Department of Mathematical Sciences

The seesaw effect of winter temperature change on the recruitment of cotton bollworms Helicoverpa armigera through mismatched phenology

Thu, 01 Jan 2015 00:00:00 GMT

The seesaw effect of winter temperature change on the recruitment of cotton bollworms Helicoverpa armigera through mismatched phenology Reddy, Gadi V. P.; Shi, Peijian; Hui, Cang; Cheng, Xiaofei; Ouyang, Fang; Ge, Feng Knowing how climate change affects the population dynamics of insect pests is critical for the future of integrated pest management. Rising winter temperatures from global warming can drive increases in outbreaks of some agricultural pests. In contrast, here we propose an alternative hypothesis that both extremely cold and warm winters can mismatch the timing between the eclosion of overwintering pests and the flowering of key host plants. As host plants normally need higher effective cumulative temperatures for flowering than insects need for eclosion, changes in flowering time will be less dramatic than changes in eclosion time, leading to a mismatch of phenology on either side of the optimal winter temperature. We term this the “seesaw effect.” Using a long-term dataset of the Old World cotton bollworm Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) in northern China, we tested this seesaw hypothesis by running a generalized additive model for the effects of the third generation moth in the preceding year, the winter air temperature, the number of winter days below a critical temperature and cumulative precipitation during winter on the demography of the overwintering moth. Results confirmed the existence of the seesaw effect of winter temperature change on overwintering populations. Pest management should therefore consider the indirect effect of changing crop phenology (whether due to greenhouse cultivation or to climate change) on pest outbreaks. As arthropods from mid- and high latitudes are actually living in a cooler thermal environment than their physiological optimum in contrast to species from lower latitudes, the effects of rising winter temperatures on the population dynamics of arthropods in the different latitudinal zones should be considered separately. The seesaw effect makes it more difficult to predict the average long-term population dynamics of insect pests at high latitudes due to the potential sharp changes in annual growth rates from fluctuating minimum winter temperatures. CITATION: Reddy, G. V. P. et al. 2015. The seesaw effect of winter temperature change on the recruitment of cotton bollworms Helicoverpa armigera through mismatched phenology. Ecology and Evolution, 5(23):5652–5661, doi:10.1002/ece3.1829.; The original publication is available at http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2045-7758

An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo

Tue, 17 Mar 2015 00:00:00 GMT

An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo Cheng, Xiao-Fei; Shi, Pei-Jian; Hui, Cang; Wang, Fu-Sheng; Liu, Guo-Hua; Li, Bai-Lian Moso bamboos (Phyllostachys edulis) are important forestry plants in southern China, with substantial roles to play in regional economic and ecological systems. Mixing broad-leaved forests and moso bamboos is a common management practice in China, and it is fundamental to elucidate the interactions between broad-leaved trees and moso bamboos for ensuring the sustainable provision of ecosystem services. We examine how the proportion of broad-leaved forest in a mixed managed zone, topology, and soil profile affects the effective productivity of moso bamboos (i.e., those with significant economic value), using linear regression and generalized additive models. Bamboo's diameter at breast height follows a Weibull distribution. The importance of these variables to bamboo productivity is, respectively, slope (25.9%), the proportion of broad-leaved forest (24.8%), elevation (23.3%), gravel content by volume (16.6%), slope location (8.3%), and soil layer thickness (1.2%). Highest productivity is found on the 25° slope, with a 600-m elevation, and 30% broad-leaved forest. As such, broad-leaved forest in the upper slope can have a strong influence on the effective productivity of moso bamboo, ranking only after slope and before elevation. These factors can be considered in future management practice. CITATION: Cheng, X.-F. et al. 2015. An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo. Ecology and Evolution, 5(8):1576–1584, doi:10.1002/ece3.1446.; The original publication is available at http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2045-7758/

Ultraproducts and Los’s Theorem: A Category-Theoretic Analysis

Wed, 01 Mar 2017 00:00:00 GMT

Ultraproducts and Los’s Theorem: A Category-Theoretic Analysis Chimes, Mark Jonathan ENGLISH ABSTRACT : Ultraproducts are an important construction in model theory, especially as applied to algebra. Given some family of structures of a certain type, an ultraproduct of this family is a single structure which, in some sense, captures the important aspects of the family, where “important” is defined relative to a set of sets called an ultrafilter, which encodes which subfamilies are considered “large”. This follows from Lo´s’s Theorem, namely, the Fundamental Theorem of Ultraproducts, which states that every first-order sentence is true of the ultraproduct if, and only if, there is some “large” subfamily of the family such that it is true of every structure in this subfamily. In this dissertation, ultraproducts are examined both from the standard model-theoretic, as well as from the category-theoretic view. Some potential problems with the categorytheoretic definition of ultraproducts are pointed out, and it is argued that these are not as great an issue as first perceived. A general version of Lo´s’s Theorem is shown to hold for category-theoretic ultraproducts in general. This makes use of the concept of injectivity of a (compact) tree, which is intended to generalize truth of first-order formulae (under given assignments of variables), and, in the category of relational structures, corresponds exactly to first-order formulae. This type of thinking leads to a means of characterizing fields in the category of rings, and a new proof that every ultraproduct of fields is a field, which takes place entirely in the category of rings (along with the inclusion of the category of fields). Finally, the family of all (category-theoretic) ultraproducts on a given family is shown to arise from the “codensity monad" of the functor which includes the category of finite families into the category of families. In this sense, it is shown that ultraproducts are a rather natural construction category-theoretically speaking.; AFRIKAANSE OPSOMMING : Ultraprodukte is ’n belangrike konstruksie in modelteorie, veral in hul toepassings in algebra. Gegewe ’n reeks strukture van ’n sekere tipe, is ’n ultraproduk van hierdie reeks ’n enkele struktuur wat, op ’n manier, die belangrikste aspekte van die reeks bevat, waar “belangrik” hier gedefinie¨er word met betrekking tot ’n versameling reekse wat ’n ultrafilter genoem word. Hierdie ultrafilter verteenwoordig watter subreekse deur die ultraproduk as “groot” beskou word. Dit is ’n gevolgtrekking van Lo´s se Stelling, dit wil sˆe, ’n eersteorde stelling is waar met betrekking tot die ultraproduk as, en slegs as, daar ’n “groot” subreeks (van die hoofreeks) bestaan sodat die stelling waar is met betrekking tot elke struktuur in di´e subreeks. In hierdie tesis word ultraprodukte uit die standarde model-teoretiese oogpunt behandel, sowel as uit die oogpunt van kategorie teorie. Potentie¨ele probleme met die kategorie-teoretiese ultraproduk word uitgelig, maar dit word geargumenteer dat hul nie so ’n groot probleem veroorsaak as wat dit blyk nie. ’n Algmene weergawe van Lo´s se stelling is bewys vir alle kategorie¨e. D´ıt maak gebruik van die konsep van injektiwiteit van ’n (kompakte) boom. Die bedoeling hiervan is om die waarheid van ’n eerste-orde stelling (onder ’n gegewe toedeling van veranderlikes) te veralgemeen. Hierdie idee ly tot ’n metode om liggame in die kategorie van groepe uit te lig, sowel as ’n nuwe bewys dat elke ultraproduk van liggame weer self ’n liggaam is. Hierdie bewys neem heeltemaal in die kategorie van groepe plaas (tesame met die funktor wat die kategorie van liggame in die kategorie van groepe insluit). Laastens, word dit angevoer dat die reeks van alle (kategorie-teoretiese) ultraprodukte van ’n gegewe reeks bestaan uit die “codigtheids monade” van die funktor wat die kategorie van eindige reekse insluit in die kategorie van oneindige reekse. Hierdie is dan ’n oortuiging dat ultraprodukte redelik natuurlik bestaan, ten minste uit die oogpunt van kategorie-teorie. Thesis (MSc)--Stellenbosch University, 2017

