High dimensional, low sample, data have singular sample covariance matrices,rendering them impossible to analyse by regular canonical correlation (CC). Byusing random subspace method (RSM) calculation of canonical correlation be-comes possible, and a Monte Carlo analysis shows resulting maximal CC canreliably distinguish between data with true correlation (above 0.5) and with-out. Statistics gathered from RSMCCA can be used to model true populationcorrelation by beta regression, given certain characteristic of data set. RSM-CCA applied on real biological data however show that the method can besensitive to deviation from normality and high degrees of multi-collinearity.

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Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The investigation of reservoir sedimentation has become an important and valuable research topic in engineering practice. Sediment deposition in reservoirs can affect ood levels, drainage for agriculture land, pumpstation and hydropower operation and navigation. An extensive review of the technical literature pertaining to suspended sediment transports as well as deposited sediment ushing from reservoirs has shown that most studies on sediment are still based on empirical formulas and experimental work, despite the availability of sophisticated computers. This is because sediment transport and particularly sediment deposition and erosion are complex processes, that involve the interaction of many physical factors which are not easily modelled numerically. In addition, most of the existing three-dimensional numerical models are not coupled hydrodynamic and sediment transport models. They first simulate the velocity field and water depth and then the concentration and bed change are calculated. Furthermore, they are not fully three-dimensional models for using layer-averaged approaches in conjunction with Saint-Venant equations. The key objective of the present research was to develop a coupled fully three-dimensional (3D) numerical model based on Navier-Stokes equations which includes both the sediment transport component and hydrodynamic parameters. In this regard, a physical model was set up in a laboratory ume in order to investigate the bottom outlet sediment ushing under pressure in a controlled environment. The proposed coupled fully 3D numerical model was used to simulate the experimental tests. Results from these simulations were in good agreement with the measurements. The geometric features of the scour hole (temporal and spatial hole development) upstream of the bottom outlet were reasonably well predicted compared to the experimental data. Furthermore, the velocity field upstream of the bottom outlet was in good agreement with measurements. The proposed numerical model can be considered reliable provided that the model is correctly set up to reflect the condition of a particular case study. Finally, the coupled fully 3D numerical model for turbulent suspended sediment transport in reservoirs was validated against a range of typical reservoir sediment transport and deposition laboratory flume cases. The proposed suspended sediment transport model successfully predicted both sediment deposition and entrainment processes and therefore, it can be used for turbulent suspended sediment transport assessments in reservoirs. / AFRIKAANSE OPSOMMING: Die ondersoek van damtoeslikking het 'n belangrike navorsing onderwerp in ingenieurswese praktyk geword. Sedimentdeponering in damme kan vloed vlakke, dreinering van landbo grond sowel as pompstasie en hidrokrag werking en navigasie benvloed. 'n Omvattende ontleding van die tegniese literatuur met betrekking tot gesuspendeerde sedimentvervoer asook die spoel van gedeponeerde sediment uit reservoirs het getoon dat die meeste studies oor sediment steeds op empiriese formules en eksperimentele werk gebaseer is, ten spyte van die beskikbaarheid van gesofistikeerde rekenaars. Dit is omdat sedimentvervoer en veral sedimentafsetting en -erosie komplekse prosesse is, wat die interaksie van baie fisiese faktore behels en nie moeiteloos numeries gemodelleer kan word nie. Daarbenewens, in die meeste van die bestaande drie -dimensionele numeriese modelle is die hidrodinamika en sedimentvervoer modelle nie gekoppel nie. Die numeriese modelle simuleer eerstens die snelheid veld en waterdiepte en dan word die sedimentkonsentrasie en bedverandering bereken. Verder is die bestaande modelle nie ten volle driedimensioneel nie, en gebruik laag-gemiddelde benadering in samewerking met Saint- Venant vergelykings. Die hoofdoelwit van die huidige navorsing was om 'n gekoppelde volle drie -dimensionele (3D) numeriese model gebaseer op Navier -Stokes-vergelykings wat beide die sediment vervoer komponent en hidrodinamiese parameters insluit, te ontwikkel. In hierdie verband is 'n fisiese model opgestel in 'n laboratorium kanaal om die bodem uitlaat spoel van sediment onder druk in 'n beheerde omgewing te ondersoek. Die voorgestelde gekoppelde 3D numeriese model is gebruik om die eksperimentele toetse na te boots. Resultate van hierdie simulasies het goed ooreengestem met die metings. Die geometriese eienskappe van die erosie gat (tyd en ruimtelike gatontwikkeling) stroomop van die bodemuitlaat was redelik goed voorspel vergeleke met die eksperimentele data. Verder is die snelheid veld stroomop van die bodem uitlaat ook goed voorspel. Die voorgestelde numeriese model kan beskou word as betroubaar met die wete dat die model korrek opgestel is om die toestand van 'n bepaalde gevallestudie te weerspiel. Ten slotte, is n gekoppelde 3D numeriese model vir turbulente gesuspendeerde sediment vervoer in reservoirs ontwikkel en getoets teen 'n reeks laboratorium kanaal eksperimente. Die voorgestelde gesuspendeerde sediment vervoer model voorspel suksesvol beide die sediment afsetting- en erosieprosesse en daarom kan dit gebruik word vir die simulasie van turbulente gesuspendeerde sediment vervoer in damme.

