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Closure and compactness in framesMasuret, Jacques 03 1900 (has links)
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: As an introduction to point-free topology, we will explicitly show the connection
between topology and frames (locales) and introduce an abstract notion, which
in the point-free setting, can be thought of as a subspace of a topological space.
In this setting, we refer to this notion as a sublocale and we will show that there
are at least four ways to represent sublocales.
By using the language of category theory, we proceed by investigating closure
in the point-free setting by way of operators. We de ne what we mean by a coclosure
operator in an abstract context and give two seemingly di erent examples
of co-closure operators of Frm. These two examples are then proven to be the
same.
Compactness is one of the most important notions in classical topology and
therefore one will nd a great number of results obtained on the subject. We
will undertake a study into the interrelationship between three weaker compact
notions, i.e. feeble compactness, pseudocompactness and countable compactness.
This relationship has been established and is well understood in topology, but
(to a degree) the same cannot be said for the point-free setting. We will give the
frame interpretation of these weaker compact notions and establish a point-free
connection. A potentially promising result will also be mentioned. / AFRIKAANSE OPSOMMING: As 'n inleiding tot punt-vrye topologie, sal ons eksplisiet die uiteensetting van
hierdie benadering tot topologie weergee. Ons de nieer 'n abstrakte konsep wat,
in die punt-vrye konteks, ooreenstem met 'n subruimte van 'n topologiese ruimte.
Daar sal verder vier voorstellings van hierdie konsep gegee word.
Afsluiting, deur middel van operatore, word in die puntvrye konteks ondersoek
met behulp van kategorie teorie as taalmedium. Ons sal 'n spesi eke operator
in 'n abstrakte konteks de nieer en twee o enskynlik verskillende voorbeelde van
hierdie operator verskaf. Daar word dan bewys dat hierdie twee operatore dieselfde
is.
Kompaktheid is een van die mees belangrikste konsepte in klassieke topologie
en as gevolg daarvan geniet dit groot belangstelling onder wiskundiges. 'n Studie
in die verwantskap tussen drie swakker forme van kompaktheid word onderneem.
Hierdie verwantskap is al in topologie bevestig en goed begryp onder wiskundiges.
Dieselfde kan egter, tot 'n mate, nie van die puntvrye konteks ges^e word nie. Ons
sal die puntvrye formulering van hierdie swakker konsepte van kompaktheid en
hul verbintenis, weergee. 'n Resultaat wat moontlik belowend kan wees, sal ook
genoem word.
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Fredholm theory in general Banach algebrasHeymann, Retha 03 1900 (has links)
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see [9]), of Fredholm
theory in the context of bounded linear operators on Banach spaces
to a theory in a Banach algebra setting. A bounded linear operator T on a
Banach space X is Fredholm if it has closed range and the dimension of its
kernel as well as the dimension of the quotient space X/T(X) are finite. The
index of a Fredholm operator is the integer dim T−1(0)−dimX/T(X). Weyl
operators are those Fredholm operators of which the index is zero. Browder
operators are Fredholm operators with finite ascent and descent. Harte’s generalisation
is motivated by Atkinson’s theorem, according to which a bounded
linear operator on a Banach space is Fredholm if and only if its coset is invertible
in the Banach algebra L(X) /K(X), where L(X) is the Banach
algebra of bounded linear operators on X and K(X) the two-sided ideal of
compact linear operators in L(X). By Harte’s definition, an element a of a
Banach algebra A is Fredholm relative to a Banach algebra homomorphism
T : A ! B if Ta is invertible in B. Furthermore, an element of the form
a + b where a is invertible in A and b is in the kernel of T is called Weyl
relative to T and if ab = ba as well, the element is called Browder. Harte
consequently introduced spectra corresponding to the sets of Fredholm, Weyl
and Browder elements, respectively. He obtained several interesting inclusion
results of these sets and their spectra as well as some spectral mapping
and inclusion results. We also convey a related result due to Harte which
was obtained by using the exponential spectrum. We show what H. du T.
Mouton and H. Raubenheimer found when they considered two homomorphisms.
They also introduced Ruston and almost Ruston elements which led
to an interesting result related to work by B. Aupetit. Finally, we introduce
the notions of upper and lower semi-regularities – concepts due to V. M¨uller.
