A graph theoretic proof of the complexity of colouring by a local tournament with at least two directed cycles

In this paper we give a graph theoretic proof of the fact that deciding whether a homomorphism exists to a fixed local tournament with at least two directed cycles is NP-complete. One of the main reasons for the graph theoretic proof is that it showcases all of the techniques that have been built up over the years in the study of the digraph homomorphism problem

A graph theoretic proof of the complexity of colouring by a local tournament with at least two directed cycles

In this paper we give a graph theoretic proof of the fact that deciding whether a homomorphism exists to a fixed local tournament with at least two directed cycles is NP-complete. One of the main reasons for the graph theoretic proof is that it showcases all of the techniques that have been built up over the years in the study of the digraph homomorphism problem

Identiteitsvorming in die Afrikaanse blogosfeer

Thesis (MA)--University of Stellenbosch, 2010.ENGLISH ABSTRACT: The aim of this study is to investigate Afrikaner identity in the Afrikaans blogosphere on the basis of the Afrikaner nasionalist identity that was forged during the twentieth century. The environment within which blogs function and its characteristics are discussed, after which the circumstances that led to the development of Afrikaner identity as well as the current sociopolitical position of Afrikaners are traced. Through quantitative analysis, the Afrikaans blogosphere is compared to this identity to discover too what extent the identity is still remnant in Afrikaans bloggers. It is concluded that Afrikaner nationalism is virtually extinct in the Afrikaans blogosphere and that the plurality of identities hosted by it are fragmented and paradoxical.AFRIKAANSE OPSOMMING: Die doel van hierdie studie is om identiteitsvorming in die Afrikaanse blogosfeer te ondersoek aan die hand van die Afrikaner-nasionalistiese identiteitskonstruk van die twintigste eeu. Aandag word geskenk aan die milieu waarbinne blogs funksioneer en hul aard, waarna die omstandighede waaronder Afrikaneridentiteit ontstaan sowel as die huidige sosio-politiese posisie van Afrikaners nagespeur word. Aan die hand van kwantitatiewe ondersoekmetodes word Afrikaanse blogs dan met die voorafgenoemde identiteit vergelyk in 'n poging om agter te kom in watter mate dit nog by Afrikaanse bloggers teenwoordig is. Die gevolgtrekking word gemaak dat Afrikaner-nasionalisme bykans afwesig is in die Afrikaanse blogosfeer en dat die pluraliteit van identiteite daarop gefragmenteerd en paradoksaal daar uitsien

On the chromatic number of commutative rings with identity

M.Sc.This thesis is concerned with one possible interplay between commutative algebra and graph theory. Specifically, we associate with a commutative ring R a graph and then set out to determine how the ring's properties influence the chromatic and clique numbers of the graph. The graph referred to is obtained by letting each ring element be represented by a vertex in the graph and joining two vertices when the product of their corresponding ring elements is equal to zero. The thesis focuses on rings that have a finite chromatic number, where the chromatic number of the ring is equal to the chromatic number of the associated graph. The nilradical of the ring plays a prominent role in these- investigations. Furthermore, the thesis also discusses conditions under which the chromatic and clique numbers of the associated graph are equal. The thesis ends with a discussion of rings with low (< 5) chromatic number and an example of a ring with clique number 5 and chromatic number 6

Modelling South African traffic for large networks - an extension of the gravity model for traffic demand modelling

Thesis (MCom)--Stellenbosch University, 2017.ENGLISH SUMMARY : Traffic congestion is a growing burden on society. Due to the complexity of modelling transportation, many approaches do not scale efficiently. Assumptions are made to estimate the locality and quantity of traffic that passes through, leaves or enters a study area. Infrastructure investment based on inaccurate transportation modelling could potentially increase congestion. Furthermore, the effects of changes in infrastructure outside a study area are also unknown. It is therefore necessary to model transportation networks at a larger scale than required before. This thesis presents a large scale traffic modelling framework, potentially capable of modelling the impact of public transport and infrastructure investment for the South African context. The framework builds on the basic procedure of the Four-Step Modelling methodology. To address the shortcomings of static trip distribution models, a proposed, temporally adjusted, doubly constrained gravity model is formulated. Kernel density functions are fitted from survey data to dene unique impedance of travel functions for each travel analysis zone. Route selection is determined by a heuristic approach to dynamic traffic assignment which is implemented in a mesoscopic traffic simulator. The proposed gravity model is iteratively calibrated using the output of the traffic simulator in a positive feedback loop to produce a trip distribution that approaches an equilibrium assignment. The gravity model calibration and validation shows that the proposed gravity model is more accurate than the single impedance of travel gravity model. The framework produces OD trip matrices, inter- and intra-zonal routes, quarter-hourly traffic flows and a measure of congestion, all which can be visualised in a GIS environment.AFRIKAANSE OPSOMMING : Verkeersopeenhopings is ‘n immertoenemende probleem in Suid-Afrika. Verskeie bestaande tegnieke wat gebruik word om verkeer te modelleer, is ondoeltreffend wanneer dit op ‘n groot skaal geimplementeer word. Aannames word gemaak oor die kwantiteit en lokaliteit van verkeer wat vanuit, na en deur die studie-area vloei. Infrastruktuurontwikkeling gebaseer op onakkurate verkeersmodellering kan die intensiteit van verkeersopeenhopings vererger. Die impak wat so ‘n verandering van infrastruktuur sal he buite die studie-area kan ook nie geevalueer word nie. Dit is daarom nodig om vervoerinfrastruktuur op ‘n groter skaal as vantevore te modelleer. Hierdie tesis bied ‘n grootskaalse verkeersmodelleringsraamwerk aan wat potensieel die impak van publieke vervoer en infrastruktuurontwikkelings kan modelleer vir die Suid-Afrikaanse konteks. Die raamwerk bou voort op die beginsels van die Vier-Stap Modelleringsmetodologie. ‘n Dubbele beperkte gravitasie model wat aangepas is, word voorgestel en geformuleer om die tekortkominge van statiese ritverspreiding modelle aan te spreek. Kerndigtheidsfunksies word gepas aan opname-data om unieke reisimpedansiefunksies te denieer vir elke verkeersanalisesone. Ritroetes word bepaal deur middel van dinamiese verkeerstoedeling wat geimplementeer is deur ‘n mesoskopiese verkeerssimulasie. Die gravitasiemodel word iteratiewelik gekalibreer deur die uitvoer van die verkeersimulasie te gebruik in ‘n positiewe terugvoer lus om konvergerende ritverdelings te produseer. Die kalibrering en validering van die voorgestelde gravitasiemodel toon aan dat dit meer akkuraat is as die enkele ritimpedansie gravitasiemodel. Die raamwerk produseer oorsprong-bestemming matrikse, inter- en intrasone roetes, kwartuurlikse verkeersvloeie en ‘n maatstaf van verkeersopeenhopings wat in ‘n GIS omgewing visualiseer kan word

