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In todays Radiotherapy Treatment Planning, RTP, it is common to use Computed Tomography, CT, together with Magnetic Resonance Imaging, MRI, where CT provides electron density information and a geometrical reference, and where MRI provides superior soft tissue contrast. To sim- plify the workflow and improve treatment accuracy, research groups have demonstrated how to exclude CT and use a MRI-only approach. In this thesis, a method for spatial distortion analysis, ultimately enabling quality assurance, QA, of the spatial accuracy of MRI, was defined, tested and evaluated. A phantom was built to cover the entire clinical Field Of View, FOV, and 6mm-diameter fluid filled paintball markers were placed in a well-defined geometrical pattern within the phantom, and used as positive contrast. The phantom was imaged with a 3D Fast Gradient Echo sequence and a 3D Fast Spin Echo sequence. The markers were identified in the image data by a MATLAB-algorithm, and the location of the center of mass was calculated for each marker and compared to a theoretical reference. The location error was defined as the spatial distortion - a measurement of the spatial accuracy. Imaging parameters were altered and the effect on the spatial accuracy was analyzed. The spatial distortions were successfully measured within the entire (maximal) clinical FOV. It was shown that high readout bandwidth reduced distortions in the frequency encoding direction. These distortions could thus be attributed to B0-inhomogeneities. It was also determined that increasing the readout bandwidth to the maximum value reduced the maximum distortions in the frequency encoding direction to the same level as the maximum distortions in the other two phase-encoding directions of the 3D acquisitions. The voxel size had a very small effect on the spatial accuracy, enabling large voxelsize to be used when imaging the phantom, to decrease the scan time. The method was deemed capable of serving as a basis for QA of the spatial accuracy of large FOV MRI, which is needed in future MRI-only RTP approaches.

La dengue est actuellement un problème de santé publique majeur en Colombie avec un fardeau sanitaire et économique important. Les facteurs environnementaux sont connus pour influencer le risque de dengue ; cependant, la forme, l'ampleur et le moment de ces relations ne sont pas clairement établis. L'ampleur et le moment des épidémies de dengue varient selon le lieu. Cette thèse a examiné les composantes temporelles des séries chronologiques hebdomadaires de cas de dengue dans les municipalités de Villavicencio, Castilla la Nueva et Puerto Lopez en Colombie de 2014 à 2019. Il a procédé à l'estimation de la forme et de l'ampleur des associations entre les cas hebdomadaires de dengue et cinq facteurs météorologiques, mesurés chaque semaine, pour chacune des municipalités à l'aide du cadre des modèles non linéaires à décalage distribué avec une distribution binomiale négative. Il a finalement comparé les associations dans les trois municipalités (urbaines, périurbaines et rurales) pour observer si les associations trouvées étaient cohérentes entre les municipalités. Les résultats ont montré que Castilla la Nueva (périurbain) avait la fréquence d'épidémies la plus élevée, avec quatre pics distincts, tandis que Puerto Lopez (rural) en avait le moins. L'ampleur du nombre d'infections était la plus élevée à Villavicencio (urbain), probablement parce qu'elle était la plus peuplée des trois. Les trois municipalités avaient toutes deux une tendance qui dépendait des pics et des creux des flambées de dengue et toutes avaient une composante saisonnière distincte. L'association avec la température, les précipitations, l'humidité relative, la vitesse du vent et la pression de surface à travers les décalages n'était pas linéaire. La non-linéarité a été présentée par un comportement en forme de dôme simple à multiple, dépendant de la municipalité. L'ampleur du risque relatif associé à chaque facteur environnemental dépendait également de la municipalité. Cette thèse propose la création d'un tableau de bord de prévisions utilisant des modèles non linéaires à décalage distribué pour chaque commune comme outil d’aide aux politiques et programmes de lutte contre la dengue. / Dengue is presently a major public health issue in Colombia with significant health and economic burden. Environmental factors are known to influence dengue risk; however the shape, strength and timing of these relationships are not clearly established. The scale and timing of dengue outbreaks vary according to location. This thesis examined the temporal components of weekly dengue cases time series in Villavicencio, Castilla la Nueva and Puerto Lopez municipalities of Colombia from 2014 to 2019. It proceeded to estimate the shape and magnitude of the associations between weekly dengue cases and five meteorological factors, measured weekly, for each of the municipalities using the Distributed lag non-linear models framework with negative binomial distribution. It finally compared the associations across the three municipalities (urban, peri urban, and rural) to observe whether the associations found were consistent across municipalities. The results showed that Castilla la Nueva (peri-urban) had the highest frequency of epidemics, with four distinct peaks, while Puerto Lopez (rural) had the fewest. The magnitude of the number of infections was greatest in Villavicencio (urban), likely as a result of it being the most populated among the three. All three municipalities both had a trend which was dependent on the peaks and troughs of dengue outbreaks and all had a distinct seasonal component. The association with temperature, precipitation, relative humidity, wind speed and surface pressure across lags were non-linear. The non-linearity was exhibited by single to multiple dome-shaped behaviour dependent on the municipality. The magnitude of the relative risk associated with each environmental factor was also dependent on the municipality. This thesis suggest the creation of a dashboard of forecasts of distributed lag non-linear models for each municipality as a policy and program aid, in the fight against dengue.