Imaginaries in dense pairs of real-closed fields

Wed, 01 Mar 2017 00:00:00 GMT

Imaginaries in dense pairs of real-closed fields Rakotonarivo, Tsinjo Odilon ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we consider the following problem: is acleq equal to dcleq in dense pairs of real-closed fields? To answer this question, we first present some results about real-closed fields, which are basically completeness, quantifier elimination and elimination of imaginaries. Then, we concentrate on the completeness and near model-completeness for the theory of dense pairs of real-closed fields. And finally, we present the key point of the thesis. Namely, we demonstrate that acleq(∅) = dcleq(∅) but there exists A such that acleq(A) 6= dcleq(A); AFRIKAANSE OPSOMMING : Imaginêres is definiëerbare ekwivalensieklasse, wat ’n belangrike rol in modelteorie speel. In hierdie tesis stel ons belang in imaginêres in dig pare van reël-geslote liggame. Meer spesifiek beskou ons die volgende probleem: is acleq gelyk aan dcleq in dig pare van reël-geslote liggame? Om hierdie vraag te beantwoord, begin ons met ’n paar resultate oor reëlgeslote liggame, namelik volledigheid, kwantoreliminasie en eliminasie van imaginêres. Daarna behandel ons die volledigheid en byna-modelvolledigheid vir die teorie van dig pare van reël-geslote liggame. Uiteindelik behandel ons die hoofresultat van hierdie tesis, d.w.s. ons bewys dat acleq(∅) = dcleq(∅) maar dat daar A bestaan sodat acleq(A) 6= dcleq(A)

Immune biomarker reference range estimation for healthy paediatric patients in South Africa

Wed, 01 Mar 2017 00:00:00 GMT

Immune biomarker reference range estimation for healthy paediatric patients in South Africa Bicko, Steve Cygu ENGLISH ABSTRACT : Understanding and quantifying human peripheral blood T-lymphocyte immunophenotypes is necessary for the diagnosis and treatment of immune and haematological disorders. This is only possible if comparison to control-data from healthy subjects is available for all the biomarkers of interest. Historical empirical studies in industrialized countries have described normal reference ranges for such biomarkers in children by grouping particular age ranges into ‘age-blocks’. Since such markers change with age this has resulted in a loss of precision in determining whether patients that lie close to the limits of age-ranges are normal or not. Previous studies have relied on fitting single exponential models to such data, which makes the simple assumption of an exponential decline in cell markers with age. However, the counts of such markers have been observed to increase from birth to between 6 months to 12 months from birth and then decrease continuously with age. There is a dearth of reference range estimation methods which are age-continuous and incorporate biologically mechanistic models. A more ideal solution would be the development of appropriate mathematical models and modelbased, age-continuous reference range estimation methods that describe such changes in a continuous manner. Such models may then be used to investigate the influence of population covariates on age-related changes in the biomarkers of interest. In this study, we employ paediatric data from a cohort of 381 healthy South African children. This is cross-sectional in design and the biomarkers described include: CD3+, CD19+, CD8+, CD4+, ratio of CD4+ naive/memory, CD18+CD56+ and CD3-CD56+. Using weighted generalized nonlinear least squares, we fit and compare single and double exponential semi-mechanistic models. An ideal model is selected based on the Akaike’s Information Criterion (AIC). The double exponential model is found to be the best fit for age-related changes in such biomarkers. This predicts that cell counts rise after birth to a maximum at approximately 12 months of age and decline in an exponential manner towards an asymptote in adulthood. This is in agreement with prior empirical and mechanistic studies. We extend the double exponential model to investigate the influence of particular covariates. The type of feeding in the first 6 months following birth is found to be the covariate with the greatest influence on age-related changes in the majority of the biomarkers investigated. A model-based method to estimate age-continuous reference ranges is then proposed. This assumes that particular reference ranges are a specified shift of the ‘running’ standard deviations of residuals away from a fitted central model function by a Z-score. We compare this method to reference ranges calculated using traditional centile curves. Centile curves demonstrate a simpler negative singleexponential decline as age advances and enable no mechanistic interpretation for this pattern. The models employed in this study may lead to the development of a laboratory tool by which individual cell-marker values may be compared to healthy agecontinuous reference ranges.; AFRIKAANSE OPSOMMING : Die diagnose en behandeling van immuun en hematologiese afwykings benodig die begrip van en kwantifisering van menslike perifere bloed T-limfosiet immuun-fenotipes. Dit is slegs moontlik indien vergelyking met data van gesonde pasiente beskikbaar is vir al die biomerkers van belang. Historiese empiriese studies in geïndustrialiseerde lande het al sulke normale verwysings waardes vir kinders beskryf, maar deur groepering van die data in spesifieke ‘ouderdoms-blokke’. Aangesien sulke biomerkers aanhoudend verander met ouderdom, het dit gelei tot ‘n verlies aan akkuraatheid in die bepaling van normaliteit van pasiënte wat naby aan die grense van sulke ouderdoms-groepe lê. Ander studies het staatgemaak op die pas van enkel-eksponensiële modelle op sodanige data, wat die eenvoudige aanname maak van ‘n eksponensiële afname in sel merkers met ouderdom. Dit was wel al waargeneem dat sulke merkers verhoog vanaf geboorte tot tussen 6 en 12 maande na geboorte en dan voortdurend daal met vergrotende ouderdom. Daar is ‘n gebrek aan verwysings waarde skattings metodes wat ouderdomaaneenlopend is en biologies meganistiese modelle inkorporeer. ‘N Meer ideale oplossing sou die ontwikkeling wees van toepaslike wiskundige verwysings waarde skattings metodes wat model-gebaseer en ouderdoms-aaneenlopend is. Sulke modelle kan dan gebruik word omdie invloed van koveranderlikes wat ouderdoms-verwante veranderinge in die biomerkers van belang veroorsaak te ondersoek. In hierdie studie gebruik ons die ouderdoms-deursnee data van ‘n groep van 381 gesonde Suid-Afrikaanse kinders. Wat die volgende biomerkers insluit: CD3+, CD19+, CD8+, CD4+, die verhouding van CD4+ naïef/geheue selle, CD18+, CD56+ en CD3-CD56+. Ons gebruik dan nielineêre kleinste kwadrate metodes om enkel en dubbel eksponensiële semi-meganistiese modelle te pas en vergelyk. Die ideale model is gekies op grond van die Akaike se inligtings Maatstaf. Sodoende bepaal ons dat die dubbel eksponensiële model die mees geskik is om ouderdoms-verwante veranderinge in sulke biomerkers aan te dui. Hierdie model voorspel dat seltellings styg na geboorte tot ‘n maksimum by ongeveer 12 maande en daarna eksponensiël daal tot ‘n asimptoot in volwassenheid. Hierdie resultaat stem ooreen met vorige empiriese en meganistiese studies. Daarna gebruik ons die dubbele eksponensiële model om die invloed van koveranderlikes te ondersoek. Die koveranderlike met die meeste invloed was die tipe voeding in die eerste 6 maande na geboorte. Model gebaseerde metode wat ouderdoms-aaneenlopende verwysings waardes skat is daarna voorgestel. Hierdie metode veronderstel dat die verwysings waardes ‘n gespesifiseerde Z-verskuiwing van die ‘lopende’ standaardafwykings van die residue vanaf die sentraal gepaste model funksie is. Ons vergelyk hierdie metode met tradisionele persentiel kurwes. Persentiel kurwes toon ‘n eenvoudiger negatiewe enkeleksponensiële daling met ouderdom, en is nie in staat om meganistiese interpretasies te maak vir hierdie patroon nie. Die modelle wat in hierdie studie voorgestel is mag lei tot die ontwikkeling van ‘n laboratorium instrument waarmee individuele sel-merker waardes kan vergelyk word met gesonde ouderdoms aaneenlopende verwysings waardes. Thesis (MSc)--Stellenbosch University, 2017

