The use of mathematical models in studying disease epidemics can be diverse, from the focused study of the role of a single determinant of the epidemic, or to the overall estimation of morbidity and mortality. In using simple deterministic models, a balance is struck between biological and social complexities, and the high data input demands of mathematical models. This thesis aims to apply the use of deterministic mathematical models to the studies of HIV and hepatitis C epidemiology in the Asia-Pacific region. In Australia, about 85% of reported HIV cases are among homosexual men. Casual homosexual partnerships made up 40% of incident HIV cases in 1995 increasing to 65% in 2004. In the state of New South Wales, it was estimated that over 7,500 people were living with HIV/AIDS in 2005, increasing to over 10,000 by 2016 with existing levels of intervention. Intervention measures were estimated to have prevented some 44,500 cases, the majority being among injecting drug users through the Needle and Syringe Programmes. Models for the HIV epidemics in developing countries were also developed incorporating multiple routes of HIV transmission. For Papua New Guinea, it was estimated 64,000 people were living with HIV/AIDS in 2005, rising to over 500,000 by 2025 with current levels of intervention. High levels of interventions, in particular increased condom use, will be required to achieve a stabilisation or reduction in HIV prevalence. In East Timor, the HIV epidemic is still in the early stages with 138 people estimated to be living with HIV/AIDS, rising to 5,000 by 2025 with minimal intervention. For HCV, models of the epidemic in Australia showed HCV incidence peaking in 1999, followed by a decline reaching 9,700 incident cases in 2005. Of 197,000 estimated chronic HCV cases in 2005, 58% had stage F 0/1 liver disease, 15% F 2/3 liver disease, and 2% HCV-related cirrhosis. Models estimated 210 and 105 people developed HCV-related liver failure and hepatocellular carcinoma, respectively. Comparisons of modelled HCV long-term sequelae projections with linkage data showed relatively good agreement, despite discrepancies in liver-related deaths. To decrease the number of chronic HCV, at least a tripling of treatment coverage would be required. These models provide estimates of the current levels of epidemics as well as projections of future scenarios under different intervention strategies, which have an important role in the planning of strategies, as well as assessment of previous epidemic conditions.

<p>The study explored the comparison of grade 8 to 10 urban and peri-urban learners&rsquo / contexts preferences in mathematical literacy. There is currently a strong emphasis on the use of contexts for school mathematics. This has been also the case for South Africa when grade 10 learners have to make a choice between mathematics and mathematical literacy as one of their compulsory subjects for grade 10. This study focused more on the use of mathematics in real life situations. Data was collected by using questionnaires developed as part of the Relevance of School Mathematics Education (ROSME) project. The questionnaire dealt with contexts preferred by grade 10 learners from urban and peri-urban areas. The data were analysed using non-parametric statistical techniques. The findings radicate that there were contexts highly preferred by learners from both urban and peri-urban areas / least preferred by learners from both areas, highly preferred by learners from periurban areas but not by learners from urban areas and least preferred by learners from urban areas but not by those from peri-urban areas and vice versa. It is recommended that contexts highly preferred by learners should be incorporated in the learning experiences of learners.</p>

No description available.

This thesis consists of a mathematical model, autopilot and guidance design of a mini ROV (Remotely Operated Underwater Vehicle) and investigates the effects of environmental forces (ocean currents etc.) on the guidance algorithms. First of all, a non-linear 6 degrees-of-freedom (DOF) mathematical model is obtained. This model includes hydrodynamics forces and moments. There is no exact calculation method for hydrodynamic coefficients / however strip theory and results of computational fluid dynamics (CFD) analysis are used to calculate their approximate values. Linear mathematical model is obtained by linearization at trim points and it is used when designing surge speed, heading and depth controller. Guidance is examined by two methods such as way point guidance by line-of-sight (LOS) and way point guidance based on optimal control. Moreover, an online obstacle avoidance algorithm is developed. This thesis ends with the subject of navigation of the vehicle under GPS-like measurements and magnetic sensors measurements.

