Faculty of Science (ETDs)

Permanent URI for this community

https://hdl.handle.net/10539/37933

Browse

Now showing 1 - 20 of 22

A Continuous Reinforcement Learning Approach to Self-Adaptive Particle Swarm Optimisation
(University of the Witwatersrand, Johannesburg, 2023-08) Tilley, Duncan; Cleghorn, Christopher
Particle Swarm Optimisation (PSO) is a popular black-box optimisation technique due to its simple implementation and surprising ability to perform well on various problems. Unfortunately, PSO is fairly sensitive to the choice of hyper-parameters. For this reason, many self-adaptive techniques have been proposed that attempt to both simplify hyper-parameter selection and improve the performance of PSO. Surveys however show that many self-adaptive techniques are still outperformed by time-varying techniques where the value of coefficients are simply increased or decreased over time. More recent works have shown the successful application of Reinforcement Learning (RL) to learn self-adaptive control policies for optimisers such as differential evolution, genetic algorithms, and PSO. However, many of these applications were limited to only discrete state and action spaces, which severely limits the choices available to a control policy, given that the PSO coefficients are continuous variables. This dissertation therefore investigates the application of continuous RL techniques to learn a self-adaptive control policy that can make full use of the continuous nature of the PSO coefficients. The dissertation first introduces the RL framework used to learn a continuous control policy by defining the environment, action-space, state-space, and a number of possible reward functions. An effective learning environment that is able to overcome the difficulties of continuous RL is then derived through a series of experiments, culminating in a successfully learned continuous control policy. The policy is then shown to perform well on the benchmark problems used during training when compared to other self-adaptive PSO algorithms. Further testing on benchmark problems not seen during training suggest that the learned policy may however not generalise well to other functions, but this is shown to also be a problem in other PSO algorithms. Finally, the dissertation performs a number of experiments to provide insights into the behaviours learned by the continuous control policy.
An Essay on Branching Time Logics
(University of the Witwatersrand, Johannesburg, 2024) Marais, Chantel
In this thesis we investigate the Priorian logics of a variety of classes of trees. These classes of trees are divided in to irreflexive and reflexive trees, and each of these has a number of subclasses, for example, dense irreflexive trees, discrete reflexive trees, irreflexive trees with branches isomorphic to the natural numbers, etc. We find finite axiomatisations for the logics of these different classes of trees and show that each logic is sound and strongly / weakly complete with respect to the respective class of trees. The methods use to show completeness vary from adapting some known constructions for specific purposes, including unravelling and bulldozing, building a network step-by-step, filtering through a finite set of formulas, as well as using some new processes, namely refining the filtration and unfolding. Once the logics have been shown to be sound and complete with respect to the different classes of trees, we also show that most of these logics are decidable, using methods that include the finite model property, mosaics and conservative extensions. Lastly, we give a glimpse into the available research on other languages used to study branching time structures, including the Peircean and Ockhamist languages, and languages that include additional modal operators like “since” and “until”
An ethnobotanical study of indigenous knowledge of the medicinal plants used by traditional healers in the rural communities of Nkomazi Local Municipality, Mpumalanga province
(University of the Witwatersrand, Johannesburg, 2024) Khoza, Nompendulo; Dukhan, Shalini; Ramalepe, Phillemon; Risenga, Ida
Traditional medicine continues to significantly impact many people’s lives amid all the advancements in modern medicine. Many rural communities in Mpumalanga province depend on indigenous traditional medicines to manage various ailments. The available research on the traditional usage of medicinal plants among rural communities in Mpumalanga is highly fragmented and under-researched. The decline of medicinal plant populations has led stakeholders to take various initiatives to counteract over-exploitation, including cultivation as a viable conservation approach. However, the scientists' inadequate understanding of the acceptance of cultivated medicinal plants by traditional healers is one of the issues contributing to the failure of medicinal plant cultivation programs. Consequently, this study aimed to document medicinal plants utilised by the Nkomazi Local Municipality's traditional healers and assess opportunities and constraints for medicinal plant conservation in the Nkomazi Local Municipality. The ethnobotanical data was obtained through semi-structured questionnaires and guided field walks with traditional healers. Individual interviews were conducted with ten traditional healers from eight villages across Nkomazi during field visits between July 2021 and February 2022. The study employed qualitative and quantitative approaches to understand traditional healers' perspectives concerning the ethnobotanical significance and medicinal plant conservation. The study found that the indigenous knowledge of medicinal plants in the Nkomazi Local Municipality is diverse, encompassing 111 species from 59 different families employed to treat 70 ailments. Most of the reported medicinal plants for this study are of Least Concern. Additionally, the top fourteen most reported species in the Nkomazi Local Municipality included commercially valuable plants such as Psidium guajava, Ricinus communis, Sclerocarya birrea, Aloe ferox, Aloe maculata, Leonotis leonurus, and Moringa oleifera. Most of the Nkomazi Local Municipality's traditional healers did not know about protected plant species and the National Environmental Management Act (NEMA). Traditional healers were aware of the decline in wild populations of medicinal plants, which they attributed to various factors such as overharvesting. Diviner’s and herbalist perception of using cultivated plants did not differ significantly (𝜒2=0.4762, df=1, P= 0. 490). The study provided a comprehensive inventory of medicinal plants utilised by Nkomazi traditional healers and essential data for future assessments of the use local use of indigenous medicinal plants.
