Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize how genetic sequences evolve over phylogenetic trees – the branching processes that describe the patterns of genetic inheritance in living organisms. It has a long history of developing progressively more sophisticated stochastic models of evolution. Through a probabilist’s lens, this can be seen as a search for more appropriate ways to parameterize discrete state continuous time Markov chains to better encode biological reality, matching the historical processes that created empirical data sets, and creating useful tools that allow biologists to test specific hypotheses about the evolution of the organisms or the genes that interest them. This dissertation is an attempt to fill some of the gaps that persist in the literature, solving what we see as existing open problems. The overarching theme of this work is how to better model variation in the action of natural selection at multiple levels: across genes, between sites, and over time. Through four published journal articles and a fifth in preparation, we present amino acid and codon models that improve upon existing approaches, providing better descriptions of the process of natural selection and better tools to detect adaptive evolution. / AFRIKAANSE OPSOMMING: Komputasionele molekulêre evolusie is ’n navorsingsarea wat poog om die evolusie van genetiese sekwensies oor filogenetiese bome – die vertakkende prosesse wat die patrone van genetiese oorerwing in lewende organismes beskryf – te karakteriseer. Dit het ’n lang geskiedenis waartydens al hoe meer gesofistikeerde waarskynlikheidsmodelle van evolusie ontwikkel is. Deur die lens van waarskynlikheidsleer kan hierdie proses gesien word as ’n soektog na meer gepasde metodes om diskrete-toestand kontinuë-tyd Markov kettings te parametriseer ten einde biologiese realiteit beter te enkodeer – op so ’n manier dat die historiese prosesse wat tot die vorming van biologiese sekwensies gelei het nageboots word, en dat nuttige metodes geskep word wat bioloë toelaat om spesifieke hipotesisse met betrekking tot die evolusie van belanghebbende organismes of gene te toets. Hierdie proefskrif is ’n poging om sommige van die gapings wat in die literatuur bestaan in te vul en bestaande oop probleme op te los. Die oorkoepelende tema is verbeterde modellering van variasie in die werking van natuurlike seleksie op verskeie vlakke: variasie van geen tot geen, variasie tussen posisies in gene en variasie oor tyd. Deur middel van vier gepubliseerde joernaalartikels en ’n vyfde artikel in voorbereiding, bied ons aminosuur- en kodon-modelle aan wat verbeter op bestaande benaderings – hierdie modelle verskaf beter beskrywings van die proses van natuurlike seleksie sowel as beter metodes om gevalle van aanpassing in evolusie te vind.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This thesis investigate the di erent available GSM bearer channels that can be used to launch a cellphone banking application. Speci c attention is given to launch such a cellphone banking application to the so called \bottom of the pyramid". In South Africa, there are an estimate 11 to 13 million people with no bank accounts. The cellphone create an ideal opportunity to be used as a tool to reach this untapped market segment that today mainly uses cash to pay for day to day living expenses. The thesis provide more information on the cellphone banking arena in South Africa as well as certain projects in other parts of the world. The thesis also highlight new devel- opments on cellphone technology that include Android and IPhone delivery channels. Focus is placed on how the cellphone banking presentation layer must be delivered through the USSD GSM bearer channel. USSD is at the current moment the ultimate channel to consider due to its extensive reach and ability to work on any GSM cellphone handset. In conclusion, although cellphone banking can be used by any person, the bene t to bring nancial services to the bottom end of the pyramid must be considered to achieve nancial inclusion. The cellphone due to its reach is the ideal medium to access this lower end market. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek beskikbare GSM selfoon kanale wat gebruik kan word om 'n selfoon bankdienste toepassing te initieer. Spesi eke aandag word gegee om so 'n selfoon bankdienste toepassing uit te rol na die sogenaamde onderste gedeelte van die bevolkings piramiede. Die tesis verskaf meer informasie oor die selfoon bankdienste arena in Suid Africa maar dit brei ook ooit oor sekere soortgelyke projekte in ander dele van die wereld. Die tesis lig ook nuwe ontwikkelings uit in selfoon tegnologie wat Android en IPhone mediums insluit. Fokus word geplaas op die selfoon bankdienste vertoning deur die USSD GSM kanaal. USSD is huidiglik die beste kanaal om te oorweeg as gevolg van die wydverspreide beskik- baarheid omdat die tegnologie op enige selfoon handstuk werk. Die uiteindelike gevolgtrekking uit die werkstuk is dat selfoon bankdienste deur enige persoon gebruik kan word, maar selfoon bankdienste is 'n goeie idee om te oorweeg om mense in te sluit uit die onderste gedeelte van die bevolkings piramiede. Die selfoon kan dus as 'n ideale medium gebruik word om hierdie mense te betrek by nansiele dienste.

