School Mathematics, Statistics and Computer Science
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Browsing School Mathematics, Statistics and Computer Science by SDG "SDG4"
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Item Application of ELECTRE algorithms in ontology selection.(2022) Sooklall, Ameeth.; Fonou-Dombeu, Jean Vincent.The field of artificial intelligence (AI) is expanding at a rapid pace. Ontology and the field of ontological engineering is an invaluable component of AI, as it provides AI the ability to capture and express complex knowledge and data in a form that encourages computation, inference, reasoning, and dissemination. Accordingly, the research and applications of ontology is becoming increasingly widespread in recent years. However, due to the complexity involved with ontological engineering, it is encouraged that users reuse existing ontologies as opposed to creating ontologies de novo. This in itself has a huge disadvantage as the task of selecting appropriate ontologies for reuse is complex as engineers and users may find it difficult to analyse and comprehend ontologies. It is therefore crucial that techniques and methods be developed in order to reduce the complexity of ontology selection for reuse. Essentially, ontology selection is a Multi-Criteria Decision-Making (MCDM) problem, as there are multiple ontologies to choose from whilst considering multiple criteria. However, there has been little usage of MCDM methods in solving the problem of selecting ontologies for reuse. Therefore, in order to tackle this problem, this study looks to a prominent branch of MCDM, known as the ELimination Et. Choix Traduisant la RÉalite (ELECTRE). ELECTRE is a family of decision-making algorithms that model and provide decision support for complex decisions comprising many alternatives with many characteristics or attributes. The ELECTRE algorithms are extremely powerful and they have been applied successfully in a myriad of domains, however, they have only been studied to a minimal degree with regards to ontology ranking and selection. In this study the ELECTRE algorithms were applied to aid in the selection of ontologies for reuse, particularly, three applications of ELECTRE were studied. The first application focused on ranking ontologies according to their complexity metrics. The ELECTRE I, II, III, and IV models were applied to rank a dataset of 200 ontologies from the BioPortal Repository, with 13 complexity metrics used as attributes. Secondly, the ELECTRE Tri model was applied to classify the 200 ontologies into three classes according to their complexity metrics. A preference-disaggregation approach was taken, and a genetic algorithm was designed to infer the thresholds and parameters for the ELECTRE Tri model. In the third application a novel ELECTRE model was developed, named ZPLTS-ELECTRE II, where the concept of Z-Probabilistic Linguistic Term Set (ZPLTS) was combined with the traditional ELECTRE II algorithm. The ZPLTS-ELECTRE II model enables multiple decision-makers to evaluate ontologies (group decision-making), as well as the ability to use natural language to provide their evaluations. The model was applied to rank 9 ontologies according to five complexity metrics and five qualitative usability metrics. The results of all three applications were analysed, compared, and contrasted, in order to understand the applicability and effectiveness of the ELECTRE algorithms for the task of selecting ontologies for reuse. These results constitute interesting perspectives and insights for the selection and reuse of ontologies.Item Financial modelling of cryptocurrency: a case study of Bitcoin, Ethereum, and Dogecoin in comparison with JSE stock returns.(2022) Kaseke, Forbes.; Ramroop, Shaun.; Mwambi, Henry Godwell.The emergency of cryptocurrency has caused a shift in the financial markets. Although it was created as a currency for exchange, cryptocurrency has been shown to be an asset, with investors seeking to profit from it rather than using it as a medium of exchange. Despite being a financial asset, cryptocurrency has distinct, stylised facts like any other asset. Studying these stylised facts allows the creation of better-suited models to assist investors in making better data-driven decisions. The data used in this thesis was of three leading cryptocurrencies: Bitcoin, Ethereum, and Dogecoin and the Johannesburg Stock Exchange (JSE) data as a guide for comparison. The sample period was from 18 September 2017 to 27 May 2021. The goal was to research the stylised facts of cryptocurrencies and then create models that capture these stylised facts. The study developed risk-quantifying models for cryptocurrencies. The main findings were that cryptocurrency exhibits stylised facts that are well-known in financial data. However, the magnitude and frequency of these stylised facts tend to differ. For example, cryptocurrency is more volatile than stock returns. The volatility also tends to be more persistent than in stocks. The study also finds that cryptocurrency has a reverse leverage effect as opposed to the normal one, where past negative returns increase volatility more than past positive returns. The study also developed a hybrid GARCH