Assessing habitat selection of grassland rodents in the Cradle of Humankind
(University of the Witwatersrand, Johannesburg, 2024) Pinto, Catiuscia-Jade; Mackay, Megan; Pillay, Neville
Habitat selection is a decision-making process undertaken by animals to select an appropriate environment suitable for fulfilling their survival and reproductive needs. These decisions are driven by a complex of biotic and abiotic factors. Habitat selection relies on how an animal interacts with its environment and is species-specific. The vegetation structure and composition influence how smaller animals, such as rodents, obtain food and cover, and are thus critical for their survival. The aim of my study was to assess the population demography and habitat selection of nocturnal rodents in two grassland sites located within the Cradle of Humankind Nature Reserve, Krugersdorp, Gauteng Province, South Africa. I obtained rodent data using Capture-Mark-Recapture (CMR) methods, and vegetation data were obtained through randomised quadrate sampling. The following six rodent species were sampled, Gerbilliscus leucogaster, Lemniscomys rosalia, Mastomys coucha, Micaelamys namaquensis, Mus minutoides and Otomys angoniensis. Rodent abundance differed between summer and winter, with winter showing a higher abundance, but richness and diversity indices did not differ significantly between sites or seasons. The three most common species, G. leucogaster, M. coucha and O. angoniensis, were selected for further population demography analyses. The demography of G. leucogaster, was mostly associated with the season since seasonal fluctuations were observed in their population size (higher in summer), reproductive activity (more active in summer) and body condition (higher in winter). Mastomys coucha was the most abundant species in the study, since it had the highest number of sampled individuals in both summer and winter, although its demography was not influenced by external factors (e.g.,, season, vegetation height, vegetation cover) recorded in both summer and winter. Otomys angoniensis had a positive relationship with vegetation height and rodents’ body condition. The three species were able to coexist with one another due to differences in foraging strategies, reproductive strategies, spatial and dietary partitioning, which help to facilitate habitat selection and illustrate that habitat selection is species specific. Key words: Rodents, habitat selection, Gerbilliscus leucogaster, Mastomys couch
Chromatic Polynomials and Certain Classes of Graphs
(University of the Witwatersrand, Johannesburg, 2023) Maphakela, Lesiba Joseph; Mphako-Banda, G.
The chromatic polynomial of a graph has been widely studied in the literature. The focus of this research is on exploring the chromatic polynomial of specific graphs that result from the application of a join operation. The chromatic polynomial of a graph can be expressed in various forms; power form, tree form, factorial form and cycle form. The expressions in various forms, such as power form, tree form, and factorial form, have been subject to comprehensive investigation. However, it should be noted that the cycle form presents relative gaps that necessitate further exploration. This work builds upon the existing literature by engaging in a discussion of the coefficients of the chromatic polynomial of a graph expressed in cycle form. To achieve this objective, we commence by presenting the general formula of the chromatic polynomial in cycle form. Following this, we introduce an algorithm that computes the chromatic polynomial of a graph in cycle form. Additionally, we outline a method for converting the chromatic polynomial of a graph from its tree form into the cycle form. Furthermore, we determine the values of the first and second terms of the chromatic polynomial in its cycle form. This research also complements the well established knowledge of the chromatic polynomial of graphs resulting from the application of a join operation. Of particular interest, we explore the joins of various classes of graphs, including the join of a null graph, N1 with a graph G, which is known as the vertex join of graph G. Building upon this framework, we extend our analysis to encompass the join of a null graph, N2, with graph G. Similarly, we present results pertaining to the join of a complete graph, Kn, with a graph G. Significantly, we conduct a thorough comparative analysis of the chromatic equivalence class among these derived classes of graphs. Lastly, we discuss the chromatic uniqueness of these derived classes of graphs, alongside introducing variations to these derived graphs by deleting their edges and subgraphs.
Chromatin accessibility changes during early monocyte-to-macrophage differentiation
(University of the Witwatersrand, Johannesburg, 2024) Xu, Yi Fan; Meyer, V.; Gentle, N .