I Australien är vattenresurserna begränsade. För lantbrukare är tillgängligheten på vatten mycket viktig. På grund av det torra klimatet kan inte de Australiensiska bönderna förlita sig på nederbörden. Bevattningssystemen är därför en viktig del i jordbrukningsindustrin. Bevattningsområdet i Coleambally ligger i södra New South Wales nära gränsen till staten Victoria. Bevattningsnätet i Coleambally förser ofta bevattningskanalerna med för mycket vatten för att vara säker på att lantbrukarna får den mängd vatten de behöver. På grund av denna tillförsel av överskottvatten går stor mängd av vatten förlorad. Design av ett bättre reglersystem skulle kunna minska den stora förlusten av vatten. En matematisk modell beskrivande dynamiken av bevattningssystemet är ett bra redskap vid en design av ett bättre reglersystem. Syftet med det här projektet var att genom systemidentifiering bygga en matematisk modell av bevattningssystemet. Modellen syftade till att beskriva vattennivån i en sträcka av bevattningskanalerna, sträckan i kanalen skulle ha två olika typer av luckor, en typ där vattnet strömmar över luckan och en annan typ där vattnet strömmar under luckan. En modell byggdes genom att parametrar från en vald modellstruktur estimerades från experimentella data. Data samlades under ett experiment som utfördes på en bevattningskanal i Coleambally. Resultatet från systemidentifieringen blev en första ordningens output error grey box modell. Modellen visar goda resultat vid validering och bör kunna användas vid design av ett bättre reglersystem. Modellen visar så god överensstämmelse med valideringsdata att den även kan användas för olika fall av simulering. / Water resources in Australia are limited. For a farmer the access to water is crucial and due to the dry climate the farmers in Australia can not rely on precipitation. Irrigation is therefore a very important part of the farming industry. The Coleambally Irrigation Area is situated in the southern parts of New South Wales close to the border of Victoria. The Irrigation Network often supplies the irrigation channels with too much water to be sure that the demand of water is satisfied. Due to this over supply a great amount of water gets wasted. Design of a bettercontrol system would be able to reduce the water wastage. A mathematical model describing the dynamics of the irrigation system can be used as a tool for the control system design. The aim of this project was to build a mathematical model with the system identification approach. The model should be able to describe the downstream water level of a single pool of an irrigation channel which has both undershot and overshot gates. A model was built by estimating unknown parameters of a chosen model structure from a set of experimental data. The data was collected from an experiment performed on the real irrigation system in Coleambally. The result of the system identification was a first order output error grey box model. The model performs well on validation data and may therefore be used for design of a more efficient control system. The model gave such good results that it additionally may be used for various simulation purposes.

The interest for cell-to-cell variation has in recent years increased in a steady pace. Several studies have shown that a large portion of the observed variation in the nature originates from the fact that all biochemical reactions are in some respect stochastic. Interestingly, nature has evolved highly advanced frameworks specialized in dealing with stochasticity in order to still be able to produce the delicate signalling pathways that are present in even very simple single-cell organisms. Such a simple organism is Saccharomyces cerevisiae, which is the organism that has been studied in this thesis. More particulary, the distribution of the transport rate in S. cerevisiae has been studied by a mathematical modelling approach. It is shown that a two-compartment model can adequately describe the flow of a yellow fluorescent protein (YFP) between the cytosol and the nucleus. A profile likelihood (PLH) analysis shows that the parameters in the two-compartment model are identifiable and well-defined under the experimental data of YFP. Furthermore, the result from this model shows that the distribution of the transport rates in the 80 studied cells is lognormal. Also, in contradiction to prior beliefs, no significant difference between recently divided mother and daughter cells in terms of transport rates of YFP is to be seen. The modelling is performed by using both standard two-stage(STS) and nonlinear mixed effect model (NONMEM). A methodological comparison between the two very different mathematical STS and NONMEM is also presented. STS is today the conventional approach in studies of cell-to-cell variation. However, in this thesis it is shown that NONMEM, which has originally been developed for population pharmacokinetic/ pharmacodynamic (PK/PD) studies, is at least as good, or in some cases even a better approach than STS in studies of cell-to-cell variation. Finally, a new approach in studies of cell-to-cell variation is suggested that involves a combination of STS, NONMEM and PLH. In particular, it is shown that this combination of different methods would be especially useful if the data is sparse. By applying this combination of methods, the uncertainty in the estimation of the variability could be greatly reduced.

