Spelling suggestions: "subject:"themathematics."" "subject:"theirmathematics.""
211 |
Support vector machines, generalization bounds, and transductionKroon, Rodney Stephen 12 1900 (has links)
Thesis (MComm)--University of Stellenbosch, 2003. / Please refer to full text for abstract.
|
212 |
An embodied conversational agent with autistic behaviourVenter, Wessel Johannes 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: In this thesis we describe the creation of an embodied conversational agent which
exhibits the behavioural traits of a child who has Asperger Syndrome. The agent is
rule-based, rather than arti cially intelligent, for which we give justi cation. We then
describe the design and implementation of the agent, and pay particular attention
to the interaction between emotion, personality and social context. A 3D demonstration
program shows the typical output to conform to Asperger-like answers, with
corresponding emotional responses. / AFRIKAANSE OPSOMMING: In hierdie tesis beskryf ons die ontwerp en implementasie van 'n gestaltegespreksagent
wat die gedrag van 'n kind met Asperger se sindroom uitbeeld. Ons regverdig
die besluit dat die agent reël-gebaseerd is, eerder as 'n ware skynintelligensie implementasie.
Volgende beskryf ons die wisselwerking tussen emosies, persoonlikheid en
sosiale konteks en hoe dit inskakel by die ontwerp en implementasie van die agent. 'n
3D demonstrasieprogram toon tipiese ooreenstemmende Asperger-agtige antwoorde
op vrae, met gepaardgaande emosionele reaksies.
|
213 |
Modelling the dynamics of methamphetamine abuse in the Western CapeKalula, Asha Saidi 03 1900 (has links)
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011. / Includes bibliography / ENGLISH ABSTRACT: The production and abuse of methamphetamine has increased dramatically in South Africa,
especially in the Western Cape province. A typical methamphetamine use cycle consists of
concealed use after initiation, addiction, treatment and recovery. The model by Nyabadza
and Musekwa in [32], is extended to include a core group, fast and slow progression to
addiction. The model is analysed analytically and numerically using mass action incidence
function and non-linear incidence function. The analysis of the model with mass action
incidence is presented in terms of the methamphetamine epidemic threshold R0. The
analysis shows that the drug free equilibrium is locally asymptotically stable when R0 <
1 and drug persistent equilibrium is locally asymptotically stable when R0 > 1. The
model also exhibits a backward bifurcation. Sensitivity analysis of the model on R0 is
performed. The most sensitive parameters are transmission rate and recruitment rate
of individuals into the core group. The non-linear incidence incorporates innovators and
behaviour change. Analytically, the model is analysed in the absence of behaviour change.
With behaviour change two cases were considered. Firstly without innovators and secondly
with innovators. In the absence of innovators the non-linear incidence reduced to standard
incidence and similar results to the ones in the first model were obtained. With the presence
of innovators there is no drug free equilibrium. Numerically we fit the model to data on
the number of patients who enter into treatment centers for rehabilitation. Using the
fitted model, we determine the prevalence and incidence of methamphetamine abuse. We
investigate the impact of behaviour change, ‘reinfection’ rate as well as uptake rate into
treatment on prevalence. Our results suggest that intervention and prevention programs
focusing on behaviour change and uptake rate into treatment would reduce the prevalence.