M¨uller obtained spectral inclusion results for spectra corresponding to upper
and lower semi-regularities. We could use them to recover certain spectral
mapping and inclusion results obtained earlier in the thesis, and some could
even be improved. / AFRIKAANSE OPSOMMING: Hierdie tesis is ‘n studie van ’n veralgemening deur R. Harte (sien [9]) van
Fredholm-teorie in die konteks van begrensde lineˆere operatore op Banachruimtes
tot ’n teorie in die konteks van Banach-algebras. ’n Begrensde lineˆere
operator T op ’n Banach-ruimte X is Fredholm as sy waardeversameling geslote
is en die dimensie van sy kern, sowel as di´e van die kwosi¨entruimte
X/T(X), eindig is. Die indeks van ’n Fredholm-operator is die heelgetal
dim T−1(0) − dimX/T(X). Weyl-operatore is daardie Fredholm-operatore
waarvan die indeks gelyk is aan nul. Fredholm-operatore met eindige styging
en daling word Browder-operatore genoem. Harte se veralgemening is gemotiveer
deur Atkinson se stelling, waarvolgens ’n begrensde lineˆere operator op
’n Banach-ruimte Fredholm is as en slegs as sy neweklas inverteerbaar is in die
Banach-algebra L(X) /K(X), waar L(X) die Banach-algebra van begrensde
lineˆere operatore op X is en K(X) die twee-sydige ideaal van kompakte
lineˆere operatore in L(X) is. Volgens Harte se definisie is ’n element a van
’n Banach-algebra A Fredholm relatief tot ’n Banach-algebrahomomorfisme
T : A ! B as Ta inverteerbaar is in B. Verder word ’n Weyl-element relatief
tot ’n Banach-algebrahomomorfisme T : A ! B gedefinieer as ’n element
met die vorm a + b, waar a inverteerbaar in A is en b in die kern van T is.
As ab = ba met a en b soos in die definisie van ’n Weyl-element, dan word
die element Browder relatief tot T genoem. Harte het vervolgens spektra
gedefinieer in ooreenstemming met die versamelings van Fredholm-, Weylen
Browder-elemente, onderskeidelik. Hy het heelparty interessante resultate
met betrekking tot insluitings van die verskillende versamelings en hulle
spektra verkry, asook ’n paar spektrale-afbeeldingsresultate en spektraleinsluitingsresultate.
Ons dra ook ’n verwante resultaat te danke aan Harte
oor, wat verkry is deur van die eksponensi¨ele-spektrum gebruik te maak.
Ons wys wat H. du T. Mouton en H. Raubenheimer verkry het deur twee
homomorfismes gelyktydig te beskou. Hulle het ook Ruston- en byna Rustonelemente
gedefinieer, wat tot ’n interessante resultaat, verwant aan werk van
B. Aupetit, gelei het. Ten slotte stel ons nog twee begrippe bekend, naamlik
’n onder-semi-regulariteit en ’n bo-semi-regulariteit – konsepte te danke
aan V. M¨uller. M¨uller het spektrale-insluitingsresultate verkry vir spektra
wat ooreenstem met bo- en onder-semi-regulariteite. Ons kon dit gebruik
om sekere spektrale-afbeeldingsresultate en spektrale-insluitingsresultate wat
vroe¨er in hierdie tesis verkry is, te herwin, en sommige kon selfs verbeter
word.
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Pricing and hedging asian options using Monte Carlo and integral transform techniquesChibawara, Trust 03 1900 (has links)
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: In this thesis, we discuss and apply the Monte Carlo and integral transform methods in
pricing options. These methods have proved to be very e ective in the valuation of options
especially when acceleration techniques are introduced. By rst pricing European call
options we have motivated the use of these methods in pricing arithmetic Asian options
which have proved to be di cult to price and hedge under the BlackScholes framework.
The arithmetic average of the prices in this framework, is a sum of correlated lognormal
distributions whose distribution does not admit a simple analytic expression. However,
many approaches have been reported in the academic literature for pricing these options.
