<p> The accuracy of a diagnostic test is often evaluated with the measures of sensitivity and specificity and the joint dependence between these two measures is captured by the receiver operating characteristic (ROC) curve. To combine multiple testing results from studies that are assumed to follow the same underlying probability law, a smooth summary receiver operating characteristic (SROC) curve can be fitted. Moses et al. (1993) proposed a least squares approach to fit the smooth SROC curve. </p> <p> In this thesis we overview the summary measures for the ROC curve in single study data as well as the summary statistics for the SROC curves in meta-analysis. These summary statistics include, the area under the curve (AUC), Q* statistic, area swept under the curve (ASC) and the partial area under the curve (pAUC). </p> <p> Our focus, however is mainly on the partial area under the SROC curve as it is being used frequently in meta-analysis of diagnostic testing. The appeal to use the pAUC instead of the full AUC is that the partial area can be used to focus on a clinically relevant region of the SROC curve where false positive rate (FPR) is small. Simulations and considerations for the use of the summary indices of the ROC and SROC curves are presented here. </p> / Thesis / Master of Science (MSc)

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Water and ion transport critically determine the performance of many functional materials and devices, from fuel cells to lithium ion batteries to soft mechanical actuators. This dissertation aims to address some fundamental issues regarding transport and anisotropy, structural heterogeneity and molecular interactions inside ionic polymers. I first discuss a main deficiency of a standard protocol for calibrating high pulsed-field-gradient NMR. I show that high gradient calibration using low γ nuclei is not amenable to measurements on slow diffusing high γ nuclei. Then I employ NMR diffusometry to investigate transport and anisotropy for a series of ionic polymers, from poly(arylene ether sulfone) hydrophilic-hydrophobic multi-block copolymers to polymer blends to perfluorosulfonate random copolymers. For the multi-block copolymers, NMR diffusion measurements yield diffusion anisotropy as a function of water uptake and block lengths. ²H NMR spectroscopy on absorbed D₂O probes membrane alignment modes. These measurements also provide insights into average defect distributions. For the blend membranes, we examine the impact of compatibilizer on their transport properties. An increase in compatibilizer significantly improves the membrane phase homogeneity confirmed by SEM and transport studies. Theories of diffusion in porous media yield changes in domain size and tortuosity that correspond to drastic changes in local restrictions to water diffusion among different blend membranes. NMR relaxometry studies yield multi-component T₁ values, which further probe structural heterogeneities on smaller scales than diffusion experiments. For the random copolymer, the exploration of ion transport reveals inter-ionic associations of ionic liquids (ILs) modulated by hydration level and ionic medium. When ILs diffuse inside ionic polymers, isolated anions diffuse faster (≥ 4X) than cations at high hydration whereas ion associations result in substantially faster cation diffusion (≤ 3X) at low hydration inside membranes, revealing prevalent anionic aggregates. Finally, I present the strategy and analytical protocol for studying ionomer membranes using ILs. The normal cation diffusion contrasts to the anomalous anion diffusion caused by local confinement structures inside the membranes, which vary drastically with temperature and hydration level. These structures correspond to a density variation of SO₃⁻ groups, which define a distribution of local electrical potentials that fluctuate with temperature and nature of ionic media. / Ph. D.

A methodology to measure a characteristic time scale (duration) of peaks in pressure and velocity data is presented. This methodology is based on the use of the Morlet and Paul wavelets. Detailed descriptions of these wavelets and their implementation procedures are given. The results show that similar time scales or durations can be measured using either Morlet or Paul wavelets. To obtain consistent results data windowing might need to be applied. Using the Paul wavelet, durations of events measured in different wind tunnel simulations are obtained and discussed. / Master of Science

Current inventories of interpersonal trait dependency are problematic because they are based on theories that fail to recognize the positive aspects of dependency. The main goal of this thesis was to develop a new inventory that takes into account theoretical advances using Robert Bornstein's definitions and identified components of interpersonal dependency. The study was broken into the following three stages: 1. Item and inventory creation, 2. Expert feedback and interrater reliability and 3. Data collection and analysis. Three-hundred fifteen undergraduates completed a questionnaire packet, consisting of a demographics section, a copy of the new inventory, and seven other inventories that measure dysfunction and well-being. Although the original hypotheses in this work were not supported, exploratory factor analysis yielded four factors. These four factors and their relevance to the measurement of interpersonal dependency are discussed and suggestions are made for future studies. / Master of Science

