In this article, we analyse similarities and differences in and between two very topical issues in today's learning disabilities, namely dyscalculia and dyslexia. More precisely, we introduce the nature of mathematics as science, which - of course - is the essence of the matter. From this, we will try to prove that dyscalculia is not a concept by itself, but merely yet another one of the sad guises of dyslexia. This will completely answer the question given by the title of the thesis.

Thesis (MSc)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: Multiprotocol Label Switching (MPLS) is a routing technology which can manage Quality of Service (QoS) in scalable connectionless networks using relatively simple packet forwarding mechanisms. This thesis considers the optimisation of the QoS offered by an MPLS network. The QoS measure used is the expected packet delay which is minimised by switching packets along optimal label switched paths (LSPs). Two mathematical models of MPLS networks are presented together with appropriate algorithms for optimally dividing the network traffic into forwarding equivalence classes (FECs), finding optimal LSPs which minimise the expected packet delay and switching these FECs along the optimal LSPs. These algorithms are applied to compute optimal LSPs for several test networks. The mathematics on which these algorithms are based is also reviewed. This thesis provides the MPLS network operator with efficient packet routing algorithms for optimising the network's QoS. / AFRIKAANSE OPSOMMING: Multiprotocol Label Switching (MPLS) is 'n roeteringsmetode om die diensvlak (QoS) van 'n skaleerbare, verbindinglose netwerk te bestuur deur middel van relatief eenvoudige versendingsmeganismes. Hierdie tesis beskou die optimering van die QoS van 'n MPLS-netwerk. Die QoS-maatstaf is die verwagte vert raging van 'n netwerk-pakkie. Dit word geminimeer deur pakkies langs optimale "label switched paths" (LSPs) te stuur. Twee wiskundige modelle van MPLS-netwerke word ondersoek. Toepaslike algoritmes word verskaf vir die optimale verdeling van die netwerkverkeer in "forwarding equivalence classes" (FECs), die soektog na optimale LSPs (wat die verwagte pakkie-vertraging minimeer) en die stuur van die FECs langs die optimale LSPs. Hierdie algoritmes word ingespan om optimale LSPs vir verskeie toetsnetwerke op te stel. Die wiskundige teorie waarop hierdie algoritmes gegrond is, word ook hersien. Hierdie tesis verskaf doeltreffende roeteringsalgoritmes waarmee 'n MPLS-netwerkbestuurderj-es die netwerk se QoS kan optimeer.