We provide a hedging strategy by manipulating the results by Geman and Yor [42] for
continuous xed strike arithmetic Asian call options. We then derive a double Laplace
transform formula for pricing continuous Asian call options following the approach by Fu
et al. [39]. By applying the multi-Laguerre and iterated Talbot inversion techniques for
Laplace transforms to the resulting pricing formula we obtain the option prices. Finally,
we discuss the shortcomings of using the Laplace transform in pricing options. / AFRIKAANSE OPSOMMING: In hierdie tesis bespreek ons Monte Carlo- en integraaltransform metodes om die pryse van
nansi ele opsies te bepaal. Hierdie metodes is baie e ektief, veral wanneer versnellingsmetodes
ingevoer word. Ons bepaal eers die pryse van Europese opsies as motivering, voordat
ons die bostaande metodes gebruik vir prysbepaling van Asiatiese opsies met rekenkundige
gemiddeldes, wat baie moeiliker is om te hanteer in die BlackScholes raamwerk. Die
rekenkundige gemiddelde van batepryse in hierdie raamwerk is 'n som van gekorreleerde
lognormale distribusies wie se distribusie nie oor 'n eenvoudige analitiese vorm beskik nie.
Daar is egter talle benaderings vir die prysbepaling van hierdie opsies in die akademiese
literatuur. Ons bied 'n verskansingsstrategie vir Asiatiese opsies in kontinue tyd met 'n
vaste trefprys aan deur die resultate van Geman en Yor [42] te manipuleer. Daarna volg
ons Fu et al. [39] om 'n dubbele Laplace transform formule vir die pryse af te lei. Deur
toepassing van multi-Laguerre en herhaalde Talbotinversie tegnieke vir Laplace transforms
op hierdie formule, bepaal ons dan die opsiepryse. Ons sluit af met 'n bespreking van die
tekortkominge van die gebruik van die Laplace transform vir prysbepaling.
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Real-time stereo reconstruction using hierarchical dynamic programming and LULU filteringSingels, Francois 03 1900 (has links)
Thesis (MSc (Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: In this thesis we consider the essential topics relating to stereo-vision and the correspondence
problem in general. The aim is to reconstruct a dense 3D scene from
images captured by two spatially related cameras. Our main focus, however, is on
speed and real-time implementation on a standard desktop PC. We wish to use
the CPU to solve the correspondence problem and to reserve the GPU for model
rendering. We discuss three fundamental types of algorithms and evaluate their
suitability to this end. We eventually choose to implement a hierarchical version of
the dynamic programming algorithm, because of the good balance between accuracy
and speed. As we build our system from the ground up we gradually introduce
necessary concepts and established geometric principles, common to most stereovision
systems, and discuss them as they become relevant. It becomes clear that the
greatest weakness of the hierarchical dynamic programming algorithm is scanline
inconsistency. We nd that the one-dimensional LULU- lter is computationally inexpensive
and e ective at removing outliers when applied across the scanlines. We
take advantage of the hierarchical structure of our algorithm and sub-pixel re nement
to produce results at video rates (roughly 20 frames per second). A 3D model
is also constructed at video rates in an on-line system with only a small delay between
obtaining the input images and rendering the model. Not only is the quality
of our results highly competitive with those of other state of the art algorithms, but
the achievable speed is also considerably faster. / AFRIKAANSE OPSOMMING: In hierdie tesis beskou ons die noodsaaklike onderwerpe wat in die algemeen verband
hou met stereovisie en die ooreenstemmingsprobleem. Die mikpunt is om 'n digte
3D toneel te rekonstrueer vanaf beelde wat deur twee ruimtelik-verwante kameras
vasgelê is. Ons hoofdoel is egter spoed, en intydse implementering op 'n standaard
rekenaar. Ons wil die SVE (CPU) gebruik om die ooreenstemmingsprobleem op
te los, en reserveer die GVE (GPU) vir model-beraping. Ons bespreek drie fundamentele
tipes algoritmes en evalueer hul geskiktheid vir hierdie doel. Ons kies
uiteindelik om 'n hiërargiese weergawe van die dinamiese programmeringsalgoritme
te implementeer, as gevolg van die goeie balans tussen akkuraatheid en spoed. Soos
wat ons ons stelsel van die grond af opbou, stel ons geleidelik nodige konsepte voor
en vestig meetkundige beginsels, algemeen tot meeste stereovisie stelsels, en bespreek
dit soos dit toepaslik word. Dit word duidelik dat skandeerlyn-strydigheid die
grootste swakheid van die hiërargiese dinamiese programmeringsalgoritme is. Ons
vind dat die een-dimensionele LULU- lter goedkoop is in terme van berekeninge,
en e ektief aangewend kan word om uitskieters te verwyder as dit dwarsoor skandeerlyne
toegepas word. Ons buit die hiërargiese struktuur van ons algoritme uit en
kombineer dit met sub-piksel verfyning om resultate te produseer teen video tempo
(ongeveer 20 raampies per sekonde). 'n 3D model word ook gekonstrueer teen video
tempo in 'n stelsel wat aanlyn loop, met slegs 'n klein vertraging tussen die verkryging
van die intree-beelde en die beraping van die model. Die kwaliteit van ons
resultate is nie net hoogs mededingend met dié van die heel beste algoritmes nie,
maar die verkrygbare spoed is ook beduidend vinniger.