Thesis (MSc)--University of Stellenbosch, 2002. / See article for abstract

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: We investigate the application of weighted tree transducers to correcting grammatical errors in natural language. Weighted finite-state transducers (FST) have been used successfully in a wide range of natural language processing (NLP) tasks, even though the expressiveness of the linguistic transformations they perform is limited. Recently, there has been an increase in the use of weighted tree transducers and related formalisms that can express syntax-based natural language transformations in a probabilistic setting. The NLP task that we investigate is the automatic correction of grammar errors made by English language learners. In contrast to spelling correction, which can be performed with a very high accuracy, the performance of grammar correction systems is still low for most error types. Commercial grammar correction systems mostly use rule-based methods. The most common approach in recent grammatical error correction research is to use statistical classifiers that make local decisions about the occurrence of specific error types. The approach that we investigate is related to a number of other approaches inspired by statistical machine translation (SMT) or based on language modelling. Corpora of language learner writing annotated with error corrections are used as training data. Our baseline model is a noisy-channel FST model consisting of an n-gram language model and a FST error model, which performs word insertion, deletion and replacement operations. The tree transducer model we use to perform error correction is a weighted top-down tree-to-string transducer, formulated to perform transformations between parse trees of correct sentences and incorrect sentences. Using an algorithm developed for syntax-based SMT, transducer rules are extracted from training data of which the correct version of sentences have been parsed. Rule weights are also estimated from the training data. Hypothesis sentences generated by the tree transducer are reranked using an n-gram language model. We perform experiments to evaluate the performance of different configurations of the proposed models. In our implementation an existing tree transducer toolkit is used. To make decoding time feasible sentences are split into clauses and heuristic pruning is performed during decoding. We consider different modelling choices in the construction of transducer rules. The evaluation of our models is based on precision and recall. Experiments are performed to correct various error types on two learner corpora. The results show that our system is competitive with existing approaches on several error types. / AFRIKAANSE OPSOMMING: Ons ondersoek die toepassing van geweegde boomoutomate om grammatikafoute in natuurlike taal outomaties reg te stel. Geweegde eindigetoestand outomate word suksesvol gebruik in ’n wye omvang van take in natuurlike taalverwerking, alhoewel die uitdrukkingskrag van die taalkundige transformasies wat hulle uitvoer beperk is. Daar is die afgelope tyd ’n toename in die gebruik van geweegde boomoutomate en verwante formalismes wat sintaktiese transformasies in natuurlike taal in ’n probabilistiese raamwerk voorstel. Die natuurlike taalverwerkingstoepassing wat ons ondersoek is die outomatiese regstelling van taalfoute wat gemaak word deur Engelse taalleerders. Terwyl speltoetsing in Engels met ’n baie hoë akkuraatheid gedoen kan word, is die prestasie van taalregstellingstelsels nog relatief swak vir meeste fouttipes. Kommersiële taalregstellingstelsels maak oorwegend gebruik van reël-gebaseerde metodes. Die algemeenste benadering in onlangse navorsing oor grammatikale foutkorreksie is om statistiese klassifiseerders wat plaaslike besluite oor die voorkoms van spesifieke fouttipes maak te gebruik. Die benadering wat ons ondersoek is verwant aan ’n aantal ander benaderings wat geïnspireer is deur statistiese masjienvertaling of op taalmodellering gebaseer is. Korpora van taalleerderskryfwerk wat met foutregstellings geannoteer is, word as afrigdata