Thesis (MSc)--Stellenbosch University , 2002. / ENGLISH ABSTRACT: Grammars with regulated rewriting are used to restrict the application of contextfree productions in order to avoid certain derivations. This enables these grammars to generate both context-free and non-context-free languages using only production rules with a context-free format. These grammars are more powerful than contextfree grammars, but usually not as powerful as context-sensitive grammars. Various grammars with regulated rewriting have been developed and some will be discussed in this thesis. Propositional linear temporal logic is a formal system used to describe truth values of propositions over time. This is done by defining a timeline together with a set of propositions. It is then possible to construct temporal logic formulae, consisting of these propositions and temporal operators, to specify the truth values of the propositions for every step in the timeline. In this thesis we define and discuss temporal grammars that combine grammars with propositionallinear temporal logic. Since a derivation can be associated with a timeline, a regulating device can be constructed from temporal logic formulae, that will control the application of productions within the derivation. The discussion on temporal grammars includes some of the properties of these grammars, while many ideas are illustrated by examples. / AFRIKAANSE OPSOMMING: Grammatikas met gereguleerde herskrywing word gebruik om 'n beperking te plaas op die toepassing van konteksvrye produksies en verhoed sodoende sekere afleidings. Hierdie grammatikas beskik oor die vermoe om beide konteksvrye en nie-konteksvrye tale te genereer deur slegs produksiereels van 'n konteksvrye formaat te gebruik. Grammatikas met gereguleerde herskrywing is dus sterker as konteksvrye grammatikas, alhoewel dit soms swakker as konteks-sensitiewe grammatikas is. 'n Verskeidenheid sulke grammatikas is al ontwikkel en sommige sal in hierdie tesis bespreek word. Proposisionele lineere temporale logika is 'n formele stelsel wat gebruik kan word om die waarheidswaardes van proposisies oor tyd te beskryf. Dit word gedoen deur 'n tydlyn, asook 'n versameling proposisies te definieer. Dit is clan moontlik om temporale operatore tesame met die proposisies te gebruik om temporale logika-formules te konstrueer wat in staat is om waarheidswaardes van die proposisies te spesifiseer vir elke oomblik in die tydlyn. In hierdie tesis word temporale grammatikas, wat grammatikas met proposisionele lineere temporale logika kombineer, gedefinieer en bespreek. Aangesien 'n afleiding met 'n tydlyn geassosieer kan word, is dit moontlik om 'n regulerende meganisme uit temporale logika-formules te konstrueer wat die toepassing van produksiereels in die afleiding kontroleer. Die bespreking van temporale grammatikas sluit 'n verskeidenheid eienskappe van die grammatikas in, asook 'n aantal voorbeelde wat ter illustrasie gebruik word.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The search for non-terminating paths within a program is a crucial part of software verification, as the detection of anfinite path is often the only manner of falsifying program termination - the failure of a termination prover to verify termination does not necessarily imply that a program is non-terminating. This document describes the development and implementation of two focussed techniques for investigating the non-termination of affine loops. The developed techniques depend on the known non-termination concepts of recurrent sets and Jordan matrix decomposition respectively, and imply the decidability of single-variable and cyclic affine loops. Furthermore, the techniques prove to be practically capable methods for both the location of non-terminating paths, as well as the generation of preconditions for non-termination. / AFRIKAANSE OPSOMMING: Sagtewareveri kasie vereis of die bewys van die beeindiging van 'n program, of die deteksie van oneindige uitvoerings. In hierdie tesis ontwikkel en implementeer ons twee tegnieke om oor die oneindige eienskap van a ene lusse te beslis. Die tegnieke wat ontwikkel word is gebaseer op konsepte soos Jordan matriksdekomposisie en herhaalde groepe wat al in die verlede gebruik is om die beeindiging van lusse te ondersoek. Die tegnieke kan gebruik word om die uitvoerbaarheid van beide een-veranderlike en sikliese a ene lusse te bepaal. Feitlik alle nie-eindige a ene lusse kan ge denti seer word en die toestande waaronder hierdie oneindige eienskap verskyn kan beskryf word.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The amount of information that users of social networks consume on a daily basis is steadily increasing. The resulting information overload is usually associated with a loss of control over the management of information sources, leaving users feeling overwhelmed. To address this problem, social networks have introduced tools with which users can organise the people in their networks. However, these tools do not integrate any automated processing. Twitter has lists that can be used to organise people in the network into topic-based groups. This feature is a powerful organisation tool that has two main obstacles to widespread user adoption: the initial setup time and continual curation. In this thesis, we investigate the problem of constructing topic-based Twitter lists. We identify two subproblems, an unsupervised and supervised task, that need to be considered when tackling this problem. These subproblems correspond to a clustering and classification approach that we evaluate on Twitter data sets. The clustering approach is evaluated using multiple representation techniques, similarity measures and clustering algorithms. We show that it is possible to incorporate a Twitter user’s social graph data into the clustering approach to find topic-based clusters. The classification approach is implemented, from a statistical relational learning perspective, with kLog. We show that kLog can use a user’s tweet content and social graph data to perform accurate topic-based classification. We conclude that it is feasible to construct useful topic-based Twitter lists with either approach. / AFRIKAANSE OPSOMMING: Die stroom van inligting wat sosiale-netwerk gebruikers op ’n daaglikse basis verwerk, is aan die groei. Vir baie gebruikers, skep hierdie oordosis inligting ’n gevoel dat hulle beheer oor hul inligtingsbronne verloor. As ’n oplossing, het sosiale-netwerke meganismes geïmplementeer waarmee gebruikers die inligting in hul netwerk kan bestuur. Hierdie meganismes is nie selfwerkend nie, maar kort toevoer van die gebruiker. Twitter het lyste geïmplementeer waarmee gebruikers ander mense in hul sosiale-netwerk kan groepeer. Lyste is ’n kragtige organiserings meganisme, maar tog vind grootskaal gebruik daarvan nie plaas nie. Gebruikers voel dat die opstelling te veel tyd in beslag neem en die onderhoud daarvan te veel moeite is. Hierdie tesis ondersoek die probleem om onderwerp-gerigte Twitter lyste te skep. Ons identisifeer twee subprobleme wat aangepak word deur ’n nie-toesig en ’n toesighoudende metode. Hierdie twee metodes hou verband met trosvorming en klassifikasie onderskeidelik. Ons evalueer beide die trosvorming en klassifikasie op twee Twitter datastelle. Die trosvorming metode word geëvalueer deur te kyk na verskillende voorstellingstegnieke, eendersheid maatstawwe en trosvorming algoritmes. Ons wys dat dit moontlik is om ’n gebruiker se Twitter netwerkdata in te sluit om onderwerp-gerigte groeperinge te vind. Die klassifikasie benadering word geïmplementeer met kLog, vanuit ’n statistiese relasionele leertoerie perspektief. Ons wys dat akkurate onderwerp-gerigte klassifikasie resultate verkry kan word met behulp van gebruikers se tweet-inhoud en sosiale-netwerk data. In beide gevalle wys ons dat dit moontlik is om onderwerp-gerigte Twitter lyste, met goeie resultate, te bou.