Current-to-pressure (I/P) converters are pneumatic devices which provide precise control of pressure in various industries – for example these devices are often used in valve positioner systems (typically found in the oil and gas industry) and tensioning systems (typically used in the packaging industry). With an increasing demand for such devices to operate in harsh environments all by delivering acceptable performance means that Current-to-pressure converters need to be carefully designed such that environmental factors have no or minimal effects on its performance. This work presents an investigation of the principles of operation of an existing I/P converter through mathematical modelling. A simulation model has been created and which allows prediction of performance of the I/P converter. This tool has been used to identify areas of poor performances through theoretical analysis and consequently led to optimisation of certain areas of the I/P converter through a design change to deliver improved performances, for instance the average percentage shift in gain at 1mA input signal (over the temperature range of -40°C to 85°C) on the new I/P converter is 2.13% compared to the average gain of 4.24% on the existing I/P converter, which represents an improvement of almost two fold. Experimental tests on prototypes have been carried out and tests results showed that improved linearity and temperature sensitivity can be expected from the new design.

Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / Using the ARFIMA (autoregressive and fractionally integrated moving aver age) model extended with sGARCH (standard generalised autoregressive con ditional heteroscedasticity) and ’gjrGARCH (Glosten-Jagannathan-Runkle gen eralised autoregressive conditional heteroscedascity) innovations, fractional in tegration approach and state space model, this study has empirically examined persistency of inflation dynamics of Ghana and South Africa, the only two coun tries in Sub-Saharan Africa with Inflation Targeting (IT) monetary policy. The first part of the analysis employed monthly CPI (Consumer Price Index) in flation series for the period January 1971 to October 2014 obtained from the Bank of Ghana (BoG), and for the period January 1995 to December 2014 ob tained from Statistics South Africa. The second part involves the estimation of threshold effect of inflation on economic growth using annual data obtained from the IMF (International Monetary Fund) database for the period 1981 to 2014, for both countries. Results from the study showed that structural breaks, long memory and non linearities (or regime shifts) are largely responsible for inflation persistence, hence the ever-changing nature of inflation rates of Ghana and South Africa. ARFIMA(3,0.35,1)-‘gjrGARCH(1,1) under Generalised Error Distribution (GED) and ARFIMA(3,0.50,1)-‘gjrGARCH(1,1) under Student-t Distribution (STD) mod els provided the best fit for persistence in the conditional mean (or level) of CPI for Ghana and South Africa, respectively. The results from these models pro vided evidence of time-varying conditional mean and volatility in CPI inflation rates of both countries. The two models also revealed an asymmetric effect of inflationary shocks, where negative shocks appear to have greater impact than positive shocks, in terms of persistence on the conditional mean with time varying volatility. This thesis proposes a model that combines fractional integration with non linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa. We tested for non-linear deterministic terms in the context of fractional integration and esti mated the fractional differencing parameters, d to be 1.11 and 1.32 respectively, for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. New ev idence from this thesis depicts that inflation rate of Ghana is highly persistent and non-mean reverting, with an estimated fractional differencing parameter, d > 1.0, and will therefore require some policy action to steer inflation back to stability. However, the South African inflation series was found to be a cyclical process with an order of integration estimated to be d = 0.7, depicting mean reversion, with the length of the cycles approximated to last for 80 months. Finally, the thesis incorporated structural breaks, long memory, non-linearity, and some explanatory variables into a state space model and estimated the threshold effect of inflation on economic growth. The empirical results suggest that inflation below the estimated levels of 9% and 6% for Ghana and South Africa respectively, will be conducive for economic growth. The policy implications of these results for both countries are as follows. First, both series had similar properties responsible for inducing inflation persistence such as structural breaks, non-linearities, long memory and asymmetric re sponse to negatives shocks - but with varied degrees of magnitude. For both countries, the conditional mean and unobserved components such as volatility for both countries were found to be time-varying. This thesis, therefore, recom mends to the BoG and the South African Reserve Bank (SARB) - responsible for monetary policies, and the Finance Ministers of both governments - respon sible for fiscal policies, to take the above-mentioned properties into account in the formulation of their monetary policies. Second, the thesis recommends that the BoG and the SARB consolidate the IT policy, since keeping inflation below the targets set of 9% and 6%, respectively for Ghana and South Africa, will boost economic growth. Third, policymakers could also design measures (monetary and fiscal policies) such as increase in interest rates, credit control, and reduction of unnecessary expenditure, among others, to control inflation due to its adverse effects on market volatility. Even though an increase in interest rates could assist in curtailing the recent and anticipated increase in inflation rates in both countries, where targets have been missed by Ghana and South Africa, it will also be prudent to legislate monetary policies around demand-supply side since the problem of both coun tries appears to be more of a structuralist than a monetarist. It is, therefore, recommended that both countries tighten the IT monetary policy in order to re duce inflation persistence. This will eventually impact on poverty and income distribution with ramifications for economic growth and/or development. The fourth implication of these results is that governments and central banks should be mindful of the actions and decisions they take, in the sense that unguarded decisions and unnecessary alarms could raise uncertainties in the economy, which could, in turn, affect the future trajectory of inflation. Finally, the thesis recommends that governments of both countries strengthen the pri vate sector, which is the engine of growth. For small and open economies such as Ghana and South Africa, this will grow the economy through job creation and restore investor confidence. / National Research Foundation (NRF), Department of Science and Technology (DST), Telkom’s Tertiary Education Support Programme (TESP) and the NRF-DST Centre of Excellence for Mathematical and Statistical Sciences (CoE-MaSS)