The differentiation of monocytes into macrophages is a crucial process that enhances the local immune response against infection by recruiting monocytes to local tissues and transforming them into macrophages. The changes in gene expression associated with this process are known to be regulated by various mechanisms, including the chromatin accessibility landscape. Previous in vitro studies have shown that promonocytic THP-1 cells can differentiate into macrophage-like cells following treatment with phorbol 12-myristate 13-acetate (PMA). While previous studies have attempted to track the differentiation process over time, there has been a lack of research specifically focusing on earlier time points. Therefore, in this study, we used various publicly available RNA-seq, ATAC-seq and ChIP-seq datasets to describe the early events involved in monocyte-to-macrophage differentiation, using THP-1 cells treated with 100 ng/ml PMA for 24 hours as the model system. ATAC-seq data were aligned to the reference human genome (GRCh38) using Bowtie2 and chromatin accessibility peaks were identified using HMMRATAC. Differentially accessible chromatin regions (|L2FC| > 2; FDR < 0.05) were identified using DiffBind, and were annotated based on their cis-regulatory features. These included promoter regions (based on the GENCODE v40 annotations of the human genome) and THP-1-specific enhancers (defined as known enhancers within the GeneHancer database with an overlapping, THP-1-specific, H3K27ac mark). These cis-regulatory features were then associated with genes found to be significantly differentially expressed in response to PMA treatment (|L2FC| > 2; p.adj < 0.05), following quantification of gene expression using Salmon and differential gene expression analysis using DESeq2. The results of this study revealed that the early response to PMA in THP-1 cells is linked to changes in both gene expression and chromatin accessibility. These changes in both gene expression and chromatin accessibility were shown to be linked with inflammatory responses and cell migration activities. Although there was only a limited association between changes in gene expression and chromatin accessibility at the 24-hour time point, opening of chromatin at promoter and enhancer regions and increased gene expression was observed for many genes previously reported to be involved in the process of monocyte-to-macrophage differentiation, including CSF1, CSF1R, and IL-1α/β. This suggests that changes in chromatin accessibility at cis-regulatory elements taking place early in the differentiation process drive the changes in gene expression necessary for monocyte-to-macrophage differentiation
Cognition in urban-dwelling yellow mongoose, Cynictis penicillata
(University of the Witwatersrand, Johannesburg, 2024) Muller, Mijke; Pillay, Neville
Cognition involves perceiving and processing environmental cues and devising appropriate behavioural responses to act on the acquired information. Studying animal cognition in an urban setting provides insight into the occurrence of behavioural changes in urban-adapted animals. This thesis aimed to investigate the cognitive abilities of a population of yellow mongoose, Cynictis penicillata, inhabiting locations with differing extents of urbanisation in South Africa. First, I investigated whether mongooses could learn to solve a puzzle box problem of increasing complexity. The mongooses were able to solve the problem at each stage of complexity, but took longer in a residential ecological estate than those frequently visiting a residential garden. These results indicated that mongooses were capable of innovation, but their problem-solving abilities were influenced by the level of disturbance in their environment. Secondly, I investigated whether mongooses exhibited cognitive flexibility. The mongooses were able to inhibit a non-rewarding behaviour, even when it was previously rewarded, in favour of a newly rewarded behaviour during the puzzle box task. Additionally, they could solve the puzzle box problem during distraction, but took longer with the most distraction, likely splitting their attention between solving the problem and remaining vigilant. Combined, the mongooses were capable of reversal learning and divided/alternating attention, providing evidence of cognitive flexibility in this mongoose population. Thirdly, I investigated the effects of a direct human approach on the problemsolving ability of mongooses. In areas of heightened human disturbances, the mongooses had reduced tolerance to humans, but were equally efficient at solving the puzzle box problem following human disturbance than those in areas of reduced human disturbance. Those more tolerant of humans improved their problem-solving efficiency, likely adapting to the disturbance. Finally, I investigated whether mongooses experienced a paradox of choice (i.e. whether too much choice can be cognitively challenging). The mongooses in my study appeared to experience cognitive difficulties when presented with extensive choice, providing support for a paradox of choice. These results provide evidence that urban-living yellow mongooses’ successful adaptation to an urban habitat may be attributed to their cognitive abilities, allowing them to exploit novel resources and flexibly adapt to the rapid environmental changes associated with urbanisation. However, the disturbance associated with urbanisation may negatively affect problem-solving efficiency, which may impact successful food acquisition, and the increased availability of resources may be cognitively challenging for urban-living yellow mongooses.