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Analysis of the effects of growth-fragmentation-coagulation in phytoplankton dynamicsOmari, Mohamed 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: An integro-differential equation describing the dynamical behaviour of phytoplankton
cells is considered in which the effects of cell division and aggregation
are incorporated by coupling the coagulation-fragmentation equation with
growth, and the McKendrick-von Foerster renewal model of an age-structured
population. Under appropriate conditions on the model parameters, the associated
initial-boundary value problem is shown to be well posed in a physically
relevant Banach space using the theory of strongly continuous semigroups of
operators, the theory of perturbation of positive semigroups and the semilinear
abstract Cauchy problems theory. In particular, we provide sufficient
conditions for honesty of the model. Finally, the results on the effects of the
growth-fragmentation-coagulation on the overall evolution of the phytoplankton
population are summarised. / AFRIKAANSE OPSOMMING: ’n Integro-differensiaalvergelyking wat die dinamiese ontwikkeling van fitoplanktonselle
beskryf, word beskou. Die uitwerking van seldeling en -aggregasie
is geïnkorporeer deur die vergelyking van koagulasie en fragmentasie met groeiaan
die McKendrick-von Foerster hernuwingsmodel van ’n ouderdomsgestruktureerde
populasie te koppel. Die teorie van sterk kontinue semigroepe van
operatore, steuringsteorie van positiewe semigroepe en die teorie van semilineêre
abstrakte Cauchy probleme word aangewend om, onder gepaste voorwaardes
met betrekking tot die model se parameters, te bewys dat die geassosieerde
beginwaarde-probleem met randvoorwaardes ‘goed gestel’ is in ’n fisies
relevante Banach-ruimte. In die besonder word voldoende voorwaardes vir eerlikheid
van die model verskaf. Ten slotte word ’n opsomming van die resultate
met betrekking tot die gekombineerde uitwerking van groei-fragmentasie- koagulasie
op die gesamentlike ontwikkeling van die fitoplanktonpopulasie verskaf.
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Modeling online social networks using Quasi-clique communitiesBotha, Leendert W. 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2011 / ENGLISH ABSTRACT: With billions of current internet users interacting through social networks, the need
has arisen to analyze the structure of these networks. Many authors have proposed
random graph models for social networks in an attempt to understand and reproduce
the dynamics that govern social network development.
This thesis proposes a random graph model that generates social networks using
a community-based approach, in which users’ affiliations to communities are explicitly
modeled and then translated into a social network. Our approach explicitly
models the tendency of communities to overlap, and also proposes a method for
determining the probability of two users being connected based on their levels of
commitment to the communities they both belong to. Previous community-based
models do not incorporate community overlap, and assume mutual members of
any community are automatically connected.
We provide a method for fitting our model to real-world social networks and demonstrate
the effectiveness of our approach in reproducing real-world social network
characteristics by investigating its fit on two data sets of current online social networks.
The results verify that our proposed model is promising: it is the first
community-based model that can accurately reproduce a variety of important social
network characteristics, namely average separation, clustering, degree distribution,
transitivity and network densification, simultaneously. / AFRIKAANSE OPSOMMING: Met biljoene huidige internet-gebruikers wat deesdae met behulp van aanlyn sosiale
netwerke kommunikeer, het die analise van hierdie netwerke in die navorsingsgemeenskap
toegeneem. Navorsers het al verskeie toevalsgrafiekmodelle vir sosiale
netwerke voorgestel in ’n poging om die dinamika van die ontwikkeling van dié
netwerke beter te verstaan en te dupliseer.
In hierdie tesis word ’n nuwe toevalsgrafiekmodel vir sosiale netwerke voorgestel
wat ’n gemeenskapsgebaseerde benadering volg, deurdat gebruikers se verbintenisse
aan gemeenskappe eksplisiet gemodelleer word, en dié gemeenskapsmodel
dan in ’n sosiale netwerk omskep word. Ons metode modelleer uitdruklik die
geneigdheid van gemeenskappe om te oorvleuel, en verskaf ’n metode waardeur
die waarskynlikheid van vriendskap tussen twee gebruikers bepaal kan word, op
grond van hulle toewyding aan hulle wedersydse gemeenskappe. Vorige modelle
inkorporeer nie gemeenskapsoorvleueling nie, en aanvaar ook dat alle lede van
dieselfde gemeenskap vriende sal wees.