gebruik. Ons kontrolestelsel is ’n geraaskanaal eindigetoestand outomaatmodel wat bestaan uit ’n n-gram taalmodel en ’n foutmodel wat invoegings-, verwyderings- en vervangingsoperasies op woordvlak uitvoer. Die boomoutomaatmodel wat ons gebruik vir grammatikale foutkorreksie is ’n geweegde bo-na-onder boom-na-string omsetteroutomaat geformuleer om transformasies tussen sintaksbome van korrekte sinne en foutiewe sinne te maak. ’n Algoritme wat ontwikkel is vir sintaksgebaseerde statistiese masjienvertaling word gebruik om reëls te onttrek uit die afrigdata, waarvan sintaksontleding op die korrekte weergawe van die sinne gedoen is. Reëlgewigte word ook vanaf die afrigdata beraam. Hipotese-sinne gegenereer deur die boomoutomaat word herrangskik met behulp van ’n n-gram taalmodel. Ons voer eksperimente uit om die doeltreffendheid van verskillende opstellings van die voorgestelde modelle te evalueer. In ons implementering word ’n bestaande boomoutomaat sagtewarepakket gebruik. Om die dekoderingstyd te verminder word sinne in frases verdeel en die soekruimte heuristies besnoei. Ons oorweeg verskeie modelleringskeuses in die samestelling van outomaatreëls. Die evaluering van ons modelle word gebaseer op presisie en herroepvermoë. Eksperimente word uitgevoer om verskeie fouttipes reg te maak op twee leerderkorpora. Die resultate wys dat ons model kompeterend is met bestaande benaderings op verskeie fouttipes.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions. / AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Nurses, midwives and clinical officers referred to as Mid-level Practioners (MLPs) play an important role in the health care system especially in rural Africa. With particular reference to rural Uganda, due to the large shortage of doctors, MLPs handle most of the duties usually meant for doctors, at health centre IV(s). From 2009 to 2011, two training interventions of MLPs were performed at 36 sites in Uganda by the Integrated Infectious Disease Capacity Building Evaluation (IDCAP). The two interventions were: Integrated Management of Infectious Diseases (IMID) and On-site Support Services (OSS) which aimed at improving MLPs’ case management for four diseases: HIV, TB, pneumonia and malaria. In this thesis, we have developed three mathematical models to investigate the effect of the two training interventions on these infectious diseases. All the models are formulated using systems of ordinary differential equations which are structured in three age groups: [0, 5), [5, 14) and [14, 50). We explored the effect of the two training interventions in the context of malaria-pneumonia, HIV-TB co-infections and the four diseases together. Our analysis shows that: i) For malaria-pneumonia, both IMID and the combination of IMID and OSS reduce the number of cases, deaths and prevalence of disease but have no effect on the incident episodes of disease. ii) Results from the HIVTB model propose that HIV and TB testing are important steps in quality of health care and are capable of offsetting slightly negative effects of reduction in ART enrollment and provision of treatment. iii) The HIV-TB-malaria-pneumonia (HTMP) model concurs with the results of the first two models and its results demonstrate that high coverage levels of the training interventions increase the positive effects that the interventions have on mortality and morbidity. Overall, our results suggest that training of MLPs is much more effective for the short term duration diseases such as malaria and pneumonia, where the baseline values for most of the performance indicators are ≥ 0.6, but not so much for long term duration diseases such as HIV and TB, whose baseline values for most of the performance indicators are < 0.6. The results further highlight that problems such as case detection and drug stock-outs need to be addressed in order for training to have substantial impact, especially in instances where the performance indicator proportions are low. / AFRIKAANSE OPSOMMING: Verpleegsters, vroedvroue en kliniese beamptes wat gesamentlik na verwys word as midvlak praktisyns (MVPs) , speel n belangrike rol in die