Convergence Results for Inertial Regularized Bilevel Variational Inequality Problems
(University of the Witwatersrand, Johannesburg, 2024) Okorie, Kalu Okam; Okeke, Chibueze Christian
In this dissertation, we introduce and study the inertial forward-reflected-backward method for approximating a solution of bilevel variational inequality problems. Our proposed method involves a single projection onto a feasible set, one functional evaluation and adopts the inertial extrapolation term. These features make our algorithm cost-effective and efficient, which is desirable when the cost operator and the feasible set have a complex structure. We incorporate the regularization technique in our method and establish that the sequences generated by our method converge strongly to a solution of the bilevel variational inequality problem studied in this work; furthermore, we modified our method by replacing the stepsizes and projection onto a feasible set with a self-adaptive non-monotonic stepsizes and projection onto a constructive halfspace, respectively. The non-monotonic stepsizes ensure that our method performs without the previous detail of the Lipschitz constant, and the projection onto a constructive halfspace is cheap since its computation is through an explicit formula. These adjustments in our method ensure an improved performance, cheap computation and easy implementation of our method. We show the strong convergence result of the iterative sequences. Lastly, we give numerical experiments comparing the performance of the proposed methods with existing methods
Elucidating the Structure-Function Relationships of Enterococcus faecium Nicotinate-Nucleotide Adenylyltransferase through X-Ray Crystallography, Computational Modelling and Binding Studies
(University of the Witwatersrand, Johannesburg, 2024) Jeje, Olamide Adetomi; Pandian, Ramesh; Achilonu, Ikechukwu A.
Nicotinate nucleotide adenylyltransferase (NNAT) is a vital enzyme at the heart of NAD biosynthesis, catalysing a crucial reaction that leads to the formation of pyridine dinucleotides. NAD+ is an essential coenzyme in numerous metabolic processes, DNA repair, and cellular signalling. Given its pivotal role, NNAT has emerged as a compelling drug target, particularly for its potential to disrupt the survival mechanisms of bacterial pathogens. By inhibiting NNAT, it is possible to undermine the metabolic integrity of these pathogens, making NNAT a promising focal point in the fight against bacterial infections and antibiotic resistance. However, understanding the structure-function relationship of Enterococcus faecium NNAT (EfNNAT) has remained elusive. Hence, this study aimed to address this gap bycharacterising EfNNAT and validating its potential as a druggable target. EfNNAT was overexpressed and purified using the Escherichia coli system and IMAC purification technique. Subsequently, biophysical characterisation was performed, followed by the determination of the three-dimensional structure in both apo and liganded forms using X-ray crystallography. High-throughput virtual screening, along with SP and XP docking, was conducted using a library of synthesizable flavonoids. Molecular dynamic simulation and fluorescence studies were employed to establish and validate the binding of identified inhibitors to EfNNAT. Successful expression and purification of EfNNAT yielded approximately 101 mg per 7.8 g of wet E. coli cells, with a purity exceeding 98%. High-resolution crystal structures of EfNNAT in native, adenine-bound, and NMN-bound forms were determined at 1.90 Å, 1.82 Å, and 1.84 Å, respectively. These structures provided insights into EfNNAT's substrate preference and revealed a potential allosteric site at the dimer interface of the NMN-bound structure. Virtual screening identified quercetin 3-O-beta-D-glucose- 7-O-beta-D-gentiobioside as the only potential inhibitor from the flavonoid library used. A 500 ns atomistic molecular dynamics simulation showed the compound interacted through hydrogen bonding and water bridges, albeit unstable within the receptor. ANS and mant-ATP fluorescence spectroscopy confirmed quercetin binding, while thermal shift assay revealed minimal impact of the inhibitor on the protein stability and structure. This study establishes a pipeline from expression and purification to structure solution and potential inhibitor identification for EfNNAT, validating its druggability. The mechanistic insights offer a foundation for advancing drug discovery efforts targeting EfNNAT and other bacterial NNAT enzymes.