model using the extreme value theorem for quantifying cryptocurrency risk. The results showed that the GJR-GARCH with GDP innovations could be used as an alternative model to calculate the VaR. The volatile nature of cryptocurrency was also compared with that of the JSE while accounting for structural breaks and while not accounting for them. The results showed that the cryptocurrencies’ volatility patterns are similar but differ from those of the JSE. The cryptocurrency was also found to be an inefficient market. This finding means that some investors can take advantage of this inefficiency. The study also revealed that structural breaks affect volatility persistence. However, this persistence measure differs depending on the model used. Markov switching GARCH models were used to strengthen the structural break findings. The results showed that two-regime models outperform single-regime models. The VAR and DCC-GARCH models were also used to test the spillovers amongst the assets used. The results showed short-run spillovers from Bitcoin to Ethereum and long-run spillovers based on the DCC-GARCH. Lastly, factors affecting cryptocurrency adoption were discussed. The main reasons affecting mass adoption are the complexity that comes with the use of cryptocurrency and its high volatility. This study was critical as it gives investors an understanding of the nature and behaviour of cryptocurrency so that they know when and how to invest. It also helps policymakers and financial institutions decide how to treat or use cryptocurrency within the economy.Item Flexible Bayesian hierarchical spatial modeling in disease mapping.(2022) Ayalew, Kassahun Abere.; Manda, Samuel.The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis was to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considered the skewnormal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considered non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model were evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD has shown the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.Item Hybrid genetic optimisation for quantum feature map design.(2024) Pellow-Jarman, Rowan.; Pillay, Anban Woolaganathan.; ILya, Sinayskiy.; Petruccione, Francesco.Good feature maps are crucial for machine learning kernel methods for effective mapping of non-linearly separable input data into a higher dimension feature space, thus allowing the data to be linearly separable in feature space. Recent works have proposed automating the task of quantum feature map circuit design with methods such as variational ansatz parameter optimization and genetic algorithms. A problem commonly faced by genetic algorithm methods is the high cost of computing the genetic cost function. To mitigate this, this work investigates the suitability of two metrics as alternatives to test set classification accuracy. Accuracy has been applied successfully as a genetic algorithm cost function for quantum feature map design in previous work. The first metric is kernel-target alignment, which has previously been used as a training metric in quantum feature map design by variational ansatz training. Kernel-target alignment is a faster metric to evaluate than test set accuracy and does not require any data points to be reserved from the training set for its evaluation. The second metric is an estimation of kernel-target alignment which further accelerates the genetic fitness evaluation by an adjustable constant factor. The second aim of this work is to address the issue of the limited gate parameter choice available to the genetic algorithm. This is done by training the parameters of the quantum feature map circuits output in the final generation of the genetic algorithm using COBYLA to improve either kernel-target alignment or root mean squared error. This hybrid approach is intended to complement the genetic algorithm structure optimization approach by improving the feature maps without increasing their size. Eight new approaches are compared to the accuracy optimization approach across nine varied binary classification problems from the UCI machine learning repository, demonstrating that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the original approach, with larger margins on training data that improve further with variational training.Item Mathematical modelling of the Ebola virus disease.(2024) Abdalla, Suliman Jamiel Mohamed.; Govinder, Keshlan Sathasiva.; Chirove, Faraimunashe.Despite the numerous modelling efforts to advise public health physicians to understand the dynamics of the Ebola virus disease (EVD) and control its spread, the disease continued to spread in Africa. In the current thesis, we systematically review previous EVD models. Further, we develop novel mathematical models to explore two important problems during the 2018-2020 Kivu outbreak: the impact of geographically targeted vaccinations (GTVs) and the interplay between the attacks on Ebola treatment centres (ETCs) and the spread of EVD. In our systematic review, we identify many limitations in the modelling literature and provide brief suggestions for future work. Our modelling findings underscore the importance of considering GTVs in areas with high infections. In