Heng Wang

This thesis studies collinearity graphs and commuting involution graphs associated with sporadic group geometries, and the conjugacy classes of semisimple elements in the exceptional Lie-type group E8(2).First we construct plane-line collinearity graphs for the sporadic simple groups and their associated minimal and maximal 2-local parabolic geometries. For such a group and geometry, the plane-line collinearity graph takes all planes of the geometry as its vertices and joins two vertices with an edge if their planes are collinear in the geometry. We construct these graphs for the groups M23, J4, Fi22, Fi23, He, Co3 and Co2. Additionally we construct a variety of collinearity graphs associated with the minimal 2-local geometries of McL.A second short study looks at the commuting involution graphs associated with the Baby Monster sporadic group. These are graphs which take a conjugacy class of involutions as its vertex set and joins two vertices with an edge if they commute. We detail information relating to two such graphs. Finally, we study the conjugacy classes of semisimple elements in the exceptional group E8(2). This study is a joint work with Ali Aubad, John Ballantyne, Alexander McGaw, Peter Neuhaus, Peter Rowley and David Ward in which we determine the structure of centralisers for all such elements including information such as fixed-space dimensions and powering up maps. The ultimate aim is to determine all maximal subgroups of E8(2). This is a lengthy ongoing project and this study forms part of that effort.

No description available.

In this thesis the utility of a bivariate gamma distribution is explored. In the field of nutritional epidemiology a nutrition density transformation is used to reduce collinearity. This phenomenon will be shown to result due to the independent variables following a bivariate gamma model. In the field of radiation oncology paired comparison of variances is often performed. The bivariate gamma model is also appropriate for fitting correlated variances. A method for simulating bivariate gamma random variables is presented. This method is used to generate data from several bivariate gamma models and the asymptotic properties of a test statistic, suggested for the radiation oncology application, is studied.

給定一個設計矩陣X,當從X刪去一列或數列以後,X的特徵結構可能產生很 大的改變。在本文中,計算帽子矩陣H的高槓桿值,刪去如此有影響力的觀 察值後,X的特徵結構是否有改變,以及探討它的條件數。舉一些特殊的定 理, 討論從X刪去一列或數列之後的條件數。因此,我們也探討近似的條件 數,考慮兩者之間有何關係。 我們計算設計矩陣X的條件數與設計矩陣X 刪去一列或數列後的條件數,及診斷刪去有影響力的列對共線性之影響。 舉二個實例,使用 Matlab軟體計算條件數,分析它們的共線性性質, 以及 討論隱藏共線性與創造共線性的強度何者為強。

For a linear regression, the traditional technique deals with a case where the number of observations n more than the number of predictor variables p (n > p). In the case n < p, the classical method fails to estimate the coefficients. A solution of the problem is the case of correlated predictors is provided in this thesis. A new regularization and variable selection is proposed under the name of Sparse Ridge Fusion (SRF). In the case of highly correlated predictor, the simulated examples and a real data show that the SRF always outperforms the lasso, eleastic net, and the S-Lasso, and the results show that the SRF selects more predictor variables than the sample size n while the maximum selected variables by lasso is n size.

The purpose of this analysis is to evaluate the usefulness of Fourier Transform Infrared (FTIR) spectroscopy in the detection of Herpes Simplex Virus 1 (hsv1) infection at an early stage. The raw absorption values were standardized to eliminate inter-sampling error. Wilcoxon-Mann-Whitney (WMW) statistic's Z score was calculated to select significant spectral regions. Partial least squares modeling was performed because of multicollinearity. Kolmogorov-Smirnov statistic showed models for healthy tissues from different time groups were not from same distribution. The additional 24 hour dataset was evaluated using the following methods. Variables were selected by WMW Z score. Difference of Composites statistic, DC, was created as a disease indicator and evaluated using area under the ROC curve, specificities, and confidence intervals using bootstrap algorithm. The specificity of DC was high, however the confidence intervals were large. Future studies are required with larger sample sizes to test this statistic's usefulness.