Thesis (PhD)--Stellenbosch University, 2013. / Please refer to full text to view abstract.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Probabilistic symbolic execution is a new approach that extends the normal symbolic execution with probability calculations. This approach combines symbolic execution and model counting to estimate the number of input values that would satisfy a given path condition, and thus is able to calculate the execution probability of a path. The focus has been on programs that manipulate primitive types such as linear integer arithmetic in object-oriented programming languages such as Java. In this thesis, we extend probabilistic symbolic execution to handle data structures, thus allowing support for reference types. Two techniques are proposed to calculate the probability of an execution when the programs have structures as inputs: an approximate approach that assumes probabilities for certain choices stay fixed during the execution and an accurate technique based on counting valid structures. We evaluate these approaches on an example of a Binary Search Tree and compare it to the classic approach which only take symbolic values as input. / AFRIKAANSE OPSOMMING: Probabilistiese simboliese uitvoering is ’n nuwe benadering wat die normale simboliese uitvoering uitbrei deur waarksynlikheidsberekeninge by te voeg. Hierdie benadering kombineer simboliese uitvoering en modeltellings om die aantal invoerwaardes wat ’n gegewe padvoorwaarde sal bevredig, te beraam en is dus in staat om die uitvoeringswaarskynlikheid van ’n pad te bereken. Tot dus vêr was die fokus op programme wat primitiewe datatipes manipuleer, byvoorbeeld lineêre heelgetalrekenkunde in objek-geörienteerde tale soos Java. In hierdie tesis brei ons probabilistiese simboliese uitvoering uit om datastrukture, en dus verwysingstipes, te dek. Twee tegnieke word voorgestel om die uitvoeringswaarskynlikheid van ’n program met datastrukture as invoer te bereken. Eerstens is daar die benaderingstegniek wat aanneem dat waarskynlikhede vir sekere keuses onveranderd sal bly tydens die uitvoering van die program. Tweedens is daar die akkurate tegniek wat gebaseer is op die telling van geldige datastrukture. Ons evalueer hierdie benaderings op ’n voorbeeld van ’n binêre soekboom en vergelyk dit met die klassieke tegniek wat slegs simboliese waardes as invoer neem.

The increasing availability of molecular data means that phylogenetic studies nowadays often use datasets which combine a large number of loci for many different species. This leads to a trade-off. On the one hand more complex models are preferred to account for heterogeneity in evolutionary processes. On the other hand simple models that can answer biological questions of interest that are easy to interpret and can be computed in reasonable time are favoured. This thesis focuses on four cases of phylogenetic analysis which arise from this conflict. - It is shown that edge weight estimates can be non-identifiable if the data are simulated under a mixture model. Even if the underlying process is known the estimation and interpretation may be difficult due to the high variance of the parameters of interest. - Partition models are commonly used to account for heterogeneity in data sets. Novel methods are presented here which allow grouping of genes under similar evolutionary constraints. A data set, containing 14 genes of the chloroplast from 19 anciently diverged species is used to find groups of co-evolving genes. The prospects and limitations of such methods are discussed. - Penalised likelihood estimation is a useful tool for improving the performance of models and allowing for variable selection. A novel approach is presented that uses pairwise dissimilarities to visualise the data as a network. It is further shown how penalised likelihood can be used to decrease the variance of parameter estimates for mixture and partition models, allowing a more reliable analysis. Estimates for the variance and the expected number of parameters of penalised likelihood estimates are derived. - Tree shape statistics are used to describe speciation events in macroevolution. A new tree shape statistic is introduced and the biases of different cluster methods on tree shape statistics are discussed.

Thesis (MSc (Mathematical Sciences)--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: In this thesis, a pricing mechanism to stimulate cooperation between nodes in ad hoc networks is explored. The model incorporates incentives for users to act as transit nodes and carry the traffic between other nodes on multi-hop paths, and to be rewarded with their own ability to send traffic. The thesis investigates the consequences of this pricing model by means of simulation of a network and illustrates the way in which network resources are allocated to users according to their geographical position. Moreover, since modelling node movements is an important aspect in ad hoc network simulation, a collective mobility model, the adaptive mobility model, is used to maximise the area coverage of the nodes. / AFRIKAANSE OPSOMMING: In hierdie tesis word ’n koste meganisme gebruik om samewerking te stimuleer tussen nodusse in ad hoc netwerke. Die model inkorporeer trekpleisters deur gebruikers te beloon om verkeer te stuur deur op te tree as transito nodusse, en verkeer tussen nodusse op multi-skakel paaie te dra. Die tesis ondersoek die ge- volge van die koste model deur die simulering van ’n netwerk, en demonstreer die manier waarop die netwerk hulpbronne geallokeer word aan gebruikers gebaseer op hulle geografiese posisie. Siende dat die modellering van nodus bewegings ’n belangrike aspek is in ad hoc netwerk simulasie, word ’n kollek- tiewe mobiliteits model sowel as ’n veranderlike mobiliteits model gebruik om die dekkings areas van die nodusse te maksimeer.

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.