Evaluating Pre-training Mechanisms in Deep Learning Enabled Tuberculosis Diagnosis
(University of the Witwatersrand, Johannesburg, 2024) Zaranyika, Zororo; Klein, Richard
Tuberculosis (TB) is an infectious disease caused by a bacteria called Mycobacterium Tuberculosis. In 2021, 10.6 million people fell ill because of TB and about 1.5 million lives are lost from TB each year even though TB is a preventable and curable disease. The latest global trends in TB death cases are shown in 1.1. To ensure a higher survival rate and prevent further transmissions, it is important to carry out early diagnosis. One of the critical methods of TB diagnosis and detection is the use of posterior-anterior chest radiographs (CXR). The diagnosis of Tuberculosis and other chest-affecting dis- eases like Pneumoconiosis is time-consuming, challenging and requires experts to read and interpret chest X-ray images, especially in under-resourced areas. Various attempts have been made to perform the diagnosis using deep learning methods such as Convolutional Neural Networks (CNN) using labelled CXR images. Due to the nature of CXR images in maintaining a consistent structure and overlapping visual appearances across different chest-affecting diseases, it is reasonable to believe that visual features learned in one disease or geographic location may transfer to a new TB classificationmodel. This would allow us to leverage large volumes of labelled CXR images available online hence decreasing the data required to build a local model. This work will explore to what extent such pre-training and transfer learning is useful and whether it may help decrease the data required for a locally trained classifier. In this research, we investigated various pre-training regimes using selected online datasets to under- stand whether the performance of such models can be generalised towards building a TB computer-aided diagnosis system and also inform us on the nature and size of CXR datasets we should be collecting. Our experiment results indicated that both supervised and self-supervised pre-training between the CXR datasets cannot significantly improve the overall performance metrics of a TB. We noted that pre-training on the ChestX-ray14, CheXpert, and MIMIC-CXR datasets resulted in recall values of over 70% and specificity scores of at least 90%. There was a general decline in performance in our experiments when we pre-trained on one dataset and fine-tuned on a different dataset, hence our results were lower than baseline experiment results. We noted that ImageNet weights initialisation yields superior results over random weights initialisation on all ex- periment configurations. In the case of self-supervised pre-training, the model reached acceptable metrics with a minimum number of labels as low as 5% when we fine-tuned on the TBX11k dataset, although slightly lower in performance compared to the super-vised pre-trained models and the baseline results. The best-performing self-supervised pre-trained model with the least number of training labels was the MoCo-ResNet-50 model pre-trained on the VinDr-CXR and PadChest datasets. These model configura- tions achieved recall scores of 81.90% and a specificity score of 81.99% on VinDr-CXR pre-trained weights while the PadChest weights scored a recall of 70.29% and a speci- ficity of 70.22%. The other self-supervised pre-trained models failed to reach scores of at least 50% on both recall or specificity with the same number of labels
Farming systems in South Africa beyond 2020: a scenario-based study, using systems analysis, of the connectivity between farming systems in the Vhembe district, Limpopo, South Africa
(University of the Witwatersrand, Johannesburg, 2024) Materechera-Mitochi, Fenji; Scholes, Mary
Agriculture is a significant contributor to the South African economy and overall development as it contributes to poverty reduction and food security. It is against this backdrop that agricultural development becomes a focus area for decision making amongst stakeholders, as it is directly linked to food systems. The traditional approach to agricultural production in the country has been one that views farming as mainly based on land ownership and yield in isolation from the broader context of the four drivers of production namely land, labour, capital and enterprise. The concept of farming systems provides a broader perspective on farming and encompasses the entire value chain for a commodity which includes production, management practices, marketing, value addition, financial resources, and policies. The South African agrarian structure is characterised by a dualism in which large-scale commercial farmers co-exist alongside small-scale farmers. This is a legacy of the apartheid system of governance. Large-scale commercial farmers, who are mostly capital intensive, have historically been regarded as the main drivers of national food security while small-scale farmers on the other hand are viewed as significant contributors to food security at a household level. Both farmers are therefore important contributors to the national agricultural economy. Research on the two types of farmers in the South African context is usually focused on the respective farmers’ approaches to production individually and does not consider them as joint ventures. This study was aimed at providing an alternative approach to viewing South Africa’s farming systems by evaluating current farming systems in the Vhembe district of Limpopo, South Africa, using systems analysis as a tool to highlight the connectivity of the interactions within and between them. The study also aimed to conceptualize scenarios for sustainable future farming systems in South Africa. The Vhembe district in the Limpopo province was chosen for the study because both largescale commercial and small-scale farmers occur and due to the favourable sub-tropical climate, the area has become a hub for the farming of numerous high value crops that contribute positively to the country’s agricultural economy. The study made use of a mixed methods approach that combined the analysis of primary data obtained from in-depth interviews and secondary data obtained from an agricultural database to identify and characterize large-scale commercial and small-scale farming systems in the Vhembe district. The study examined the drivers of production for three different commodities, macadamia nuts, mangos and avocado iii pears, the two types of farming systems and their connectivity. The study was grounded on the conceptual framework of systems thinking and used a systems analysis tool i.e., causal loop diagrams to analyse the connectivity between the two farming systems. Lastly, the study developed conceptual scenarios using a deductive scenario method to conceptualise scenarios for the future of the two farming systems and the different commodities. Key findings of the study showed that farming systems need to be understood through the lens of the four drivers of production. Land as a driver of production interacts with multiple other factors in shaping the management of a sustainable farming system. Examples of these factors include the link between land availability, ownership and farm size, decision-making and resource allocation tied to land management practices, and socio-economic considerations including the diversification of livelihoods by incorporating non-farm income and the farmers’ adaptability to uncertainties such as climate change. The findings also revealed that there are interconnections between the two types of farming systems presenting potential for enhanced production and commercial opportunities. The conceptual scenarios developed in the study and the systems thinking tool of causal loop diagrams proved to be valuable tools to inform decision making and policy development. The study’s main conclusion points to the potential of large-scale commercial and small-scale farming systems in South Africa operating as joint ventures in the future and enhancing the sustainability of agricultural production and livelihoods. It also recommends the use of systems thinking that includes social, financial and environmental values and impacts in decision making for agricultural development.