Thermodynamics analysis of variable viscosity hydromagnetic Couette flow in a rotating system with Hall effects

Fri, 20 Nov 2015 00:00:00 GMT

Thermodynamics analysis of variable viscosity hydromagnetic Couette flow in a rotating system with Hall effects Makinde, Oluwole D.; Eegunjobi, Adetayo S.; Tshehla, M. Samuel In this paper, we employed both first and second laws of thermodynamics to analyze the flow and thermal decomposition in a variable viscosity Couette flow of a conducting fluid in a rotating system under the combined influence of magnetic field and Hall current. The non-linear governing differential equations are obtained and solved numerically using shooting method coupled with fourth order Runge–Kutta–Fehlberg integration technique. Numerical results obtained for velocities and temperature profiles are utilized to determine the entropy generation rate, skin fictions, Nusselt number and the Bejan number. By plotting the graphs of various values of thermophysical parameters, the features of the flow characteristics are analyzed in detail. It is found that fluid rotation increases the dominant effect of heat transfer irreversibility at the upper moving plate region while the entropy production is more at the lower fixed plate region. CITATION: Makinde, O. D., Eegunjobi, A. S. & Tshehla, M. S. 2015. Thermodynamics analysis of variable viscosity hydromagnetic Couette flow in a rotating system with Hall effects. Entropy, 17(11):7811-7826, doi:10.3390/e17117811.; The original publication is available at http://www.mdpi.com/journal/entropy

Whole body modelling of glucose metabolism in malaria patients

Wed, 01 Mar 2017 00:00:00 GMT

Whole body modelling of glucose metabolism in malaria patients Green, Kathleen ENGLISH ABSTRACT : Diagnosing a patient with a disease is typically done by considering a list of clinical symptoms. For severe malaria two of the key pathophysiological indicators for poor chances of survival are hypoglycemia (blood glucose < 2.2 mmol/L) and lactic acidosis (blood lactate > 5 mmol/L). These could be due to accelerated glycolytic flux (conversion of glucose to lactate) in parasite infected red blood cells, anaemia brought about by the parasites destroying the red blood cells, or reduced perfusion resulting from coagulation of red blood cells (parasites change the red blood cell shape) in the bloodstream. To date, no mathematical models exist that can quantify the relative contribution of increased glycolytic flux to hypoglycemia and lactic acidosis. In this study we constructed a physiologically relevant model of human glucose metabolism that contains the molecular mechanisms of erythrocyte and Plasmodium glycolysis. This allows for the investigation of the extent to which hypoglycaemia and lactic acidosis can be explained by the increased metabolic burden of the parasite. This was accomplished by combining three independent models of glucose metabolism in the parasite, red blood cell and the whole body to form a model of glucose metabolism at the level of the whole body that now contained mechanistic detail of reactions at the level of the red blood cell and malaria parasite (the green1 model). Predictions from the green1 model were compared to clinical data which showed that the increased glycolytic flux caused by the presence of the parasites could be sufficient to explain clinical symptoms of hypoglycemia and lactic acidosis seen in malaria patients. It was seen that for the strength of this modelling technique to be tested, better quality data are needed to validate the model predictions. Furthermore with local and global sensitivity analysis it was observed that there are reactions and parameters in the Plasmodium glycolysis pathway that could guide the development of possible drug targets that could lead to a reversal of hypoglycemia and lactic acidosis.; AFRIKAANSE OPSOMMING : Diagnose van ’n pasiënt met ’n siekte word tipies gedoen deur die oorweging van ’n lys kliniese simptome. Vir ernstige malaria is twee van die belangrikste patofisiologiese aanwysers vir swak kanse op oorlewing hipoglukemie (bloedglukose <2.2 mmol/L) en laktaatversuring (bloed laktaat> 5 mmol/L). Dit kan wees as gevolg van versnelde glikolitiese fluksie (omskakeling van glukose na laktaat) in parasietgeinfekteerde rooibloedselle, bloedarmoede teweeg gebring word deur die vernieteging van rooibloedselle deur parasiete, verminderde perfusie as gevolg van koagulasie van rooibloedselle (parasiete verander die rooibloedselle se vorm) in die bloedstroom. Tot op datum, bestaan geen wiskundige modelle wat die relatiewe bydrae van verhoogde glikolitiese vloed te hipoglukemie en laktaatversuring kan kwantifiseer. In hierdie studie het ons ’n fisiologies relevante model van menslike glukose metabolisme gebou wat die molekulêre meganismes van direritrosiet en Plasmodium glikolise bevat. Dit maak voorsiening vir die ondersoek na die mate waarin hipoglukemie en laktaatversuring verduidelik kan word deur die verhoogde glikolitiese las van die parasiet. Dit is bewerkstellig deur die kombinering van drie onafhanklike modelle van glukose metabolisme in die parasiet, rooibloedselle en die hele liggaam om ’n model van glukose metabolisme te vorm op die vlak van die hele liggaam wat nou meganistiese besonderhede van reaksies vervat op die vlak van die rooibloedsel en malariaparasiet (die green1 model). Voorspellings van die green1 model is vergelyk met kliniese data wat toon dat die verhoogde glikolitiese fluksie wat veroorsaak word deur die teenwoordigheid van die parasiete voldoende is om kliniese simptome van hipoglukemie en laktaatversuring gesien in malaria pasiënte te verduidelik. Dit is gesien dat vir die krag van hierdie modelle tegniek om getoets te word, ’n beter gehalte data benodig word om die model voorspellings te versterk. Verder met plaaslike en globale sensitiwiteitsanalise is dit opgemerk dat daar reaksies en parameters in die Plasmodium glikolitiese pad is wat lig kan werp op die ontwikkeling van moontlike dwelm-teikens en sodoende kan lei tot ’n ommekeer van hipoglukemie en laktaatversuring.; Thesis (MSc)--Stellenbosch University, 2017