No description available.

<p>The basal ganglia form an important structure centrally placed in the brain. They receive input from motor, associative and limbic areas, and produce output mainly to the thalamus and the brain stem. The basal ganglia have been implied in cognitive and motor functions. One way to understand the basal ganglia is to take a look at the diseases that affect them. Both Parkinson's disease and Huntington's disease with their motor problems are results of malfunctioning basal ganglia. There are also indications that these diseases affect cognitive functions. Drug addiction is another example that involves this structure, which is also important for motivation and selection of behaviour.</p><p>In this licentiate thesis I am laying the groundwork for a detailed model of the striatum, which is the input stage of the basal ganglia. The striatum receives glutamatergic input from the cortex and thalamus, as well as dopaminergic input from substantia nigra. The majority of the neurons in the striatum are medium spiny (MS) projection neurons that project mainly to globus pallidus but also to other neurons in the striatum and to both dopamine producing and GABAergic neurons in substantia nigra. In addition to the MS neurons there are fast spiking (FS) interneurons that are in a position to regulate the firing of the MS neurons. These FS neurons are few, but connected into large networks through electrical synapses that could synchronise their effect. By forming strong inhibitory synapses on the MS neurons the FS neurons have a powerful influence on the striatal output. The inhibitory output of the basal ganglia on the thalamus is believed to keep prepared motor commands on hold, but once one of them is disinhibited, then the selected motor command is executed. This disinhibition is initiated in the striatum by the MS neurons.</p><p>Both MS and FS neurons are active during so called up-states, which are periods of elevated cortical input to striatum. Here I have studied the FS neurons and their ability to detect such up-states. This is important because FS neurons can delay spikes in MS neurons and the time between up-state onset and the first spike in the MS neurons is correlated with the amount of calcium entering the MS neuron, which in turn might have implications for plasticity and learning of new behaviours. The effect of different combinations of electrical couplings between two FS neurons has been tested, where the location, number and strength of these gap junctions have been varied. I studied both the ability of the FS neurons to fire action potentials during the up-state, and the synchronisation between neighbouring FS neurons due to electrical coupling. I found that both proximal and distal gap junctions synchronised the firing, but the distal gap junctions did not have the same temporal precision. The ability of the FS neurons to detect an up-state was affected by whether the neighbouring FS neuron also received up-state input or not. This effect was more pronounced for distal gap junctions than proximal ones, due to a stronger shunting effect of distal gap junctions when the dendrites were synaptically activated.</p><p>We have also performed initial stochastic simulations of the Ca²⁺-calmodulin-dependent protein kinase II (CaMKII). The purpose here is to build the knowledge as well as the tools necessary for biochemical simulations of intracellular processes that are important for plasticity in the MS neurons. The simulated biochemical pathways will then be integrated into an existing model of a full MS neuron. Another venue to explore is to build striatal network models consisting of MS and FS neurons and using experimental data of the striatal microcircuitry. With these different approaches we will improve our understanding of striatal information processing.</p>