Aspects of multipath channel characterization

M.Ing.In this thesis we investigated the characterization of wireless communication channels. The characterization of the channel itself focused on the analog as well as the discrete domains. This was done to provide a more complete treatment than that which is usually found in the literature (which normally focuses" on either one of the domains). We also provide a discussion on the basic issues that arise when trying to characterize a wireless communication channel. The analog characterization proceeded by means of the impulse response of the chan­ nel. We calculated the scattering function of the channel as well as the Delay and Doppler Power Spectra. From the wideband data we also derived the equivalent Narrowband en­ velope and phase and investigated the probability density functions of these. We also implemented the GMSK modulation scheme, used in the GSM system, in software. This included a simulation of the additive white Gaussian noise channel as well as the Rayleigh fading channel, the two most common assumed models. A complete discussion is provided on this implementation. The implementation above was used to obtain discrete channel models of GMSK on a Rayleigh fading channel. This also provided us with the opportunity to compare the performance of three of the most common discrete channel models : the Gilbert model, the Gilbert-Elliott model and the Fritchman model. Lastly we obtained equations that describe the behaviour of the Gilbert model's parameters as a function of average signal­ to-noise ratio

A grammatical framework for the computational parsing of written Afrikaans sentences

Thesis (PhD)--Stellenbosch University, 2019.ENGLISH ABSTRACT: This dissertation investigates which grammatical framework is best suited to computationally represent and parse written Afrikaans sentences. This knowledge is necessary to build a large scale Afrikaans treebank – a resource which does not yet exist, but is a critical prerequisite for advanced endeavours in Afrikaans natural language processing. To gain this knowledge, we formally describe the building blocks of written Afrikaans from the perspectives of two major grammatical frameworks: constituency grammar and dependency grammar. Using these formal descriptions, we construct the first linguistically motivated treebank for Afrikaans, annotated with both constituency and dependency graphs. We perform k-fold cross-validation on multiple variations of this treebank with four state of the art sentence parsers, and fine-comb the results. Combining insights from the formal descriptions of written Afrikaans with the data obtained during parser evaluation, we conclude that dependency grammar outperforms constituency grammar at computationally representing the syntactic structure of written Afrikaans sentences under the conditions tested.AFRIKAANSE OPSOMMING: Hierdie proefskrif ondersoek watter grammatikale raamwerk meer geskik is vir die rekenaarmatige voorstelling en ontleding van geskrewe Afrikaanse sinne. Hierdie kennis is nodig om ’n grootskaalse Afrikaanse boombank te bou – ’n hulpbron wat tans ontbreek, maar ’n kritiese voorvereiste is vir gevorderde Afrikaanse natuurlike taalverwerking. Ten einde hierdie kennis te verwerf, beskryf ons die boublokke van geskrewe Afrikaans formeel vanuit die perspektiewe van twee dominante grammatikale raamwerke: samestellingsgrammatiek (”constituency grammar”) en afhanklikheidsgrammatiek (“dependency grammar”). Hierdie formele beskrywings word ingespan om die eerste taalkundig gemotiveerde Afrikaanse boombank te bou wat annotasies vanuit beide grammatikale raamwerke bevat. Met verskeie variasies van hierdie boombank voer ons dan k-voudige kruisvalidering uit met vier toonaangewende sinsontleders en fynkam hul resultate. Aan die hand van hierdie resultate, sowel as die teoretiese insigte verkry tydens die formele beskrywings van geskrewe Afrikaans, lei ons af dat afhanklikheidsgrammatiek samestellingsgrammatiek oortref vir die rekenaarmatige voorstelling van die sintaktiese struktuur van geskrewe Afrikaanse sinne binne die getoetsde toestande.Doctora

A graph theoretic proof of the complexity of colouring by a local tournament with at least two directed cycles

In this paper we give a graph theoretic proof of the fact that deciding whether a homomorphism exists to a fixed local tournament with at least two directed cycles is NP-complete. One of the main reasons for the graph theoretic proof is that it showcases all of the techniques that have been built up over the years in the study of the digraph homomorphism problem

The complexity of colouring by locally semicomplete digraphs

AbstractIn this paper we establish a dichotomy theorem for the complexity of homomorphisms to fixed locally semicomplete digraphs. It is also shown that the same dichotomy holds for list homomorphisms. The polynomial algorithms follow from a different, shorter proof of a result by Gutjahr, Welzl and Woeginger