The double Heston model via filtering methods

Thu, 01 Dec 2016 00:00:00 GMT

The double Heston model via filtering methods Namundjebo, Elia N ENGLISH ABSTRACT : Stochastic volatility models are well-known for their ability to generate a volatility smile for financial securities. The development of the stochastic volatility models followed shortly after the crash of 1987 which violates the Black-Scholes model which has constant volatility. In this study we introduce non-linear filtering methods to estimate the implied volatilities of the Double Heston model. We compare our results to the Standard Heston model. The non-linear filtering methods used are the extended Kalman filter, the unscented Kalman filter and the particle filter. We combine the filtering methods together with the maximum likelihood estimation method to estimate the model's hidden parameters. Our numerical results show that the Double Heston model ts the market implied volatilities better than the Standard Heston model. The particle lter also performs better than the other two filters.; AFRIKAANSE OPSOMMING : Stogastiese wisselvalligheid modelle is goed bekend vir hul vermoë om'n wisselvalligheid glimlag vir finansiële sekuriteite te genereer. Die ontwikkeling van die stogastiese wisselvalligheid modelle het gevolg kort nadat die ongeluk van 1987 wat die Black-Scholes model wat konstant wisselvalligheid oortree het. In hierdie studie stel ons nie-lineêre filter metodes voor om die ge lmpliseerde wisselings in die Double Heston Model te skat. Ons vergelyk ons resultate aan die Standard Heston model. Die nie-lineêre lter metodes wat gebruik word is die uitgebreide Kalman filter, die reuklose Kalman filter en die deeltjies fillter. Ons kombineer die filter metodes saam met die maksimum annneemlikheidsberaming metode om verborge parameters van die model te skat. Ons numeriese resultate dui daarop dat die Double Heston model pas die mark geïmpliseerde volatiliteit en beter as die Standard Heston model. Die deeltjie filter presteer ook beter as die ander twee fillters. Thesis (MSc)--Stellenbosch University, 2016

An integrated framework modelling susceptibility to tuberculosis in homogeneous and admixed populations

Thu, 01 Dec 2016 00:00:00 GMT

An integrated framework modelling susceptibility to tuberculosis in homogeneous and admixed populations Gebremariam, Zoe Zerihun ENGLISH ABSTRACT : In spite of the wide variety of anti-tuberculosis drugs, tuberculosis (TB), caused by mycobacterium tuberculosis (MTB), is the second leading infectious disease after Human Immunode ciency Virus (HIV) or Acquired Immunode ciency Syndrome (AIDS), and one of the leading causes of human death from infectious diseases, especially in Sub-Saharan Africa. Approximately onethird of the world population are latently infected with MTB, of which, 10 % progress to active TB. Obstacles in TB control include lengthy treatment regimens of more than 6 months, drug resistance, lack of an e ective vaccine and limited knowledge and incomplete information about factors that trigger the progression of an MTB infection to disease. Moreover, the association of TB and HIV or AIDS has also promoted all of the conditions of an explosive increase in TB incidence and prevalence. Several studies suggest that host genetic factors also a ect susceptibility and resistance to TB. Genome wide association study (GWAS) provides a way of examining many common variants in di erent populations to see if any variant is associated with a trait by searching for small variations, called single nucleotide polymorphisms (SNPs). However, it is well known that GWAS alone is insu cient to elucidate the genetic structure of a complex disease and may lead to non conclusive results. In this thesis, we use a post association analysis, which has been suggested as a new paradigm to GWAS, to elucidate and analyze human genetic susceptibility in relation to the infecting MTB by combining association signals from GWAS and available functional and comparative genomics information for human and MTB. We have identi ed 6 disease associated genes for the admixed South Africa coloured (SAC) population and 8 disease associated genes for the homogeneous Ghana-Gambia population. We used a graph-based approach to establish a relationship between these di erent disease associated genes and front-line drug targets in relation to MTB. Furthermore, we performed Gene Ontology (GO) process and pathway enrichment analyses. These yielded subnetworks, enriched processes and pathways that may play critical role in TB immunogenicity and pathogenesis. We also investigated ancestry-speci c TB risk in the SAC population and results revealed that the African Khomani (Sub-Kalahari San) ancestry highly contributes to disease risk in this population observed to be highly susceptible to TB. Several studies have been conducted on identifying candidate genes conferring risk susceptibility to TB. However, most of these studies only analysed relationships between these genes and the host system. Here, we have also considered the pathogen system, thus combining host, pathogen and host-pathogen protein-protein functional interactions to examine relationships between host TB susceptibility and pathogenesis. Furthermore we perform functional relationships between identi ed candidate genes and front-line drug targets based on these functional networks. This may enhance our understanding about TB susceptibility and pathogenesis, and enhance research for TB drug and vaccine development.; AFRIKAANSE OPSOMMING : Ten spyte van die wye verskeidenheid van anti-tuberkulose dwelms, tuberkulose (TB), wat veroorsaak word deur Mycobacterium tuberculosis (MTB), is die tweede grootste aansteeklike siektes ná Menslike Immuniteitsgebrekvi- rus (MIV) of Verworwe Immuniteitsgebreksindroom (VIGS), en een van die grootste oorsake van menslike dood van aansteeklike siektes, veral in Sub- Sahara Afrika. Ongeveer een derde van die wêreld se bevolking is sluimerend besmet is met MTB, waarvan, 10 % vordering aktiewe TB. Struikelblokke in TB beheer sluit in langbehandelingsregimes van meer as 6 maande, weerstand teen die medikasie, 'n gebrek aan 'n doeltre ende entstof en beperkte kennis en onvolledige inligting oor faktore wat die verloop van 'n MTB infeksie teen siektes veroorsaak. Daarbenewens het die vereniging van TB en MIV of vigs ook bevorder al die voorwaardes van 'n plofbare toename in TB voorkoms en die voorkoms. Verskeie studies dui daarop dat gasheer genetiese faktore ook 'n invloed vatbaarheid en weerstand teen TB. Genoom wye assosiasie studie (GWAS) bied 'n manier om die behandeling van baie algemene variante in verskillende bevolkings om te sien of enige variant is wat verband hou met 'n eienskap deur te soek vir klein variasies, genoem enkele nukleotied polimor smes (SNPs). Dit is egter bekend dat GWAS alleen onvoldoende is om die genetiese struktuur van 'n komplekse siekte toe te lig en kan lei tot nie afdoende resultate. In hierdie tesis, gebruik ons 'n post vereniging analise, wat as 'n nuwe paradigma te GWAS het voorgestel, om toe te lig en te ontleed menslike genetiese vatbaarheid met betrekking tot die besmet MTB deur die kombinasie van assosiasie seine van GWAS en beskikbaar funksionele en vergelykende genomika inligting vir menslike en MTB. Ons het 6 siekte geassosieer genevir die venmeng Suid-Afrika gekleurde (SAC) bevolking en 8 siekte geassosieer gene vir die homogene Ghana-Gambië bevolking geïdenti seer. Ons gebruik 'n gra ek gebaseerde benadering tot 'n verhouding tussen die verskillende siektes wat verband hou gene en tussen siekte gene en front-line dwelm teikens te stel met betrekking tot MTB. Verder het ons uitgevoer Gene Ontologie (GO) proses en pad verryking ontleed. Hierdie opgelewer sub-netwerke, verryk prosesse en roetes wat kritieke rol kan speel in die TB immunogenisiteit en patogenese. Ons ondersoek ook afkoms spesi eke TB risiko in die SAC bevolking en resultate het getoon dat die Afrikaanse Khomani (Sub-Kalahari San) afkoms hoogs dra by tot siekte risiko in hierdie bevolking waargeneem hoogs vatbaar vir TB te wees. Verskeie studies is gedoen op die identi sering van kandidaat gene wat die risiko vatbaarheid vir TB verleen. Maar die meeste van hierdie studies het net ontleed verhoudings tussen hierdie gene en die gasheer stelsel. Hier het ons ook gekyk na die patogeen stelsel, dus die kombinasie van gasheer, patogene en gasheer-patogeen proteïen-proteïen funksionele interaksies om verhoudings tussen gasheer TB vatbaarheid en patogenese is oorweeg. Verder voer ons funksionele verwantskappe tussen geïdenti seer kandidaat gene en voorste lyn dwelm mikpunte gebaseer op hierdie funksionele netwerke. Dit kan ons begrip oor TB vatbaarheid en patogenese verbeter, en verbeter navorsing vir TB dwelm en entstof ontwikkeling. Thesis (MSc)--Stellenbosch University, 2016