published_or_final_version / abstract / Computer Science / Master / Master of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Obstetrics and Gynaecology / Doctoral / Doctor of Philosophy

This dissertation presents the results of an investigation into the performance characteristics of a unique hemispherical SPECT (single-photon emission computed tomography) imaging system capable of producing three-dimensional (3D) tomographic images of the human brain. The system is completely stationary and collects all necessary views of the patient simultaneously, with no system motion. The imager consists of twenty small (10cm x 10cm crystal area), digital gamma cameras arranged in a hemispherical pattern around the patient's head and a hemispherical lead aperture. The hemispherical aperture is positioned between the cameras and the head and contains a large number of pinholes; in this way each camera sees a number of overlapping pinhole projections of the radioactive distribution within the patient's brain. The initial investigation of the performance characteristics of a 3D SPECT system of this design were carried out using a computer simulation in which effects due to radiometry, finite pinhole size, finite detector resolution, photon noise, and object attenuation were included. We used a digital 3D brain phantom as the test object and an iterative search algorithm to perform the reconstructions. The simulations were used to compare the performance of a variety of system configurations. Based upon the results of the simulation study, we constructed a laboratory prototype of the 3D SPECT system, which we used to further characterize the expected performance of a clinical imaging system of the same design. Prior to collecting SPECT data we calibrated the imaging system, which required that we efficiently measure and store the spatially variant system response function. These calibration data were then included in the reconstructions of the SPECT phantoms that we imaged. A number of different SPECT phantoms were imaged to demonstrate the system performance. We measured a reconstructed spatial resolution of 4.8mm full-width at half-maximum and a full-system sensitivity of 36cps/μCi, where both values were measured for a point source in air located at the center of the field of view. We also describe an analysis that we performed to determine the equivalent, non-multiplexed system sensitivity; using this method, we found that the equivalent sensitivity was 79% of the measured value for the system configuration and the particular task that we investigated.

The representation theory of infinite dimensional groups is in its infancy. This paper is an attempt to apply the orbit method to a particular infinite dimensional group, the spin extension of the restricted unitary group. Our main contribution is in showing that various homogeneous spaces for this group admit measures which can be used to realize the unitary structure for the standard modules.

When modelling pollutants in the atmosphere, it is nearly impossible to get perfect results as the chemical and mechanical processes that govern pollutant concentrations are complex. Results are dependent on the quality of the meteorological input as well as the emissions inventory used to run the model. Also, models cannot currently take every process into consideration. Therefore, the model may get results that are close to, or show the general trend of the observed values, but are not perfect. However, due to the lack of observation stations, the resolution of the observational data is poor. Furthermore, the chemistry over large bodies of water is different from land chemistry, and in North America, there are no stations located over the great lakes or the ocean. Consequently, the observed values cannot accurately cover these regions. Therefore, we have combined model output and observational data when studying ozone concentrations in north eastern North America. We did this by correcting model output at observational sites with local data. We then interpolated those corrections across the model grid, using a Kriging procedure, to produce results that have the resolution of model results with the local accuracy of the observed values. Results showed that the corrected model output is much improved over either model results or observed values alone. This improvement was observed both for sites that were used in the correction process as well as sites that were omitted from the correction process.