Ons verskaf ’n metode om ons model se parameters te pas op sosiale netwerk
datastelle en vertoon die vermoë van ons model om eienskappe van sosiale netwerke
te dupliseer. Die resultate van ons model lyk belowend: dit is die eerste gemeenskapsgebaseerde
model wat gelyktydig ’n belangrike verskeidenheid van sosiale
netwerk eienskappe, naamlik gemiddelde skeidingsafstand, samedromming, graadverdeling,
transitiwiteit en netwerksverdigting, akkuraat kan weerspieël.
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Parallel likelihood calculations for phylogenetic treesHayward, Peter 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Phylogenetic analysis is the study of evolutionary relationships among organisms.
To this end, phylogenetic trees, or evolutionary trees, are used to
depict the evolutionary relationships between organisms as reconstructed from
DNA sequence data. The likelihood of a given tree is commonly calculated
for many purposes including inferring phylogenies, sampling from the space of
likely trees and inferring other parameters governing the evolutionary process.
This is done using Felsenstein’s algorithm, a widely implemented dynamic
programming approach that reduces the computational complexity from exponential
to linear in the number of taxa. However, with the advent of efficient
modern sequencing techniques the size of data sets are rapidly increasing beyond
current computational capability.
Parallel computing has been used successfully to address many similar
problems and is currently receiving attention in the realm of phylogenetic
analysis. Work has been done using data decomposition, where the likelihood
calculation is parallelised over DNA sequence sites. We propose an alternative
way of parallelising the likelihood calculation, which we call segmentation,
where the tree is broken down into subtrees and the likelihood of each subtree
is calculated concurrently over multiple processes. We introduce our proposed
system, which aims to drastically increase the size of trees that can be practically
used in phylogenetic analysis. Then, we evaluate the system on large
phylogenies which are constructed from both real and synthetic data, to show
that a larger decrease of run times are obtained when the system is used. / AFRIKAANSE OPSOMMING:Filogenetiese analise is die studie van evolusionêre verwantskappe tussen
organismes. Filogenetiese of evolusionêre bome word aangewend om die evolusionêre
verwantskappe, soos herwin vanuit DNS-kettings data, tussen organismes
uit te beeld. Die aanneemlikheid van ’n gegewe filogenie word oor die
algemeen bereken en aangewend vir menigte doeleindes, insluitende die afleiding
van filogenetiese bome, om te monster vanuit ’n versameling van sulke
moontlike bome en vir die afleiding van ander belangrike parameters in die evolusionêre
proses. Dit word vermag met behulp van Felsenstein se algoritme,
’n alombekende benaderingwyse wat gebruik maak van dinamiese programmering
om die berekeningskompleksiteit van eksponensieel na lineêr in die aantal
taxa, te herlei. Desnieteenstaande, het die koms van moderne, doeltreffender
orderingsmetodes groter datastelle tot gevolg wat vinnig besig is om bestaande
berekeningsvermoë te oorskry.
Parallelle berekeningsmetodes is reeds suksesvol toegepas om vele soortgelyke
probleme op te los, met groot belangstelling tans in die sfeer van filogenetiese
analise. Werk is al gedoen wat gebruik maak van data dekomposisie, waar
die aanneemlikheidsberekening oor die DNS basisse geparallelliseer word. Ons
stel ’n alternatiewe metode voor, wat ons segmentasie noem, om die aanneemlikheidsberekening
te parallelliseer, deur die filogenetiese boom op te breek in
sub-bome, en die aanneemlikheid van elke sub-boom gelyklopend te bereken
oor verskeie verwerkingseenhede. Ons stel ’n stelsel voor wat dit ten doel het
om ’n drastiese toename in die grootte van die bome wat gebruik kan word in
filogenetiese analise, teweeg te bring. Dan, word ons voorgestelde stelsel op
groot filogenetiese bome, wat vanaf werklike en sintetiese data gekonstrueer is,
evalueer. Dit toon aan dat ’n groter afname in looptyd verkry word wanneer
die stelsel in gebruik is.