Projections are made to determine the possible long term trends of the prevalence of
methamphetamine abuse in the Western Cape. We give suggestions related to data that
should be collected from a modelling perspective. / AFRIKAANSE OPSOMMING: Die vervaardiging en misbruik van metamfetamien het dramaties in Suid-Afrika toegeneem,
veral in die Wes-Kaap provinsie. ’n Tipiese metamfetamien gebruiksiklus bestaan uit heimlike
gebruik na aanvang, verslawing, behandeling en herstel. Die model deur Nyabadza en
Musekwa in [32], is uitgebrei om ’n kerngroep in te sluit, vinnige en stadige verloop tot
verslawing. Die model is analities en numeries ontleed deur van massa-aksie insidensie
funksie en ’n nie-liniêre insidensie funksie gebruik te maak. Die ontleding van die model
met massa-aksie insidensie word voorgestel in terme van die metamfetamien epidemiese
drempel R0. Die ontleding toon dat die dwelmvrye ewewig lokaal asimptoties stabiel is as
R0 < 1 en die dwelmblydende ewewig is lokaal asimptoties stabiel as R0 > 1. Die model
beeld ook ’n terugwaartse bifurkasie uit. Sensitiwiteitsontleding van die model ten opsigte
van R0 is uitgevoer. Die mees sensitiewe parameters is die oordraagbaarheidskoers
en die rekrute koers van individue in die kerngroep in. Die nuwelinge en gedragsverandering
word deur die nie-liniêre insidensie opgeneem. Analities, is die model ontleed in
die afwesigheid van gedragsverandering. Met gedragsverandering is twee gevalle beskou.
Eerstens sonder nuwelinge en tweedens met nuwelinge. In die afwesigheid van nuwelinge is
die nie-liniêre insidensie herlei tot standaard insidensie en soortgelyke resultate is verkry,
as dié wat in die eerste model verkry is. Met die aanwesigheid van nuwelinge is daar geen
dwelmvrye ewewig nie. Numeries pas ons die model aan die data wat betrekking het met
die aantal pasiënte wat in rehabilitasie sentra opgeneem word vir behandeling. Deur die
gepaste model te gebruik, het ons die voorkoms en insidensie van metamfetamien misbruik
bepaal. Ons ondersoek die impak van gedragsverandering, “re-infeksie” koers sowel as die
koers van opname in behandeling op voorkoms. Ons resultate toon dat intervensie- en
voorkomingsprogramme sal voorkoms verlaag, wat op die gedragsverandering en die koers
van opname in behandeling konsentreer. Die model is ook gebruik om die aantal metamfetamien
gebruikers te projekteer. Ons maak voorstelle verwant aan die data, wat vanuit
‘n modellerings-oogpunt ingesamel moet word.
|
214 |
Modelling the effect of HIV on age-specific incidence of active TB disease : a comparison between Taiwan and Cape Town MetropoleWinkler, Dietrich Maximilian Albert 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: See full text / AFRIKAANSE OPSOMMING: Sien volteks
|
215 |
Liquidity risk and no arbitrageEl Ghandour, Laila 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In modern theory of finance, the so-called First and Second Fundamental Theorems of Asset
Pricing play an important role in pricing options with no-arbitrage. These theorems gives a
necessary and sufficient conditions for a market to have no-arbitrage and for a market to be
complete. An early version of the First Fundamental Theorem of Asset Pricing was proven
by Harrison and Kreps [30] in the case of a finite probability space. A more general version
was proven by Harrison and Pliska [31] in the case of a finite probability space and discrete
time. In the case of continuous time, Delbaen and Schachermayer [19] introduced a more
general concept of no-arbitrage called "No-Free Lunch With Vanishing Risk" (NFLVR),
and showed that for a locally-bounded semimartingale price process NFLVR is essentially
equivalent to the existence of an equivalent local martingale measure.
The goal of this thesis is to review the theory of arbitrage pricing and the extension of
this theory to include liquidity risk. At the current time, liquidity risk is a key challenge
faced by investors. Consequently there is a need to develop more realistic pricing models
that include liquidity risk. We present an approach to liquidity risk by Çetin, Jarrow and
Protter [10]. In to this approach the liquidity risk is embedded into the classical theory
of arbitrage pricing by having investors act as price takers, and assuming the existence
of a supply curve where prices depend on trade size. This framework assumes that the
quantity impact on the price transacted is momentary. Using trading strategies that are
both continuous and of finite variation allows one to avoid liquidity costs. Therefore, the
First and Second Fundamental Theorems of Asset Pricing and the Black-Scholes model
can be extended. / AFRIKAANSE OPSOMMING: In moderne finansiële teorie speel die sogenaamde Eerste en Tweede Fundamentele Stellings
van Bateprysbepaling ’n belangrike rol in die prysbepaling van opsies in arbitrage-vrye
markte. Hierdie stellings gee nodig en voldoende voorwaardes vir ’n mark om vry van
arbitrage te wees, en om volledig te wees. ’n Vroeë weergawe van die Eerste Fundamentele
Stelling was deur Harrison en Kreps [30] bewys in die geval van ’n eindige waarskynlikheidsruimte.