Next generation wireless systems are being designed to provide ubiquitous broadband link access to information infrastructure. Diversity techniques play a vital role in supporting such high speed connections over radio channels by mitigating the detrimental effects of multiuser interference and multipath fading. Equal gain combining (EGC) diversity receiver is of practical interest because of its reduced complexity relative to optimum maximal ratio combining scheme while achieving near-optimal performance. Despite this, the literature on EGC receiver performance is meager owing to difficulty in deriving the probability density function of the diversity combiner output. This problem is further compounded when the diversity paths are correlated. Since spatial, pattern, or polarization diversity implementations at a mobile handset are usually limited to a small diversity order with closely spaced antenna elements (owing to cost and ergonomic constraints), any performance analysis must be revamped to account for the effects of branch correlation between the combined signals. This thesis presents a powerful characteristic function method for evaluating the performance of a two-branch EGC receiver in Nakagami-m channels with non-independent and non-identical fading statistics. The proposed framework facilitates efficient error probability analysis for a broad range of modulation/detection schemes in a unified manner. The thesis also examines the efficacy of an average diversity combiner in slotted direct sequence spread-spectrum access packet radio networks. A two-dimensional EGC diversity combining scheme is introduced, wherein a corrupted packet is retained and combined with its retransmission at the bit level to produce a more reliable packet. The mathematical analysis of the average diversity combiner presented in this thesis is sufficiently general to handle generalized fading channel models with independent fading statistics for a myriad of digital modulation schemes. / Master of Science

Geomantic culture, deeply rooted in China's rich traditions, stands out as one of the most captivating and mysterious aspects of the country's heritage. In thousands of years, this enigmatic blend of metaphysics and geomancy has significantly shaped the lives of the Chinese people. Its historical success in predicting and judging risks has made it a valuable tool for investors in the field of real estate. In this case, research on the influence of risks of metaphysics and geomancy becomes necessarily important to facilitate investors to own relatively feasible tools when participating in economic activities. In this dissertation, I collect property transaction data in a district of city of Beijing in China in August 2023, and examine how various geomantic characteristics affect property prices. I identify sixteen indicators of geomantic factors, among which four are variables of community characteristics (location, shape, main entrance and road), four are building characteristics (position, orientation, floor and house number), and eight are internal characteristics of residences (house type, layout, daylighting, ventilation, color scheme, five elements, door and window). Quantification of these 16 characteristic variables can be divided as quantitative quantification and qualitative quantification, and the method to quantify indicators in accordance with the actual situation is an innovative content of indicator quantification of this paper. Employing multiple linear regressions, I find that 10 out of the 16 characteristic variables, including location, shape, main entrance, road, position, orientation, floor, house number, house type, and layout, are significantly related to property prices. I also compare the strength of the effect of each geomantic characteristic variable on property prices through standardized regression. Community location of the property has the greatest influence on prices. a building's position is at the second most important factor. House number and layout seem having the least effect on property transaction prices. My research suggests that homeowners in China care about the geomantic characteristics of their property, hence are willing to pay a higher price for more favorable geomantic characteristics. This study also offers useful guidance for real estate developers how to maximize profits through improving geomantic characteristics of their property development. / Global Finance

We consider the regularization of some equivariant Euler classes of certain infinite-dimensional vector bundles over a finite-dimensional manifold M using the framework of zeta-regularized products [35, 53, 59]. An example of such a regularization is the Atiyah–Witten regularization of the T-equivariant Euler class of the normal bundle v(TM) of M in the free loop space LM [2]. In this thesis, we propose a new regularization procedure — W-regularization — which can be shown to reduce to the Atiyah–Witten regularization when applied to the case of v(TM). This new regularization yields a new multiplicative genus (in the sense of Hirzebruch [26]) — the ^Γ-genus — when applied to the more general case of a complex spin vector bundle of complex rank ≥ 2 over M, as opposed to the case of the complexification of TM for the Atiyah–Witten regularization. Some of its properties are investigated and some tantalizing connections to other areas of mathematics are also discussed. We also consider the application of W-regularization to the regularization of T²- equivariant Euler classes associated to the case of the double free loop space LLM. We find that the theory of zeta-regularized products, as set out by Jorgenson–Lang [35], Quine et al [53] and Voros [59], amongst others, provides a good framework for comparing the regularizations that have been considered so far. In particular, it reveals relations between some of the genera that appeared in elliptic cohomology, allowing us to clarify and prove an assertion of Liu [44] on the ˆΘ-genus, as well as to recover the Witten genus. The ^Γ₂-genus, a new genus generated by a function based on Barnes’ double gamma function [5, 6], is also derived in a similar way to the ^Γ-genus. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