Lessons for South Africa’s proposed social security retirement reforms from the experience of other sub-Saharan African countries
(University of the Witwatersrand, Johannesburg, 2024) Walker, Stephen
The South African government intends reforming its current social security system, including retirement benefits. Views on how this should be done vary, even within government. Proposals often take the experience of other countries into consideration but there is limited literature on the experience of other sub-Saharan African countries. The region is experiencing demographic change, especially reduced infant mortality, reduced fertility and increasing old age longevity. Here South Africa is advanced relative to other countries in the region, despite the high unemployment levels. South Africa’s informal sector is large relative to developed countries, but smaller than elsewhere in Sub-Saharan Africa. Countries in the region have tried several approaches when introducing reform. Level A non- contributory pensions in South Africa are advanced, relative to most countries in the region. Most other countries have mandatory, contributory, government-run level B funds, the closest equivalent in South Africa is the Unemployment Insurance Fund. DB level B schemes are the norm. However, many countries are experiencing strain on the financial sustainability of these schemes and a number of countries have had to increase scheme contributions or reduce benefits. Occupational retirement funds in South Africa are well established and have experienced significant reforms recently. South Africa’s level C2 occupational retirement fund coverage is not mandated by government but is high relative to other countries in the region, even those with compulsory coverage under level C1. South Africa is still relatively new to introducing contributory pensions for informal sector workers. Other countries have tried various approaches under both levels D1 and D2 without finding a perfect solution. The research shows that maximising coverage requires all pension types. Pension reform is an iterative process, there is no perfect solution and phasing-in change is best. Government should make decisions on what incremental improvements can be made and start implementing these. The sequencing of reforms is important, what happens at each level of pension provision will influence what can and should be done at the next level. South Africa should move towards universalisation of non-contributory pensions but needs to do so in a cost-effective manner. The experience in other countries in the region should be considered when setting goals for coverage of informal sector workers by a level D1 or D2 contributory scheme. Compulsory contributory pensions should be introduced for formal sector workers, shifting from a level C2 to a level C1 approach. Expanding the Unemployment Insurance Fund to cater for retirement benefits as opposed to creating a new level B national fund should be explored.
Predicting Future Stock Price with Sentiment Analysis: Recurrent vs. Attention Based Learning for Regression Tasks
(University of the Witwatersrand, Johannesburg, 2023-08) Mcdonald, Bernard; Nasejje, Justine
Stock price prediction is a lucrative challenge as successful prediction could yield significant profits for investors – attracting research utilising novel data sources and modelling techniques. This research aimed to accurately predict the future closing price of the top five stocks of the NASDAQ100 index by leveraging Twitter data and recent advancements in machine learning. Three representations of large-scale Twitter data were derived: company, stock market, and general public sentiment. Company sentiment and stock market sentiment were Granger-causal (p < 0.10) for the closing price of four and two of the five companies considered, respectively. Five stock price prediction models were built: ARIMA, RNN, LSTM, GRU, and a novel Transformer model. A hyperparameter grid search selected feature subsets containing sentiment data as optimal in sixteen of the twenty (80%) model-dataset combinations fitted. Assessed using the RMSE, all the machine learning models outperformed the ARIMA model. The attention-based Transformer model outperformed the recurrent models in both predictive performance and model computational training efficiency. The model produced test RMSEs of 1.22, 2.07, 35.54, 16.61, and 4.95 when predicting the closing price of Apple, Microsoft, Amazon, Alphabet, and Facebook respectively.