Elliptic curve cryptography

Thu, 01 Dec 2016 00:00:00 GMT

Elliptic curve cryptography Louw, Gerard Jacques ENGLISH ABSTRACT : In this thesis we present a selection of Diffie-Hellman cryptosystems, which were classically formulated using the multiplicative group of a finite field, but which may be generalised to use other group varieties such as elliptic curves. We also describe known attacks on special cases of such cryptosystems, which manifest as solutions to the discrete logarithm problem for group varieties, and the elliptic curve discrete logarithm problem in particular. We pursue a computational approach throughout, with a focus on the development of practical algorithms.; AFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nie Thesis (MSc)--Stellenbosch University, 2016

A mathematical model for onchocerciasis and its treatment with ivermectin

Thu, 01 Dec 2016 00:00:00 GMT

A mathematical model for onchocerciasis and its treatment with ivermectin Omondi, Evans Otieno ENGLISH ABSTRACT : Onchocerciasis is a human disease that is caused by the filirial worm Onchocerca volvulus. It occurs close to oxygen rich flowing streams and rivers in the inter-tropical zones. The disease is a serious public health problem and any control interventions must be effective so as to eliminate it from the population. A rational control intervention method is through mass administration of ivermectin. In this study, a non-linear mathematical model is formulated to model the transmission dynamics and spread of onchocerciasis disease. First, a mathematical model is formulated to evaluate the impact of long term mass treatment of onchocerciasis with ivermectin. The model basic reproduction number is computed and the stability analysis presented. The model is found to exhibit a backward bifurcation so that for R0 less than unity is not sufficient to eradicate the disease from the population and the need is to lower R0 to below a certain threshold, Rc0 for effective disease control. Optimal control theory is applied to investigate the control strategies for eliminating onchocerciasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagin’s Maximum Principle. The simulation results demonstrate that the maximum implementation of vector control, personal protection strategies and enhanced mass treatment with ivermectin strategies in the epidemic are of very critical impacts in the optimal control. This gives a theoretical interpretation to the practical experiences that the insecticide and use of insect repellents are important in the control of onchocerciasis. The model is extended to assess the effectiveness of mass administration using impulsive differential equations since the treatment itself is considered to be impulsive. The basic reproduction number is derived and we establish that the global dynamics are completely determined by the values of R0. The disease-free equilibrium is globally asymptotically stable for basic reproduction number R0 < 1, while for R0 > 1, a unique endemic equilibrium exists and is globally asymptotically stable. We then use the model to determine the threshold for the proportion of infected individuals that reduces the infection in the human (host) population. Finally, we present numerical simulations results. Sensitivity analysis reveals that the most sensitive parameters in the onchocerciasis epidemic are the human transmission contact rate bh , the vector transmission contact rate bv and vector death rate μv. The numerical results show that efficiency of the mass administration of ivermectin contributes a greater impact on the disease dynamics and moves the system towards the disease free state.; AFRIKAANSE OPSOMMING : Onchocerciasis is ’n menslike siekte wat veroorsaak word deur die filariese wurm Onchocerca volvulus. Dit kom voor naby suurstofryke vloeiende strome en riviere in intertropiese met ivermektien strategieë in die epidemie van kritiese belang is in die optimale kontrole. Dit gee ’n teoretiese verklaring vir die praktiese ondervinding dat insekgif en die gebruik van (insek) afweermiddels belangrik is in die kontrole van onchocerciasis. Die model word uitgebrei om die effektiwiteit van massa toedien vas te stel deur die gebruik van impulsiewe differensiaalvergelykings aangesien die behandeling self as impulsief beskou word. Die basiese voorplantingsgetal word afgelei en ons bevestig dat die globale dinamika volledig bepaal word deur die waardes van R0. Die siektevrye ewewig is globaal asimptoties stabiel wanneer die voortplantingsgetal R0 < 1, terwyl daar vir R0 > 1 ’n unieke endemiese ewewig bestaan wat globaal asimptoties stabiel is. Ons gebruik dan die model om die drumpel van persentasie van besmette individue te bepaal wat die besmetting in die menslike (gasheer) bevolking verminder. Laastens bied ons uitslae van numeriese simulasies aan. Sensitiwiteitsanalise toon aan dat die mees sensitiewe parameters in die onchocerciasis epidemie die menslike oordragsverhouding bh, die vektoroordragskontakverhouding bv en die vektordoodsverhouding μv is. Die numeriese uitslae toon dat die die effektiwiteit van massa toedien van ivermektien ’n groter invoed op die siekte se dinamika het en die stelsel na die siektevrye toestand beweeg sones. Hierdie siekte is ’n ernstige publieke gesondheidsgevaar en enige kontrole ingrypings moet effektief wees om dit uit die bevolking uit te wis. ’n Rasionele kontrole ingrypingsmetode is die massa toedien van ivermektien. In hierdie studie word ’n nie-lineêre wiskundige model geformuleer om die oordrags- en verspreidingsdinamika van die onchocerciasis siekte te modelleer. Eerstens word ’n wiskundige model geformuleer om die impak van langtermyn massabehandeling van onchoncersiasis met ivermektien te bepaal. Die model se basiese voortplantingsgetal word bereken en die stabiliteitsanalise word aangebied. Die model word bevind om ’n terugwaardse bifurkasie ten toon te stel sodat die voorwaarde R0 kleiner as eenheid nie genoeg is om die siekte uit die bevolking uit te wis nie en dat dit nodig is om R0 te verlaag tot onder ’n sekere drumpel Rc0 vir effektiewe siektekontrole. Optimale kontrole teorie word met tydafhanklike kontroles toegepas om die kontrole strategieë om onchocerciasis uit te wis te bestudeer. Die karakterisering van die optimale kontrole word uitevoer met Pontryagin se Maksimumbeginsel. Die uitslae van die simulasie wys dat die maksimum uitvoering van vektorkontrole, persoonlike beskermingstrategieë en verbeterde massabahandeling Thesis (MSc)--Stellenbosch University, 2016