gesondheidsorg sisteem, veral in landelike dele van Afrika. Met spesifieke verwysing na gesondheid sentrums in Uganda, waar daar te min dokters is, hanteer MVPs die meeste van die pligte wat eintlik deur dokters verrig moet word. Vanaf 2009 tot 2011 is twee opleidingsprogramme vir MVPs by 36 fasiliteite in Uganda deur die Integrated Infectious Disease Capacity Building Evaluation (IDCAP) organisasie aangebied. Die twee programme staan bekend as: Integrated Management of Infectious Diseases (IMID) and On-site Support Services (OSS). Beide die programme stel ten doel om die MVPs se pasint bestuur vir die siektes MIV, tuberkulose (TB), longontsteking en malaria te verbeter. Drie wiskundige modelle word in hierdie tesis ontwikkel om die effek van die opleidingsprogramme op hierdie oordraagbare siektes te ondersoek. Al die modelle word geformuleer deur gebruik te maak van stelsels van gewone differensiaal vergelykings wat gestruktureer is in drie ouderdomsgroepe: [0, 5), [5, 14) en [14, 50). Die effek van die opleidings programme word in die konteks van longontstekingmalaria mede-infeksie, MIV- TB mede-infeksie en al vier siektes gelyk, ondersoek. Die analise wys dat: i) Vir longontsteking-malaria mede-infeksie het beide IMID en die kombinasie van IMID en OSS die aantal siekte-gevalle, sterftes en die prevalensie van die siektes verminder, maar het geen effek op die insidensie van siekte-gevalle nie. ii) Resultate van die MIV-TB model dui aan dat MIV en TB toetsing n belangrike aspek van die gehalte van sorg is en dat dit die effense negatiewe effek van die afname in ART inskrywing en voorsiening van behandeling, teenstaan. iii) Die MIV-TB-longontsteking-malaria model (HTMP) stem ooreen met die resultate van die bogenoemde twee modelle en demonstreer dat ho dekking van die opleidingsprogramme die positiewe effek van die programme op mortaliteit en morbiditeit verhoog. In geheel stel die resultate van hierdie studie voor dat die opleiding van MVPs baie meer effektief is vir die korttermyn siektes soos malaria en longontsteking waarvoor die meeste van die beginwaardes van die prestasie-aanwysers ≥ 0.6 is, maar nie soveel vir lang-termyn siektes soos MIV en TB waarvoor die meeste van die beginwaarde van die prestasie-aanwysers < 0.6 is. Die resultate dui verder aan dat opleiding nie voldoende is wanneer die prestasie-aanwysers < 0.6 is nie en dat probleme soos die opsporing van siekte-gevalle en n gebrek aan medisyne by die klinieke aangespreek moet word vir opleiding om aansienlike impak te hê.

Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / In this thesis we consider the modelling of a particular layout optimisation problem, namely, the LEGO construction problem. The LEGO construction problem, in short, concerns the optimal layout of a set of LEGO bricks to represent a given object. Our goal is to develop a software package which LEGO enthusiasts can use to construct LEGO sculptures for any real-world object. We therefore not only consider the layout optimisation problem, but also the generation of the input data required by the LEGO construction problem. We show that by using 3D geometric models to represent the real-world object, our implemented voxelisation technique delivers accurate input data for the LEGO construction problem. The LEGO construction problem has previously been solved with optimisation techniques based on simulated annealing, evolutionary algorithms, and a beam search approach. These techniques all indicate that it is possible to generate LEGO building instructions for real-world objects, albeit not necessarily in reasonable time. We show that the LEGO construction problem can be modelled easily with cellular automata, provided that cells are considered as clusters which can merge or split during each time step of the evolution of the cellular automaton. We show that the use of cellular automata gives comparable layout results in general, and improves the results in many respects. The cellular automata method requires substantially less memory and generally uses fewer LEGO bricks to construct the LEGO sculpture when using comparable execution times.