Relaxed Inertial Algorithm for Solving Equilibrium Problems
(University of the Witwatersrand, Johannesburg, 2024) Elijah, Nwakpa Chidi
In this dissertation, we propose and study two relaxed inertial methods for solving equilibrium problems. In our first proposed method, we establish that the generated sequence of our proposed method weakly converges to a solution of the equilibrium problems. We apply this proposed method to variational inequality and fixed point problems. Further- more, a modification of the first method leads us to our second iterative method. Again, we established that the sequence generated by this method converges strongly to a solution of the equilibrium problems. Our proposed methods involve self-adaptive stepsizes and hence, do not require the fore knowledge of the Lipschitz constants for implementation. In each of our proposed methods, the convergence is established when the associated cost bifunction is pseudomonotone and satisfies the Lipschitz-type condition
Skyrmions and vectorial wavefunctions
(University of the Witwatersrand, Johannesburg, 2024) Ornelas, Pedro; Forbes , Andrew
The study and generation of robust structured light stand as compelling areas of focus in the exploration of future classical and quantum photonic technologies. While the appeal of structuring light in all its degrees of freedom (DOFs) is undeniable, achieving the generation of intricate light resilient to noise from multiple sources, such as faulty detectors, stray white light, and atmospheric turbulence, is imperative for its practical integration into forthcoming technologies. Recently, there has been a lot of interest in generating states of light with identifiable topological features which are robust to local deformations thus providing such states with a possible mechanism for noise rejection. Topological structures known as optical skyrmions have garnered a lot of interest in the optics community of late as their magnetic counterparts have shown great promise as potential low-power information carriers. It has been shown that skyrmionic structures may be realised in classical free-space optical beams where their spatial and polarization DOFs are appropriately combined and manipulated to generate what are known as vector beams. Furthermore with the emergence of quantum structured light allowing for the manipulation of an individual photon’s DOFs, such topological structures may also be utilized as a resource for photonic based quantum technologies. In this dissertation we investigate the generation of classical optical skyrmions through the use of Bessel-Gaussian optical modes possessing interesting propagation dynamics which mimic magnetic systems under the application of a magnetic field. Furthermore, we extend the study of optical skyrmions to the quantum realm by generating and characterizing the topology of the quantum analogue to classical vector beams: hybrid entangled states where the spatial DOF of one photon is entangled with the polarization DOF of another. In this case the skyrmionic topology emerges as a shared property of both photons and can be identified through investigating their mutual correlations. We postulate a novel topological characterization of entangled states with the corollary that smooth deformations of these states do not change their topology and thus do not change how they are characterized. We show that the topology remains intact even when entanglement is fragile and further discuss how a typical mechanism for entanglement decay can be characterized as a smooth deformation. Lastly, we investigate the topological resilience of hybrid entangled states in the presence of isotropic noise usually attributed to external sources. We demonstrate the invariance of the topology of these states to varying levels of isotropic noise and discuss the associated mechanism for this invariance.
Structural Characterization of Bimetal-Phosphate Based Solid-State Electrolytes: A PXRD, PDF and XAS Study
(University of the Witwatersrand, Johannesburg, 2024) Nkala, Gugulethu Charmaine; Billing, David G.; Billing, Caren; Vila, Fernando D.; Forbes, Roy P.
In this work, NASICON-type lithium titanium phosphate (LiTi2(PO4)3, LTP) was synthesized following the conventional solid-state reaction methodology. Single and double-doped formulations of LTP were made, with the primary objective of improving the room-temperature ionic conductivity, for their application as potential solid-state electrolytes for all-solid-state Li ion batteries. The primary characterization technique applied was ambient-temperature powder X-ray diffraction (PXRD) at both laboratory and synchrotron experimental conditions. The Rietveld refinement approach was used to determine the qualitative and quantitative phase compositions of each sample, revealing the rhombohedral (R-3c, space group #167) main phase, with phosphate-based secondary phases. Total scattering data, through the pair distribution function (PDF) was applied, revealing lattice site preference during the substitution of Ti with Al, Sn and Dy at the 12c site. Further analysis through small-box modelling indicated the local structure deviation below 10 Å, from rhombohedral (R-3c) to monoclinic (P21/n, space group #14). The application of experimental X-ray absorption spectroscopy (XAS) revealed a stable 4+ oxidation state for Ti regardless of doping. However, the extended X-ray absorption fine structure (EXAFS) data showed that the replacement of Ti with Sn results in heavy disorder and subsequent changes in the PO4 tetrahedra, corroborating the findings from Raman spectroscopy. Theoretical XAS spectra were computed using FEFF, providing insights into the origins of experimentally observed XAS features from first-principles. Applying electrochemical impedance spectroscopy (EIS) to assess the ambient-temperature ionic conductivity, co-doped systems showed an improvement in the conductivity. The application of characterization techniques at various length scales has been demonstrated to provide insights into the mechanisms governing the performance of the solid-state electrolytes.
The Assessment of the Current Geographical Information System (GIS) initiatives in the public enterprises of Swaziland
(University of the Witwatersrand, Johannesburg, 2022) Khumalo, Malungisa Blessing; Adam, Elhadi
There is a growing use of geographic information systems (GIS) within the public sector in many countries. GIS require considerable financial resources and investment in information and communication technology (ICT) and human resources, which are primarily financed by public funds. The growth in adoption is partly influenced by the promising potential of GIS that has been widely discussed in the literature on GIS. The usefulness and application of GIS in aiding decision making and in public policy formulation and implementation have also been widely discussed in the literature on GIS. To examine the effectiveness of GIS in public policy, one has to develop a mechanism for measuring the success achieved by the implementation of GIS in decision making. However, the methodologies for the evaluation of the use of GIS in the public sector are mainly lacking. The aims of this research were to evaluate the effective use of GIS in the public sector in Swaziland. Three organisations were selected, namely the Swaziland Posts and Telecommunications (SPTC), Swaziland Water Services Corporation (SWSC) and Swaziland National Housing Board (SNHB). Like in most developing countries, the lack of GIS evaluation to improve implementation is a challenge for these organisations. The current GIS applications at SPTC, SWSC and SNHB were evaluated using maturity, value and GIS product assessments. Four methods of analysis were used for data analysis: GIS maturity calculation; relative frequency of maturity calculation; gap analysis; and GIS value assessment. The results found that the SPTC, SWSC and SNHB were all in the exploitation stage of maturity. The overall relative frequency of maturity in the dimensions is the following: 35% of indicators are in the exploration stage; 56% are in the exploitation stage; and 9% are in the enterprise stage. The gap analysis shows that the organisations are in the exploitation stage of maturity. Cost prevention, coordination, employee satisfaction, better data management, time saving and better quality of information were regarded as the main ways in which GIS add value to organisations. The GIS product assessment results show that the overall compliance rate with the cartographic standards is 57.09%.