<p>The major advantage of position sensitive radiation detector systems lies in their ability to non invasively map the regional distribution of the emitted radiation in real-time. Three of such detector systems were studied in this thesis, gamma-cameras, positron cameras and CMOS image sensors. A number of physical factors associated to these detectors degrade the qualitative and quantitative properties of the obtained images. These blurring factors could be divided into two groups. The first group consists of the general degrading factors inherent to the physical interaction processes of radiation with matter, such as scatter and attenuation processes which are common to all three detectors The second group consists of specific factors inherent to the particular radiation detection properties of the used detector which have to be separately studied for each detector system. Therefore, the aim of this thesis was devoted to the development of computational methods to enable quantitative molecular imaging in PET, SPET and in vivo patient dosimetry with CMOS image sensors.</p><p>The first task was to develop a novel quantitative dual isotope method for simultaneous assessments of regional lung ventilation and perfusion using a SPET technique. This method included correction routines for photon scattering, non uniform attenuation at two different photon energies (140 and 392 keV) and organ outline. This quantitative method was validated both with phantom experiments and physiological studies on healthy subjects.</p><p>The second task was to develop and clinically apply a quantitative method for tumour to background activity uptake measurements using planar mammo-scintigraphy, with partial volume compensation.</p><p>The third stage was to produce several computational models to assess the spatial resolution limitations in PET from the positron range, the annihilation photon non-collineairy and the photon depth of interaction.</p><p>Finally, a quantitative image processing method for a CMOS image sensor for applications in ion beam therapy dosimetry was developed.</p><p>From the obtained phantom and physiological results it was concluded that the methodologies developed for the simultaneous measurement of the lung ventilation and perfusion and for the quantification of the tumour malignancy grade in breast carcinoma were both accurate. Further, the obtained models for the influence that the positron range in various human tissues, and the photon emission non-collinearity and depth of interaction have on PET image spatial resolution, could be used both to optimise future PET camera designs and spatial resolution recovery algorithms. Finally, it was shown that the proton fluence rate in a proton therapy beam could be monitored and visualised by using a simple and inexpensive CMOS image sensor.</p>

The major advantage of position sensitive radiation detector systems lies in their ability to non invasively map the regional distribution of the emitted radiation in real-time. Three of such detector systems were studied in this thesis, gamma-cameras, positron cameras and CMOS image sensors. A number of physical factors associated to these detectors degrade the qualitative and quantitative properties of the obtained images. These blurring factors could be divided into two groups. The first group consists of the general degrading factors inherent to the physical interaction processes of radiation with matter, such as scatter and attenuation processes which are common to all three detectors The second group consists of specific factors inherent to the particular radiation detection properties of the used detector which have to be separately studied for each detector system. Therefore, the aim of this thesis was devoted to the development of computational methods to enable quantitative molecular imaging in PET, SPET and in vivo patient dosimetry with CMOS image sensors. The first task was to develop a novel quantitative dual isotope method for simultaneous assessments of regional lung ventilation and perfusion using a SPET technique. This method included correction routines for photon scattering, non uniform attenuation at two different photon energies (140 and 392 keV) and organ outline. This quantitative method was validated both with phantom experiments and physiological studies on healthy subjects. The second task was to develop and clinically apply a quantitative method for tumour to background activity uptake measurements using planar mammo-scintigraphy, with partial volume compensation. The third stage was to produce several computational models to assess the spatial resolution limitations in PET from the positron range, the annihilation photon non-collineairy and the photon depth of interaction. Finally, a quantitative image processing method for a CMOS image sensor for applications in ion beam therapy dosimetry was developed. From the obtained phantom and physiological results it was concluded that the methodologies developed for the simultaneous measurement of the lung ventilation and perfusion and for the quantification of the tumour malignancy grade in breast carcinoma were both accurate. Further, the obtained models for the influence that the positron range in various human tissues, and the photon emission non-collinearity and depth of interaction have on PET image spatial resolution, could be used both to optimise future PET camera designs and spatial resolution recovery algorithms. Finally, it was shown that the proton fluence rate in a proton therapy beam could be monitored and visualised by using a simple and inexpensive CMOS image sensor.

The aim of this thesis was to investigate the use of effect sizes to report the results of statistical credit rating models in a more practical way. Rating systems in the form of statistical probability models like logistic regression models are used to forecast the behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers. Therefore, model results were reported in terms of statistical significance as well as business language (practical significance), which business experts can understand and interpret. In this thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into standardised and measurable units, which can be reported practically. These effect sizes indicated strength of correlations between variables, contribution of variables to the odds of defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability between high and low risk customers. / Statistics / M. Sc. (Statistics)