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A visual programming environment for authoring ASD therapy toolsMsiska, Mwawi Fred 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: 3D virtual environments can be used as therapy tools in patients with autism spectrum
disorders (ASDs); however, the development of such tools is time-consuming.
A 3D virtual environment development platform for such tools has been developed
specifically for the South African context, because of the language and culture
sensitivity of these therapy tools.
The 3D virtual environment development platform has a Lua scripting interface
for specifying logic in the virtual environments. Lua is a textual programming
language, and presents a challenge to ASDs therapists’ ability to create therapy
tools without engaging an expert programmer.
The aim of this research was to investigate the design and implementation of a
visual programming environment to support non-expert programmers in scripting
within the 3D virtual environment development platform.
Various visual program representation techniques, reported in the literature, were
examined to determine their appropriateness for adoption in our design. A visual
programming language based on the “building-block” approach was considered the
most suitable. The research resulted in the development of a visual script editor
(VSE), based on an open source framework called the OpenBlocks library.
The VSE successfully alleviated the syntax burden that textual programming languages
place on non-expert programmers. The fitness of purpose of our VSE was
exemplified in a sample 3D virtual environment that was scripted using the VSE.
Despite the success, we argue that the applicability of the “building-block” approach
is limited to domain-specific programming languages due to the absence of
visual expressions for defining user-defined types, and for specifying hierarchy. / AFRIKAANSE OPSOMMING: Geen opsomming
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Probabilistic modelling of the evolution of ecological interaction networksMinoarivelo, Henintsoa Onivola 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: In any ecological system, organisms need to interact with each other for their survival. Such interactions form ecological networks which are usually very complex. Nevertheless, they
exhibit well de ned patterns; these regularities are often interpreted as products of meaningful
ecological processes. As the networks are evolving through time, biological evolution
is one of the factors that affects ecological network architecture. In this work, we develop a
mathematical model that represents the evolution through time of such ecological interaction
networks. The problem is approached by modelling network evolution as a continuous time
Markov process, in such a way that the interactions in which a parent species is involved
are potentially inherited by its descendant species. This approach allows us to infer ecological
parameters and ecological network histories from real-world network data, as well as
to simulate ecological networks under our model. While ecologists have long been aware of
the in uence of evolutionary processes in shaping ecological networks, we are now able to
evaluate the importance of such in uence. / AFRIKAANSE OPSOMMING: In enige ekologiese stelsel benodig organismes wisselwerkings met mekaar ten einde te oorleef.
Sulke interaksies vorm ekologiese netwerke wat gewoonlik baie kompleks is maar nogtans
goed-gede nieerde patrone vertoon. Hierdie patrone word dikwels geïnterpreteer as die produk
van betekenisvolle ekologiese prosesse. Aangesien die netwerke met die verloop van
tyd ontwikkel, is biologiese ewolusie een van die faktore wat ekologiese netwerkargitektuur
beïnvloed. In hierdie studie ontwikkel ons 'n wiskundige model wat die ewolusie van sulke
ekologiese interaksienetwerke voorstel. Die probleem word benader deur netwerkewolusie as
'n kontinue-tyd Markov-proses te modelleer, op so 'n manier dat die interaksies waarin 'n
voorouerspesie betrokke is potensieel oorerf kan word deur die afstammelingspesies. Hierdie
benadering laat ons toe om ekologiese parameters en ekologiese netwerkgeskiedenisse vanuit
regte-wêreld data af te lei, sowel as om ekologiese netwerke onder ons model te simuleer.
Alhoewel ekoloë al lank reeds bewus is van die invloed wat ewolusionêre prosesse het op die vorming van ekologiese netwerke, is ons nou in staat om die belangrikheid van hierdie
invloed te evalueer.