The Large N Limit of Heavy Operator Excitations
(University of the Witwatersrand, Johannesburg, 2023-07) Carlson, Warren Anthony; De Mello Koch, Robert
Operators with bare dimension of order N are studied. These are restricted Schur polynomials labeled by Young diagrams with two long rows or two long columns and are heavy operators in the large N limit. A dramatic simplification of the action of the dilatation operator on these states is found, where the diagonalization of the dilatation operator reduces to solving three-term recursion relations. The solutions to these recursion relations reduce the spectrum of the dilatation operator to that of decoupled harmonic oscillators, showing that these systems are integrable at large N. Then, generating functions for bound states of two giant gravitons are constructed and an extension to more than two giant gravitons is sketched. These generating functions are integrals over auxiliary variables that encode the symmetrization and anti-symmetrization of the fields in the restricted Schur polynomials and give a simple construction of eigenfunctions of the dilatation operator. These generating functions are shown to be eigenfunctions of the dilatation operator in the large N limit. As a byproduct, this construction gives a natural starting point for systematic 1/N expansions of these operators. This includes the prospect to generate asymptotic representations of the symmetric group and its characters via the restricted Schur polynomials. Finally, the asymptotic expansion of the three-point function is computed in three BMN limits by varying one parameter in the large N limit. It is argued that these asymptotic expansions encode non-perturbative effects and are related by a parametric Stokes phenomenon.
The role of invariants in obtaining exact solutions of differential equations
(University of the Witwatersrand, Johannesburg, 2024) Ahmed, Mogahid Mamoon Abkar; Kara, A.H.
We show here that variational and gauge symmetries have additional appli- cations to the integrability of differential equations. We present a general method to construct first integrals for some classes. In particular, we present a broad class of diffusion type equations, viz., the Fisher Kolmorov and Fitzhugh Nagumo equations, which satisfy the Painlev´e properties of their respective travelling wave forms and solitons. It is then shown how a study of invari- ance properties and conservation laws is used to ‘twice’ reduce the equations to solutions. We further constructing the first integrals of a large class of the well-known second-order Painlev´e equations. In some cases, variational and gauge symmetries have additional applications following a known Lagrangian in which case the first integral is obtained by Noether’s theorem. Generally, it is more convenient to adopt the ‘multiplier’ approach to find the first integrals. The main chapters of this thesis have either been published or submitted for publication in accredited journals. The contents of Chapters 2, 3 and 5 has been published ([54], [55]). All computations were done either by hand or Maple
Two-dimensional turbulent classical and momentumless thermal wakes
(University of the Witwatersrand, Johannesburg, 2023-07) Mubai, Erick; Mason, David Paul
The two-dimensional classical turbulent thermal wake and the two-dimensional momentumless turbulent thermal wake are studied. The governing partial differential equations result from Reynolds averaging the Navier-Stokes, the continuity and energy balance equations. The averaged Navier-Stokes and energy balance equations are closed using the Boussinesq hypothesis and an analogy of Fourier’s law of heat conduction. They are further simplified using the boundary layer approximation. This leads to one momentum equation with the continuity equation for an incompressible fluid and one thermal energy equation. The partial differential equations are written in terms of a stream function for the mean velocity deficit that identically satisfies the continuity equation and the mean temperature difference which vanishes on the boundary of the wake. The mixing length model and a model that assumes that the eddy viscosity and eddy thermal conductivity depend on spatial variables only are analysed. We extend the von Kármán similarity hypothesis to thermal wakes and derive a new thermal mixing length. It is shown that the kinematic viscosity and thermal conductivity play an important role in the mathematical analysis of turbulent thermal wakes. We obtain and use conservation laws and associated Lie point symmetries to reduce the governing partial differential equations to ordinary differential equations. As a result we find new analytical solutions for the two-dimensional turbulent thermal classical wake and momentumless wake. When the ordinary differential equations cannot be solved analytically we use a numerical shooting method that uses the two conserved quantities as the targets.

Browse

Browsing Faculty of Science (ETDs) by SDG "SDG-4: Quality education"

Results Per Page

Sort Options