Geometry of Complex Polynomials: On Sendov's Conjecture

Thu, 01 Dec 2016 00:00:00 GMT

Geometry of Complex Polynomials: On Sendov's Conjecture Chalebgwa, Taboka Prince ENGLISH ABSTRACT : Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a paper that appeared in 2014, Dégot proved that, for each α ε (0, 1), there is an integer N such that for any polynomial P(z) with degree greater than N, P(a) = 0 and all zeroes inside the unit disk, the disk │z- α│ ≤ 1 contains a critical point of P(z). Basing on this result, we derive an explicit formula N(a) for each α ε (0, 1) and, furthermore, obtain a uniform bound N for all a ε [α,β] where 0 < α < β < 1. This addresses the questions posed in Dégot’s paper.; AFRIKAANSE OPSOMMING : Die vermoede van Sendov lui dat, as alle nulpunte van ’n komplekse polinoom P(z) van graad minstens twee binne die eenheidssirkel lê, dan is daar ’n kritieke punt van P(z) binne ’n afstand van een van elke nulpunt. In die artikel wat 2014 verskyn het, het Dégot bewys dat daar vir elke a ε (0, 1) ’n heelgetal N bestaan sodat, vir elke polinoom P(z) van graad groter as N met P(a) = 0 en met alle nulpunte binne die eenheidskyf, die skyf │z- α│≤1 ’n kritieke punt van P(z) bevat. Gebaseer op hierdie werk bepaal ons ’n formule N(a) vir elke a ε (0, 1), en verder bepaal ons ’n uniforme bogrens N vir alle a ε [α,β] waar 0 < α < β < 1. Dit spreek die vrae aan wat in Dégot se artikel gestel is. Thesis (MSc)--Stellenbosch University, 2016

Solving embedding problems with bounded ramification

Thu, 01 Dec 2016 00:00:00 GMT

Solving embedding problems with bounded ramification Ramiharimanana, Nantsoina Cynthia ENGLISH ABSTRACT : Given a Galois extension K/K0 of number fields, a finite group G, and an epimorphism α: G→ Gal(K/K0) with solvable kernel, our goal is to embed K into a Galois extension N of K0 with Galois group Gal(N/K0) ≅ G such that the restriction map resN=K: Gal(N/K0) → Gal(K/K0) coincides with α and │Ram(N/K0)│ ≤│ Ram(K│K0) │+ Ω (│Ker(α)│). Here Ram(N│K0) is the finite set of primes of K0 that ramify in N and Ω (│Ker (α) │) is the number of the prime divisors, counted with multiplicity, of │Ker (α). We achieve our goal under two conditions: first, the number of roots of unity in K should be relatively prime to the order of Ker(α). The second one demands that each local embedding problem resulted from the original one should be "weakly solvable". In fact, our solution locally coincides with finitely many "local weak solutions" given in advance. Our result strengthens a former result of Neukirch in [Neu79], where the same embedding problem satisfying the same conditions is solved without giving a bound on the ramification. In particular, the above mentioned local conditions are satisfied if the epimorphism α has a section. This leads to a well known result of Shafarevich that does not assume the condition on the roots of unity but pays with a huge number of ramified primes (that appears when one analyses Shafarevich's proof). Like in [Neu79], our proof uses class field theory in its cohomological approach. The bounding of the ramification is based, in addition to the above mentioned tools, on a strengthening of a lemma of [GeJ98].; AFRIKAANSE OPSOMMING : Laat K/K0 'n Galois uitbreiding van getalleliggame wees, G 'n eindige groep, en α: G→ Gal(K/K0) 'n epimorfisme met oplosbare kern. Ons doel is om K in 'n Galois uitbreiding N van K0 in-te-bed sodat die Galois groep Gal(N/K0) ≅ G; en sodat die beperkingsafbeelding resN=K: Gal(N/K0) → Gal(K/K0) ooreenstem met α en │Ram(N=K0) │ ≤│+Ram(K/K0)+ Ω (│Ker(α ) │). Hier is Ram(N/K0) die eindige versameling van priemdelers van K0 wat in N vertak, en Ω (│Ker(α) │) is die aantal priemdelers van │Ker(α) │, getel met multiplisiteit. Ons bereik hierdie doelstelling onderhewig aan twee voorwaardes: Eerstens moet die aantal wortels van eenheid in K relatief priem wees aan die orde van Ker (α). Tweedens eis ons dat elke lokale inbeddingsprobleem, wat volg uit die oorspronklike een, "swak oplosbaar" moet wees. Meer presies gestel, sal ons oplossing lokaal ooreenstem met 'n eindige aantal "lokaal swak oplossings" wat vooraf gegee word. Ons resultaat versterk 'n vroeer resultaat van Neukirch in [Neu79], waar 'n inbeddingsprobleem wat dieselfde voorwaardes bevredig opgelos word, maar sonder die grens op die aantal vertakkings. In die besonder word die lokale voorwaardes bevredig mits die epimorfisme α 'n snitafbeelding besit. Hieruit volg dan ook die bekende resultaat van Shafarevich, wat nie die voorwaarde oor die wortels van eenheid benodig nie, maar gevolglik 'n baie groot aantal priemdelers wat vertak veroorsaak (hierdie opmerking word gesien wanneer sy bewys in detail bestudeer word). Soos in [Neu79], maak ons gebruik van klasliggaamteorie met 'n kohomologiese benadering. Die begrensdheid van die aantal priemdelers wat vertak maak ook gebruik van 'n versterking van 'n hulpstelling uit [GeJ98]. Thesis (PhD)--Stellenbosch University, 2016