particular, we find that implementing GTVs in regions with high infections so that the total vaccinations are increased by 60% decreases the cumulative cases by 15%. On the other hand, we need to increase the vaccinations to more than 1000% to achieve the 15% decrease in EVD cases if we implement GTVs in areas with low infections. On the impact of the attacks on ETCs, we find that due to the attacks on ETCs, the cumulative cases increased by more than 17% during the 2018-2020 Kivu outbreak. We also find that when 10% of the hospitalised individuals flee the attacks on ETCs after spending only three days under treatment, the cumulative cases increased by more than 30% even if these individuals all returned to the ETCs three days later. On the other hand, if only half of these individuals returned to ETCs for treatment, the cumulative cases increase by approximately 50%. Further, when these patients spend one more day in the community, after which they all return to ETCs, the cumulative cases rise by an additional 10%. Global sensitivity analysis also confirmed these findings. To conclude, our literature systematic review is used to identify many critical factors which were overlooked in previous EVD models. Our modelling findings show that the attacks on ETCs can be destructive to the efforts of EVD response teams. Hence, it is important for decision-makers to tackle the reasons for community distrust and address the roots of the hostility towards ETCs. We also find that GTVs can be used to contain the spread of EVD when ring vaccinations, contact tracing and antiviral treatments cannot successfully control the spread of EVD.Item Statistical study on childhood malnutrition and anaemia in Angola, Malawi and Senegal.(2023) Khulu, Mthobisi Christian.; Ramroop, Shaun.; Habyarimana, Faustin.Malnutrition and anaemia continue to be a concern to the future of developing countries. This thesis aimed to examine the risk factors associated with malnutrition and anaemia among under five-year-old children in Angola, Malawi and Senegal. Statistical models and techniques have improved over the years to give more insight into malnutrition and anaemia, in terms of demographic, socio-economic, environmental, and geographic factors. This thesis also assessed the spatial epidemiological overlaps between childhood malnutrition and anaemia diseases which can lead to various advantages in intervention planning, monitoring, controlling and total elimination of such diseases, especially in high-risk regions. This is a secondary data analysis where national representative data from the three countries was used. The Demographic and Health Survey data from Angola, Malawi and Senegal were merged to create a pooled sample which was then used for all the analyses conducted in this study. The relationship between exploratory variables to malnutrition and anaemia was assessed to obtain variables that explain the two outcomes. Consequently, a generalized linear mixed model was used to investigate the significance of the child-level, community-level and household-level factors to malnutrition and anaemia separately. The relationship between the two diseases was further examined using the three joint modelling approaches: (1) a joint generalised linear mixed model; (2) a structural equation model, and (3) a bivariate copula geo-additive model. For each model employed, the significant factors of both malnutrition and anaemia were identified. The GLMM results on malnutrition revealed that children’s place of residence, age, gender, mother’s level of schooling, wealth status, birth interval and birth order significantly explain malnutrition at the 5% level of significance. Whereas, the GLMM results on anaemia revealed that children‘s age, gender, mother’s level of schooling, wealth status and nutritional status significantly explain anaemia at 5% level of significance. The findings of copula geo-additive modelling of malnutrition and anaemia indicated that there is an association between malnutrition and anaemia. There was a strong association observed between malnutrition and anaemia in the north-west districts of Angola when compared to other districts. The results imply that the policymakers of Angola, Senegal and Malawi can control anaemia through the intervention of malnutrition controlling. The overall findings of this study provide meaningful insight to the policymakers of Angola, Malawi and Senegal which will lead to the implementation of interventions that can assist in achieving the Sustainable Development Goal (SDG) of 25 deaths per 1 000 live births by 2030. To properly eradicate all the causes of malnutrition and anaemia, programs such as parental education, financial education, children's dietary focus programs and mobile health facilities could add a significant value. The results also highlighted the national priority areas related to child-related factors, household factors and environmental factors for childhood malnutrition and anaemia morbidity control. It also provided policy makers with valuable geographical information for developing and implementing effective intervention. There is a greater need for partnership and collaboration among the studied countries to achieve the SGD target.