’n Meer algemene weergawe was daarna gepubliseer deur Harrison en Pliska
[31] in die geval van ’n eindige waarskynlikheidsruimte en diskrete tyd. In die geval van
kontinue tyd het Delbaen en Schachermayer [19] ’n meer algemene konsep van arbitragevryheid
ingelei, naamlik “No–Free–Lunch–With–Vanishing–Risk" (NFLVR), en aangetoon dat
vir lokaalbegrensde semimartingaalprysprosesse NFLVR min of meer ekwivalent is aan die
bestaan van ’n lokaal martingaalmaat.
Die doel van hierdie tesis is om ’n oorsig te gee van beide klassieke arbitrageprysteorie,
en ’n uitbreiding daarvan wat likideit in ag neem. Hedendaags is likiditeitsrisiko ’n
vooraanstaande uitdaging wat beleggers die hoof moet bied. Gevolglik is dit noodsaaklik
om meer realistiese modelle van prysbepaling wat ook likiditeitsrisiko insluit te ontwikkel.
Ons bespreek die benadering van Çetin, Jarrow en Protter [10], waar likiditeitsrisiko in
die klassieke arbitrageprysteorie ingesluit word deur die bestaan van ’n aanbodkromme
aan te neem, waar pryse afhanklik is van handelsgrootte. In hierdie raamwerk word aangeneem
dat die impak op die transaksieprys slegs tydelik is. Deur gebruik te maak van
handelingsstrategië wat beide kontinu en van eindige variasie is, is dit dan moontlik om
likiditeitskoste te vermy. Die Eerste en Tweede Fundamentele Stellings van Bateprysbepaling
en die Black–Scholes model kan dus uitgebrei word om likiditeitsrisiko in te sluit.
|
216 |
American Monte Carlo option pricing under pure jump levy modelsWest, Lydia 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: We study Monte Carlo methods for pricing American options where the stock price dynamics follow
exponential pure jump L évy models. Only stock price dynamics for a single underlying are considered.
The thesis begins with a general introduction to American Monte Carlo methods. We then consider two
classes of these methods. The fi rst class involves regression - we briefly consider the regression method of
Tsitsiklis and Van Roy [2001] and analyse in detail the least squares Monte Carlo method of Longsta and
Schwartz [2001]. The variance reduction techniques of Rasmussen [2005] applicable to the least squares
Monte Carlo method, are also considered. The stochastic mesh method of Broadie and Glasserman [2004]
falls into the second class we study. Furthermore, we consider the dual method, independently studied
by Andersen and Broadie [2004], Rogers [2002] and Haugh and Kogan [March 2004] which generates a
high bias estimate from a stopping rule. The rules we consider are estimates of the boundary between the
continuation and exercise regions of the option. We analyse in detail how to obtain such an estimate in
the least squares Monte Carlo and stochastic mesh methods.
These models are implemented using both a pseudo-random number generator, and the preferred choice
of a quasi-random number generator with bridge sampling. As a base case, these methods are implemented
where the stock price process follows geometric Brownian motion.
However the focus of the thesis is to implement the Monte Carlo methods for two pure jump L évy
models, namely the variance gamma and the normal inverse Gaussian models. We first provide a broad
discussion on some of the properties of L évy processes, followed by a study of the variance gamma model
of Madan et al. [1998] and the normal inverse Gaussian model of Barndor -Nielsen [1995]. We also provide
an implementation of a variation of the calibration procedure of Cont and Tankov [2004b] for these models.
We conclude with an analysis of results obtained from pricing American options using these models. / AFRIKAANSE OPSOMMING: Ons bestudeer Monte Carlo metodes wat Amerikaanse opsies, waar die aandeleprys dinamika die patroon
van die eksponensiële suiwer sprong L évy modelle volg, prys. Ons neem slegs aandeleprys dinamika vir 'n
enkele aandeel in ag.