Computational and theoretical analysis of human diseases associated with infectious pathogens

Thu, 01 Jan 2015 00:00:00 GMT

Computational and theoretical analysis of human diseases associated with infectious pathogens Noutchie, Suares Clovis Oukouomi; Kwuimy, Cedrick Aurelien Kitio; Tewa, Jean Jules; Nyabadza, Farai; Bildik, Necdet Mathematical models and computer simulations are useful experimental tools for building and testing theories, assessing quantitative conjectures, answering specific questions, determining sensitivities to changes in parameter values, and estimating key parameters from data. Understanding the transmission characteristics of infectious diseases in communities, regions, and countries can lead to better approaches to decreasing the transmission of these diseases. CITATION: Noutchie, S. C. O. et al. 2015. Computational and theoretical analysis of human diseases associated with infectious pathogens. BioMed Research International, 2015, Article ID 431706, doi:10.1155/2015/431706.; The original publication is available at https://www.hindawi.com/journals/bmri

DSaaS : a cloud service for persistent data structures

Fri, 01 Apr 2016 00:00:00 GMT

DSaaS : a cloud service for persistent data structures Le Roux, Pierre Bernard; Kroon, Steve; Bester, Willem In an attempt to tackle shortcomings of current approaches to collaborating on the development of structured data sets, we present a prototype platform that allows users to share and collaborate on the development of data structures via a web application, or by using language bindings or an API. Using techniques from the theory of persistent linked data structures, the resulting platform delivers automatically version-controlled map and graph abstract data types as a web service. The core of the system is provided by a Hash Array Mapped Trie (HAMT) which is made confluently persistent by path-copying. The system aims to make efficient use of storage, and to have consistent access and update times regardless of the version being accessed or modified. CITATION: Le Roux, P. B., Kroon, S. & Bester, W. 2016. DSaaS : a cloud service for persistent data structures. CLOSER 2016: 6th International Conference on Cloud Computing and Services Science, Rome, Italy, 23-25 April 2016.; The original publication is available at http://closer.scitevents.org/

Binary closure operators

Tue, 01 Mar 2016 00:00:00 GMT

Binary closure operators Abdalla, Abdurahman Masoud ENGLISH ABSTRACT : In this thesis we provide a new foundation to categorical closure operators, using more elementary binary closure operators on posets. The original goal of the thesis was to study a categorical closure operator in terms of the family of closure operators on the posets of subobjects. However, this does not allow to express hereditariness, which is an important property of a categorical closure operator. Representing instead a categorical closure operator in terms of the family of binary closure operators on the posets of subobjects, xes this problem. Moreover, the structure of a binary closure operator on a poset is self-dual, unlike that of a unary closure operator or that of a categorical closure operator, and this duality has a useful application in the study of properties of closure operators on categories, where it groups properties of categorical closure operators in dual pairs, and allows to unify results which relate these properties to each other.; AFRIKAANSE OPSOMMING : In hierdie tesis verskaf ons, deur gebruik te maak van meer elementêre binêre afsluitingsoperatore op parsiële geordende versamelings, 'n nuwe grondslag tot kategoriese afsluitingsoperatore. Die aanvanklike doel van die tesis was om 'n kategoriese afsluitingsoperator in terme van die familie van afsluitingsoperatore op parsiële die geordende versamelings van subobjekte te bestudeer. Dit laat egter nie toe om oorer ikheid, wat 'n belangrike eienskap van kategoriese operatore is, uit te druk nie. Hierdie probleem word opgelos deur 'n kategoriese operator in terme van die familie van binêre afsluitingsoperatore op parsiële die geordende versamelings van subobjekte te verteenwoordig. Bykomend is die struktuur van 'n binêre afsluitingsoperator op 'n parsiële geordende versameling self-duaal, in teenstelling met di e van 'n unêre of kategoriese afsluitingsoperator. Hierdie dualiteit het 'n nuttige toepassing in die studie van eienskappe van afsluitingsoperatore op kategorieë, waar dit eienskappe van kategoriese afsluitingsoperatore in duale pare groepeer en toelaat dat resultate, wat hierdie eienskappe in verband hou met mekaar, verenig word. Thesis (PhD)--Stellenbosch University, 2016

