Combinatorial matrices related with Reciprocal Pascal and Super Catalan matrices
(2019)Abstract. In this paper, we present a number of combinatorial matrices that are generalizations or variants of the super Catalan matrix and the reciprocal Pascal matrix. We present explicit formul for LUdecompositions of ... -
An analysis of security protocols for lightweight systems
(Stellenbosch : Stellenbosch University, 2022-04)ENGLISH SUMMARY: Security is hard to maintain in distributed systems especially for communicating agents restricted to lightweight computations, as in the Internet of Things, which struggle to implement strong cryptographic ... -
Image Classification with Graph Neural Networks
(Stellenbosch : Stellenbosch University, 2022-04)ENGLISH SUMMARY: Convolutional neural networks (CNNs) are a prominent and ubiquitous part of machine learning. They have successfully achieved consistent state-of-the-art performance in areas such as computer vision. ... -
Investigations on the Wigner derivative and on an integral formula for the quantum 6j symbols
(Stellenbosch : Stellenbosch University, 2022-04)ENGLISH SUMMARY: wo separate studies are done in this thesis: 1. TheWigner derivative is the partial derivative of dihedral angle with respect to opposite edge length in a tetrahedron, all other edge lengths remaining fixed. ... -
MAVSCOT : a fuzzy logic-based HIV diagnostic system with indigenous multi-lingual interfaces for rural Africa
(Public Library of Science, 2020-11-06)HIV still constitutes a major public health problem in Africa, where the highest incidence and prevalence of the disease can be found in many rural areas, with multiple indigenous languages being used for communication by ... -
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 ... -
Prejudice, privilege, and power : conflicts and cooperation between recognizable groups
(AIMS Press, 2019)The problem of cooperation remains one of the fundamental questions in the fields of biology, sociology, and economics. The emergence and maintenance of cooperation are naturally affected by group dynamics, since individuals ... -
The definable (p,q)-theorem for dense pairs of certain geometric structures
(Stellenbosch : Stellenbosch University, 2021-12)ENGLISH ABSTRACT: The definable (p, q)-conjecture is a model-theoretic version of a (p, q)- theorem in combinatorics, which was expressed in the form of a question by A. Chernikov and P. Simon in 2015. Researchers have ... -
A complete study of the ramification for any separable cubic global function field
(Springer, 2019)We explicitly describe the ramified places in any separable cubic extension of a cubic global function field in terms of a unique given parameter. This is all done using the uniqueness of the purely cubic closure, which ... -
Large deviations of random walks on random graphs
(American Physical Society, 2019-02-26)We study the rare fluctuations or large deviations of time-integrated functionals or observables of an unbiased random walk evolving on Erdös-Rényi random graphs, and construct a modified, biased random walk that explains ... -
Mixed convective flow of a visco elastic fluid between two porous parellel plates
(Blue Eyes Intelligence Engineering and Sciences Publication, 2019)A diagnostic answer for the problem of sincerely grew loose convective circulation between two vertical parallel plates has been inspected in this paper. The trademark highlights of various parameters were talked about in ... -
On the centroid of increasing trees
(Episciences.org, 2019)A centroid node in a tree is a node for which the sum of the distances to all other nodes attains its minimum, or equivalently a node with the property that none of its branches contains more than half of the other nodes. ... -
Quadratic Pade approximation : numerical aspects and applications
(Steklov Mathematical Institute, 2019)Pad´e approximation is a useful tool for extracting singularity information from a power series. A linear Pad´e approximant is a rational function and can provide estimates of pole and zero locations in the complex plane. ... -
On the inducibility of small trees
(Episciences, 2019)The quantity that captures the asymptotic value of the maximum number of appearances of a given topological tree (a rooted tree with no vertices of outdegree 1) S with k leaves in an arbitrary tree with sufficiently large ... -
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 ... -
Exponential damping : the key to successful containment of COVID-19
(Frontiers Media, 2021-01-08)Due to its excessive capacity for human-to-human transmission, the 2019 coronavirus disease (COVID-19) has now been declared a global public health emergency. Here we propose a simple model based on exponential infectious ... -
Impact of COVID-19 pandemic on mobility in ten countries and associated perceived risk for all transport modes
(PLOS, 2021-02-01)The restrictive measures implemented in response to the COVID-19 pandemic have triggered sudden massive changes to travel behaviors of people all around the world. This study examines the individual mobility patterns for ...
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