Die tesis begin met 'n algemene inleiding tot Amerikaanse Monte Carlo metodes. Daarna bestudeer
ons twee klasse metodes. Die eerste behels regressie - ons bestudeer die regressiemetode van Tsitsiklis
and Van Roy [2001] vlugtig en analiseer die least squares Monte Carlo metode van Longsta and Schwartz
[2001] in detail. Ons gee ook aandag aan die variansie reduksie tegnieke van Rasmussen [2005] wat van
toepassing is op die least squares Monte Carlo metodes. Die stochastic mesh metode van Broadie and
Glasserman [2004] val in die tweede klas wat ons onder oë neem. Ons sal ook aandag gee aan die dual
metode, wat 'n hoë bias skatting van 'n stop reël skep, en afsonderlik deur Andersen and Broadie [2004],
Rogers [2002] and Haugh and Kogan [March 2004] bestudeer is. Die reëls wat ons bestudeer is skattings
van die grense tussen die voortsettings- en oefenareas van die opsie. Ons analiseer in detail hoe om so 'n
benadering in die least squares Monte Carlo en stochastic mesh metodes te verkry.
Hierdie modelle word geï mplementeer deur beide die pseudo kansgetalgenerator en die verkose beste
quasi kansgetalgenerator met brug steekproefneming te gebruik. As 'n basisgeval word hierdie metodes
geï mplimenteer wanneer die aandeleprysproses 'n geometriese Browniese beweging volg.
Die fokus van die tesis is om die Monte Carlo metodes vir twee suiwer sprong L évy modelle, naamlik
die variance gamma en die normal inverse Gaussian modelle, te implimenteer. Eers bespreek ons in breë
trekke sommige van die eienskappe van L évy prossesse en vervolgens bestudeer ons die variance gamma
model soos in Madan et al. [1998] en die normal inverse Gaussian model soos in Barndor -Nielsen [1995].
Ons gee ook 'n implimentering van 'n variasie van die kalibreringsprosedure deur Cont and Tankov [2004b]
vir hierdie modelle. Ons sluit af met die resultate wat verkry is, deur Amerikaanse opsies met behulp van
hierdie modelle te prys.
|
217 |
Understanding the impact of an HIV intervention package for adolescentsBruce, Faikah 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Adolescents are regarded as a high risk group in South Africa with the highest
human immunodeficiency virus (HIV) incidence occurring in this group. Prevention
among adolescents is therefore a key in decreasing the HIV burden.
This thesis aims to assist in the design of trials by simulating the potential outcomes
of a combination prevention trial in adolescents. We develop a stochastic
individual-based model stratified by sex and age. We then use this model to
determine the impact of various prevention packages on HIV incidence among
adolescents participating in a hypothetical trial over a three year period. The
trial that is simulated involves an intervention arm, in which adolescents are
offered a choice of a prevention methods (including medical male circumcision
(MMC), oral pre-exposure prophylaxis (PrEP) and antiretroviral-based vaginal
microbicides (ARV-VM)), and a control arm. We predict that the impact
of a full prevention package on HIV incidence would be a 46% per personyear(
PPY) (95% CI 45–47%) risk reduction. The combination of MMC and
PrEP has a substantial impact on HIV incidence in males, with a 51% PPY
(95% CI 49–53%) relative risk of HIV infection. Offering women the choice of
PrEP, a microbicide gel or a microbicide in the form of a vaginal ring would be
less effective, with a 57% PPY (95% CI 56–58%) relative risk of HIV acquisition.