Fredholm theory in ordered Banach algebras

Tue, 01 Mar 2016 00:00:00 GMT

Fredholm theory in ordered Banach algebras Benjamin, Ronalda Abigail Marsha ENGLISH ABSTRACT : Since its inception, Fredholm theory has become an important aspect of spectral theory. Among the spectra arising within Fredholm theory is the Weyl spectrum which has been intensively studied by several authors, both in the operator case and in the general situation of Banach algebras. The Weyl spectrum of a bounded linear operator T on a Banach space X is the set T K2K(X) s(T + K), where s(T) denotes the spectrum of T and K(X) the closed ideal of all compact operators on X. A recent result by E. A. Alekhno shows that, if “Banach space" is replaced by an arbitrary complex Banach lattice E, then the Weyl spectrum of T on E can be made more precise, and takes on the form T 0 K2K(E) s(T + K). By an ordered Banach algebra (OBA) we mean a complex unital Banach algebra A containing an algebra cone; that is, a subset C which contains the unit of A and is closed under addition, multiplication and positive scalar multiplication. As is well-known, the algebra of all bounded linear operators on a complex Banach lattice is an important example of an OBA. If A denotes an arbitrary OBA with algebra cone C, B a Banach algebra and T : A ! B a homomorphism with N(T) = fa 2 A : Ta = 0g indicating the null space of T, then the Weyl spectrum T c2N(T) s(a + c) of a 2 A is in general strictly contained in the set T c2C\N(T) s(a + c) — see Example 4.1.13. As a result of this, we investigate the latter set, which we shall refer to as the upperWeyl spectrum of a 2 A. In this work the concept of the upper Browder spectrum of a will also be introduced and results related to these spectra and the underlying sets of elements on which these spectra are defined will be given. This thesis aims to present initial steps taken in the effort of unifying the theory of positivity in OBAs with the general Fredholm theory in Banach algebras.; AFRIKAANSE OPSOMMING : Sedert die bekendstelling daarvan, het die Fredholmteorie ‘n belangrike aspek van spektraalteorie geword. Onder die spektra wat ontstaan in Fredholmteorie is die Weyl spektrum, wat alreeds in diepte bestudeer is deur verskeie outeurs, beide in die operatorkonteks en in willekeurige Banach algebras. Die Weyl spektrum van ‘n begrensde lineêre operator T op ’n Banach ruimte X is die versameling T K2K(X) s(T + K), waar s(T) die spektrum van T voorstel en K(X) die geslote ideaal van kompakte operatore op X. ‘n Resultaat wat onlangs deur E. A. Alekhno bewys is, toon dat, as “Banach ruimte" vervang word met ‘n willekeurige Banach rooster E, dan kan die voorstelling van dieWeyl spektrum van T op E meer presies gemaak word, en dit word gegee deur T 0 K2K(E) s(T + K). Met ‘n geordende Banach algebra (GBA) bedoel ons ’n komplekse unitale Banach algebra A wat ‘n algebra-keël bevat; dit is, ‘n deelversameling C wat die eenheid van A as element het en wat geslote is onder optelling, vermenigvuldiging en positiewe skalaarvermenigvuldiging. Die versameling van begrensde lineêre operatore op ’n komplekse Banach rooster is ’n belangrike voorbeeld van ’n GBA. As A ‘n willekeurige GBA met algebra-keël C voorstel, B ‘n Banach algebra en T : A ! B ‘n homomorfisme met N(T) = fa 2 A : Ta = 0g die nulruimte van T, dan is dieWeyl spektrum T c2N(T) s(a+c) van a 2 A in die algemeen eg bevat in die versameling T c2C\N(T) s(a + c) — kyk na Voorbeeld 4.1.13. As gevolg hiervan, ondersoek ons die laasgenoemde versameling, wat ons die bo-Weyl spektrum van a 2 A sal noem. In hierdie werk word die konsep van die bo-Browder spektrum van a ook bekend gestel en resultate wat verband hou met hierdie spektra en met die onderliggende versamelings van elemente waarop hierdie spektra gedefineer is sal gegee word. Die doel van hierdie tesis is die bekendstelling van die beginstappe wat geneem is in die poging om die teorie van positiwiteit in GBAs Thesis (PhD)--Stellenbosch University, 2016

Modelling of the invasion dynamics of plasmodium falciparum merozoites into red blood cells

Tue, 01 Mar 2016 00:00:00 GMT

Modelling of the invasion dynamics of plasmodium falciparum merozoites into red blood cells Meiring, Maynard ENGLISH ABSTRACT : BACKGROUND The physiological symptoms of P. falciparum infection are associated with a 48 hour replication cycle whereby parasites (merozoites) invade susceptible red blood cells (RBCs), develop and multiply within these now infected RBCs and eventually rupture them, releasing 8 to 32 daughter merozoites which are free to di use through their environment and may subsequently invade other available RBCs and begin a new replication cycle. OBJECTIVES: To develop a novel, parameterised mechanistic mathematical model which describes the dynamics of merozoite invasion during the initial stages of malarial infection. Furthermore, to determine if the dispersal of daughter merozoites can be modelled by a random walk model and extrapolated to a di usion process. APPROACH: Two novel mathematical models were constructed to describe the dynamics of the aforementioned invasion process { a deterministic model consisting of four coupled ordinary di erential equations and a stochastic, random walk model. In addition, several forms of the mechanistic model were built to accommodate multiply-invaded RBCs. These parasitised RBCs are those which have been invaded by more than one merozoite; a phenomenon largely absent from modelling exercises seen in the literature. The novelty of the models pertains to the inclusion of a "merozoite-erythrocyte complex" or MEC. This is an unstable, intermediary species which forms after the initial interaction between a free merozoite and susceptible RBC but before successful invasion may occur. CONCLUSION: The most signi cant conclusion gained from this research was that while the mathe- matical models were constructed in a theoretically sound manner in which all interactions were based on observable phenomena, the data required to robustly validate these models and acquire accurate estimates for the parameters was not available.; AFRIKAANSE OPSOMMING : Geen Afrikaanse opsomming geskikbaar nie Thesis (MSc)--Stellenbosch University, 2016

Contributions to the analysis of approximate counting

Tue, 01 Mar 2016 00:00:00 GMT

Contributions to the analysis of approximate counting Prodinger, Helmut ENGLISH ABSTRACT : Approximate Counting is a classical technique with very challenging questions re- lated to its performance analysis. It is also somewhat similar to parameters around Digital Search trees. Surprising links to q-analysis and the theory of partitions exist. The author has contributed to the analysis during the last decades; the relevant pa- pers have been collected in this thesis. Some emphasis is on a recent development, namely, to introduce a parameter m (m counters instead of one).; AFRIKAANSE OPSOMMING : Benaderde Aftelling is 'n klassieke tegniek met baie uitdagende vrae in verband met sy prestasie-analise. Dit is ook verwant aan parameters van digitale soekbome. Daar bestaan 'n verrassende verband met q-analise en die teorie van partisies. Die outeur het in die afgelope dekades tot hierdie analise bygedra; die relevante artikels is in hierdie tesis versamel. Klem word getoon op 'n onlangse ontwikkeling, naamlik om 'n parameter m (m tellers in plaas van een) by te voeg. Thesis (PhD)--Stellenbosch University, 2016

On the validity of evolutionary models with site-specific parameters

Thu, 10 Apr 2014 00:00:00 GMT

On the validity of evolutionary models with site-specific parameters Scheffler, Konrad; Murrell, Ben; Pond, Sergei L. Kosakovsky Evolutionary models that make use of site-specific parameters have recently been criticized on the grounds that parameter estimates obtained under such models can be unreliable and lack theoretical guarantees of convergence. We present a simulation study providing empirical evidence that a simple version of the models in question does exhibit sensible convergence behavior and that additional taxa, despite not being independent of each other, lead to improved parameter estimates. Although it would be desirable to have theoretical guarantees of this, we argue that such guarantees would not be sufficient to justify the use of these models in practice. Instead, we emphasize the importance of taking the variance of parameter estimates into account rather than blindly trusting point estimates – this is standardly done by using the models to construct statistical hypothesis tests, which are then validated empirically via simulation studies. CITATION: Scheffler, K., Murrell, B. & Pond, S. L. K. 2014. On the validity of evolutionary models with site-specific parameters. PLoS ONE, 9(4):e94534, doi:10. 1371/journal.pone.0094534.; The original publication is available at http://journals.plos.org/plosone