This research work has made an effort to understand a novel line of radio frequency power amplifiers (RFPAs) that address initiatives for efficiency enhancement and linearity compensation to harmonize the fifth generation (5G) campaign. The objective is to enhance the performance of an orthogonal frequency division multiplexing-long term evolution (OFDM-LTE) transmitter by reducing the nonlinear distortion of the RFPA. The first part of this work explores the design and implementation of 15.5 W class AB RF power amplifier, adopting a balanced technique to stimulate efficiency enhancement and redeeming exhibition of excessive power in the transmitter. Consequently, this work goes beyond improving efficiency over a linear RF power amplifier design; in which a comprehensive investigation on the fundamental and harmonic components of class F RF power amplifier using a load-pull approach to realise an optimum load impedance and the matching network is presented. The frequency bandwidth for both amplifiers was allocated to operate in the 2.620-2.690 GHz of mobile LTE applications. The second part explores the development of the behavioural model for the class AB power amplifier. A particular novel, Hammerstein-Wiener based model is proposed to describe the dynamic nonlinear behaviour of the power amplifier. The RF power amplifier nonlinear distortion is approximated using a new linear parameter approximation approach. The first and second-order Hammerstein-Wiener using the Normalised Least Mean Square Error (NLMSE) algorithm is used with the aim of easing the complexity of filtering process during linear memory cancellation. Moreover, an enhanced adaptive Wiener model is proposed to explore the nonlinear memory effect in the system. The proposed approach is able to balance between convergence speed and high-level accuracy when compared with behavioural modelling algorithms that are more complex in computation. Finally, the adaptive predistorter technique is implemented and verified in the OFDM transceiver test-bed. The results were compared against the computed one from MATLAB simulation for OFDM and 5G modulation transmitters. The results have confirmed the reliability of the model and the effectiveness of the proposed predistorter. / Fundacão para a Ciência e a Tecnologia, Portugal, under European Union’s Horizon 2020 research and innovation programme ... grant agreement H2020-MSCA-ITN- 2016 SECRET-722424 I also acknowledge the role of the National Space Research and Development Agency (NASRDA) Sokoto State Government Petroleum Technology Trust Fund (PTDF)

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