<p>The olfactory system is believed to be the oldest sensory system. It developed to detect and analyse chemical information in the form of odours, and its organisation follows the same principles in almost all living animals - insects as well as mammals. Likely, the similarities are due to parallel evolution - the same type of organisation has arisen more than once. Therefore, the olfactory system is often assumed to be close to optimally designed for its tasks. Paradoxically, the workings of the olfactory system are not yet well known, although several milestone discoveries have been made during the last decades. The most well-known is probably the disovery of the olfactory receptor gene family, announced in 1991 by Linda Buck and Richard Axel. For this and subsequent work, they were awarded a Nobel Prize Award in 2004. This achievement has been of immense value for both experimentalists and theorists, and forms the basis of the current understanding of olfaction. The olfactory system has long been a focus for scientific interest, both experimental and theoretical. Ever since the field of computational neuroscience was founded, the functions of the olfactory system have been investigated through computational modelling. In this thesis, I present the basis of a biologically realistic model of the olfactory system. Our goal is to be able to represent the whole olfactory system. We are not there yet, but we have some of the necessary building blocks; a model of the input from the olfactory receptor neuron population and a model of the olfactory bulb. Taking into account the reported variability of geometrical, electrical and receptor-dependent neuronal characteristics, we have been able to model the frequency response of a population of olfactory receptor neurons. By constructing several olfactory bulb models of different size, we have shown that the size of the bulb network has an impact on its ability to process noisy information. We have also, through biochemical modelling, investigated the behaviour of the enzyme CaMKII which is known to be critical for early olfactory adaptation (suppression of constant odour stimuli).</p> / <p>Luktsystemet anses allmänt vara det äldsta sensoriska systemet. Det utvecklades för att upptäcka och analysera kemisk information i form av lukter, och det är organiserat efter samma principer hos nästan alla djurarter: insekter så väl som däggdjur. Troligen beror likheterna på parallell evolution -- samma organisation har uppstått mer än en gång. Därför antas det ofta att luktsystemet är nära optimalt anpassat för sina arbetsuppgifter. Paradoxalt nog är luktsystemets arbetssätt ännu inte väl känt, även om flera banbrytande framsteg gjorts de senaste decennierna. Det mest välkända är nog upptäckten av genfamiljen av luktreceptorer, som tillkännagavs 1991 av Linda Buck och Rikard Axel. För detta och efterföljande arbete belönades de med Nobelpriset år 2004. Upptäckten har varit mycket värdefull för både experimentalister och teoretiker, och formar grunden för vår nuvarande förståelse av luktsystemet. Luktsystemet har länge varit ett fokus för vetenskapligt intresse, både experimentellt och teoretiskt. Ända sedan fältet beräkningsbiologi grundades har luktsystemet undersökts genom datormodellering. I denna avhandling presenterar jag grunden för en biologiskt realistisk modell av luktsystemet. Vårt mål är att kunna representera hela luktsystemet. Så långt har vi ännu inte nått, men vi har några av de nödvändiga byggstenarna: en modell av signalerna från populationen av luktreceptorceller, och en modell av luktbulben. Genom att ta hänsyn till nervcellernas rapporterade variationer i geometriska, elektriska och receptor-beroende karaktärsdrag har vi lyckats modellera svarsfrekvenserna från en population av luktreceptorceller. Genom att konstruera flera olika stora modeller av luktbulben har vi visat att storleken på luktbulbens cellnätverk påverkar dess förmåga att behandla brusig information. Vi har också, genom biokemisk modellering, undersökt beteendet hos enzymet CaMKII, som är kritiskt viktigt för adaptering (undertryckning av ständigt närvarande luktstimuli) i luktsystemet.</p>

The embryonic stem cell (ESC) microenvironment contains various localized physical and biochemical cues to direct cell fate. Current approaches for microenvironmental regulation rely on restricting cell behaviour to control endogenous signals such as secreted ligands. This report presents a microfluidic device that can directly manipulate the removal of autoregulatory ligands from culture and control the activation of Signal Transducer and Activator of Transcription-3 (Stat3) in ESCs. Specifically, the response of Stat3 was measured under diffusive and convective mass transfer regimes. A Brownian dynamics algorithm was also developed to simulate ligand transport and predict cellular response under these conditions. Stat3 activation under perfusion culture was found to depend on flow rate and axial distance in the flow direction. Long-term perfusion also allowed for the formation of a sustained gradient of Stat3 activation that led to selective loss of ESC pluripotency. These results demonstrate the utility of microfluidic culture for stem cell bioengineering applications.