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Calculating the risk of infection of mycobacterium tuberculosis in endemic settingsJohnstone-Robertson, Simon Peter 03 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The annual risk of infection (ARI), a measure of recent transmission, has been described as the most
important parameter in tuberculosis (TB) epidemics. Nevertheless, mounting evidence suggests all
factors contributing to TB transmission are not yet completely understood. This research was
performed to investigate the role various parameters, e.g. overcrowding, period of infectivity,
ventilation, and infectivity of source cases, play in TB transmission. An established airborne
transmission risk model, the Wells-Riley equation (WRE), was modified to account for scenarios
where unknown numbers of infectious individuals may be present. Subsequently, the ARI for three
indoor locations conducive to TB transmission were calculated. Two locations (households and
minibus taxis) were identified in a social mixing survey conducted within a South African
community where TB is endemic as a part of this research. The third location (prison) was
identified in an earlier independent study in the same community. The impact various interventions
could have in reducing the ARI associated with each location was explored. Poor ventilation, severe
overcrowding, extended exposure periods, and high incidence rates contributed to high TB
transmission risks in each location. The household-associated ARI was related to the number of
resident adults. Current TB control programs will only reduce the ARI if household ventilation
levels are improved simultaneously. Similar reductions in the ARI could be achieved by trebling
current ventilation levels or by separating child and adult sleeping areas. Neighbouring households
can also contribute substantially to the ARI. The minibus taxi-associated ARI for drivers and
commuters was considerable but readily reduced by opening windows or keeping the fresh-air fan
on. Reducing TB case prevalence through active or passive case-finding would reduce the ARI
substantially. The prison-associated ARI was proportional to levels of overcrowding. No single
intervention, such as improved ventilation, decreased lock-up time, or improved case-finding,
would decrease the ARI substantially, but concurrent implementation of all of them to meet national
or international standards would. This research shows TB is not only transmitted in epidemics by
highly infectious TB cases, but that any TB case, no matter how infectious, has the potential to
infect susceptible people under the right conditions. / AFRIKAANSE OPSOMMING:Die jaarlikse infeksierisiko (ARI) – maatstaf van onlangse siekteoordrag – word as die
belangrikste parameter in tuberkulose- (TB-)epidemies bestempel. Nietemin dui toenemende
bewyse daarop dat nie álle faktore wat tot TB-oordrag bydra, volledig verstaan word nie. Hierdie
navorsing is onderneem om ondersoek in te stel na die rol van verskillende parameters –
byvoorbeeld oorbevolking, tydperk van aansteeklikheid, ventilasie en die aansteeklikheid van
brongevalle – in TB-verspreiding. Gevestigde model vir die raming van siekteverspreiding deur
die lug, die Wells-Riley-vergelyking (WRE), is aangepas vir scenario’s waar onbekende aantal
aansteeklike individue moontlik aanwesig is. Daarna is die ARI bereken vir drie ingeslote ruimtes
wat TB-oordrag bevorder. Twee van die ruimtes (huishoudings en minibustaxi’s) is ten tyde van die
navorsing uitgewys in sosialevermengingsopname in Suid-Afrikaanse gemeenskap waar TB
endemies is. Die derde ruimte (gevangenisse) is uitgewys in vroeëre onafhanklike studie in
dieselfde gemeenskap. Die navorser het gevolglik bepaal watter moontlike impak verskillende
intervensies op die verlaging van die ARI in elke ruimte het. Swak ventilasie, ernstige
oorbevolking, verlengde blootstellingstydperke en hoë voorkomsyfers het in elke ruimte tot hoë
TB-oordragrisiko bygedra. Die huishoudingsverwante ARI het verband gehou met die aantal
volwassenes wat in die huis woon. Huidige TB-beheerprogramme sal slegs die ARI kan verlaag
indien huishoudelike ventilasievlakke terselfdertyd verbeter word. Drie keer beter ventilasievlakke
of die skeiding van kinders en volwassenes se slaapareas kan soortgelyke verlagings in die ARI
teweegbring. Buurhuishoudings kan ook aansienlik tot die ARI bydra. Die minibustaxi-verwante
ARI vir bestuurders en pendelaars was beduidend, maar kan betreklik maklik verlaag word deur
vensters oop te maak of die varslugwaaier aan te hou. Die vermindering van die voorkoms van TBgevalle
deur aktiewe óf passiewe gevalle-opsporing kan die ARI ook beduidend verlaag. Die
gevangenisverwante ARI het met vlakke van oorbevolking verband gehou. Geen enkele intervensie
soos beter ventilasie, korter toesluittye of beter gevalle-opsporing sal die ARI aansienlik verlaag
nie, maar die gelyktydige inwerkingstelling van ál hierdie intervensies in pas met nasionale of
internasionale standaarde kan wél. Hierdie navorsing toon dat TB in epidemies nie net deur hoogs
aansteeklike TB-gevalle oorgedra word nie, maar dat enige TB-geval, ongeag hoe aansteeklik, die
siekte in die regte omstandighede na vatbare mense kan oordra.
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