This is not substantially different from the relative risk estimated when
the vaginal ring alone is offered, as the ring is assumed to be the most accept able of the three prevention methods. We determine a sample size requirement
of approximately 1013 in each arm of a trial would achieve 80% power to detect
a statistically significant reduction in HIV risk. We find that the relative risk
is sensitive to the assumed degree of correlation between condom use and the
acceptability of the prevention method. We also find that the most efficient
trial design may be to offer both MMC and PrEP to males but to offer only
a microbicide ring to females. Further work is required to better understand
the processes by which adolescent prevention method choices are made. / AFRIKAANSE OPSOMMING: Adolessente word beskou as ‘n hoe risiko groep in Suid Afrika, met die hoogste
menslike immuniteitsgebrekvirus (MIV) insidensie in hierdie groep. Voorkoming
van MIV onder adolessente is daarom noodsaaklik om die MIV las te
verminder. Die doel van hierdie tesis is om te help met die ontwerp van studies
deur die moontlike uitkomste van ‘n kombinasie-voorkoming studie in adolessente
te simuleer. Ons het ‘n stogastiese individu-gebaseerde model, gestratifiseer
met betrekking tot seks en ouderdom, ontwikkel. Ons het toe die model
gebruik om die impak van ‘n verskeinheid van voorkomingspakette op MIV insidensie
onder adolessente wat deelneem aan ‘n hipotetiese proef oor ‘n drie jaar
periode, te bepaal. Die proef wat gesimuleer word behels a intervensie groep,
waarin die jong volwassenes ‘n keuse van voorbehoedings metodes (insluitende
mediese manlike besnydenis (MMB), pre-blootstelling profilakse (PrBP) en
anti-retrovirale vaginale mikrobisiedes (ARV-VM)) aangebied word, en ‘n kontrole
groep. Ons voorspel dat die impak van ‘n volle voorkomingspaket op MIV
insidensie ‘n 46% per persoon-jaar (PPJ) (95% VI 47–47%) risiko vermindering
sal wees. Die kombinasie van MMB en PrBP het ‘n substansiele impak
op MIV insidensie onder mans, met ‘n relatiewe risiko van MIV infeksie van
51% PPJ (95% VI 49–53%). Om die keuse van PrBP, ‘n mikrobisiede gel of
‘n mikrobisiede in die vorm van ‘n vaginale ring aan vrouens te bied, is minder
effektief, met ‘n relatiewe risiko van MIV infeksie van 57% PPJ (95% VI 56%–58%). Hierdie verskil nie substansieel van die beraamde relatiewe risiko
in die geval waar slegs die vaginale ring gebied word nie, aangesien daar aanvaar
word dat die ring die mees aanvaarde van die drie voorkomingsmetodes is.
Ons het bepaal dat ‘n steekproef van ongeveer 1013 individue in elke arm van
die proef nodig is om ‘n 80% kans te he om ‘n statisties betekenisvolle afname
in MIV-risiko te bespeur. Ons vind dat die relatiewe risiko sensitief is tot die
aanvaarde graad van die korrelasies tussen kondoom-gebruik en die aanvaarding
van die voorkomings metodes. Ons het ook gevind dat dit mag wees dat
die mees doeltreffende proef ontwerp is om beide MMB en PrBP vir mans en
slegs ‘n mikrobisiede ring vir vrouens te bied. Verdere werk word benodig om
die prosesse waarby jong volwassenes keuses maak oor voorkomingsmetodes te
verstaan.
|
218 |
Modelling the dynamics of HIV related malignanciesAkinlotan, Deborah Morenikeji 04 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In recent years, HIV-associated cancers have proven to be the bane of our time, since HIV is
decimating humanity across the globe, even in the twilight of the last century. Cancer rates
continue to rise in developing countries, where 95% of the world’s HIV-infected population
lives, yet less than 1% have access to antiretroviral therapy. HIV-infected individuals have
a higher proclivity to develop cancers, mainly from immunosuppression. An understanding
of the immunopathogenesis of HIV-related cancers (HRC) is therefore a major prerequisite
for rationally developing and/or improving therapeutic strategies, developing immunotherapeutics
and proplylatic vaccines. In this study, we explore the pathology of HIV-related
cancer malignancies, taking into account the pathogenic mechanisms and their potential
for improving the treatment of management of these malignancies especially in developing
countries. We mathematically model the dynamics of malignant tumors in an HIV-free environment,
investigate the impact of cancer malignancies on HIV-positive patients and explore
the benefits of various therapeutic intervention strategies in the management of HIV-related
cancers. We present two deterministic models of infectious diseases to implement these, and
they were analysed. We use HIV-related lymphomas in the Western Cape of South Africa
as a case study. We validated the proposed models using lymphoma incidence data from
the Tygerberg Lymphoma Study Group (TLSG), Tygerberg Hospital, Western Cape, South
Africa. We show that the increasing prevalence of HIV increases lymphoma cases, and thus,
other HIV-related cancers. Our models also suggests that an increase in the roll-out of the
HAART program can reduce the number of lymphoma cases in the nearest future, while it
averts many deaths. Furthermore, the results indicate that a highly crucial factor to consider
in the prognosis of the incidence of lymphoma (and other cancer types) in HIV-infected
patients is their CD4 cell count, irrespective of whether the patient has developed an HRC
or not.
|
219 |
Bifibrational duality in non-abelian algebra and the theory of databasesWeighill, Thomas 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics in
non-abelian algebra, which is based on replacing the framework of a category
with that of a category equipped with a functor to it. We also make some first
steps towards a possible link between this theory and the theory of databases
in computer science. Both of these theories are based around the study of
Grothendieck bifibrations and their generalisations. The main results in this
thesis concern correspondences between certain structures on a category which
are relevant to the study of categories of non-abelian group-like structures, and
functors over that category. An investigation of these correspondences leads
to a system of dual axioms on a functor, which can be considered as a solution
to the proposal of Mac Lane in his 1950 paper "Duality for Groups" that
a self-dual setting for formulating and proving results for groups be found.
The part of the thesis concerned with the theory of databases is based on a
recent approach by Johnson and Rosebrugh to views of databases and the view
update problem. / AFRIKAANSE OPSOMMING: In hierdie tesis word ’n self-duale kategoriese benadering tot verskeie onderwerpe
in nie-abelse algebra ontwikkel, wat gebaseer is op die vervanging van
die raamwerk van ’n kategorie met dié van ’n kategorie saam met ’n funktor
tot die kategorie. Ons neem ook enkele eerste stappe in die rigting van ’n skakel
tussen hierdie teorie and die teorie van databasisse in rekenaarwetenskap.
Beide hierdie teorieë is gebaseer op die studie van Grothendieck bifibrasies
en hul veralgemenings. Die hoof resultate in hierdie tesis het betrekking tot
ooreenkomste tussen sekere strukture op ’n kategorie wat relevant tot die studie
van nie-abelse groep-agtige strukture is, en funktore oor daardie kategorie.
’n Verdere ondersoek van hierdie ooreemkomste lei tot ’n sisteem van duale
aksiomas op ’n funktor, wat beskou kan word as ’n oplossing tot die voorstel
van Mac Lane in sy 1950 artikel “Duality for Groups” dat ’n self-duale konteks
gevind word waarin resultate vir groepe geformuleer en bewys kan word. Die
deel van hierdie tesis wat met die teorie van databasisse te doen het is gebaseer
op ’n onlangse benadering deur Johnson en Rosebrugh tot aansigte van
databasisse en die opdatering van hierdie aansigte.
|
220 |
Explicit class field theory for rational function fieldsRakotoniaina, Tahina 12 1900 (has links)
Thesis (MSc (Mathematical Sciences))--Stellenbosch University, 2008. / Class field theory describes the abelian extensions of a given field K in terms of various
class groups of K, and can be viewed as one of the great successes of 20th century
number theory. However, the main results in class field theory are pure existence
results, and do not give explicit constructions of these abelian extensions. Such
explicit constructions are possible for a variety of special cases, such as for the field Q
of rational numbers, or for quadratic imaginary fields. When K is a global function
field, however, there is a completely explicit description of the abelian extensions of
K, utilising the theory of sign-normalised Drinfeld modules of rank one. In this thesis
we give detailed survey of explicit class field theory for rational function fields over
finite fields, and of the fundamental results needed to master this topic.
|
Page generated in 0.076 seconds