We consider the regularization of some equivariant Euler classes of certain infinite-dimensional vector bundles over a finite-dimensional manifold M using the framework of zeta-regularized products [35, 53, 59]. An example of such a regularization is the Atiyah–Witten regularization of the T-equivariant Euler class of the normal bundle v(TM) of M in the free loop space LM [2]. In this thesis, we propose a new regularization procedure — W-regularization — which can be shown to reduce to the Atiyah–Witten regularization when applied to the case of v(TM). This new regularization yields a new multiplicative genus (in the sense of Hirzebruch [26]) — the ^Γ-genus — when applied to the more general case of a complex spin vector bundle of complex rank ≥ 2 over M, as opposed to the case of the complexification of TM for the Atiyah–Witten regularization. Some of its properties are investigated and some tantalizing connections to other areas of mathematics are also discussed. We also consider the application of W-regularization to the regularization of T²- equivariant Euler classes associated to the case of the double free loop space LLM. We find that the theory of zeta-regularized products, as set out by Jorgenson–Lang [35], Quine et al [53] and Voros [59], amongst others, provides a good framework for comparing the regularizations that have been considered so far. In particular, it reveals relations between some of the genera that appeared in elliptic cohomology, allowing us to clarify and prove an assertion of Liu [44] on the ˆΘ-genus, as well as to recover the Witten genus. The ^Γ₂-genus, a new genus generated by a function based on Barnes’ double gamma function [5, 6], is also derived in a similar way to the ^Γ-genus. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

The strategic decision making process (SDMP) is a major issue in organisations. It is part of the larger topic of strategic management and related to strategic planning. Achievement of strategic objectives outlined in the strategic plan of an organisation depends on the decisions taken through the process. Yet the literature shows that the concept of SDMP is not well understood and organisations find it difficult to develop and implement an SDMP, particularly Higher Education Institutions (HEIs). The literature indicates that decisions are taken in organizations in different ways for example using intuition, data, collaboration and ad-hoc considerations. In addition contextual factors are argued to affect the SDMP although very little research has been conducted to explain how contextual factors affect SDMP they do in HEIs. Some examples of contextual factors namely decision process characteristics have been identified and discussed as part of the SDMP literature in industry. However, lack of knowledge about SDMP and how contextual factors influence SDMP is regarded as to be a major obstacle for HEIs in taking decisions and choosing the best alternative amongst available decisions. This research seeks to contribute to address this important issue. Whilst there are many strategic decision characteristics (contextual factors) identified in the literature, this research focuses on decision importance. The rationale for choosing decision importance was that there is always some concern in the minds of the decision makers in the HEIs on what constitutes an important decision. What is considered as important decision while the decision is being taken may prove to be less important after implementation if there is no clear understanding of how to assign importance to a decision. Even in the industrial sector, Elbanna and Child (2007) it has been argued that decision importance has not been studied well. Relying upon the theoretical model developed by Elbanna and Child and other arguments found in the literatue, this research argued that the SDMP is a combination of relationships between decision characteristics, SDMP characteristics and decision outcomes that are influenced by environmental factors. As far as environmental factors were concerned environmental uncertainty was chosen as an external environment factor while organisational performance was chosen as the internal contextual factor. These two factors were argued to moderate the relationship between SDMP characteristics and SDMP outcomes and theoretical support for this conceptualisation was taken from the model developed by Elbanna and Child. A research model was developed to address the research questions, and the aim of the study was “to examine the different decision specific characteristic, SDMP characteristic and SDMP process outcome variables and develop a relationship amongst them in the context of HEIs in a changing environment”. The research was conducted in the United States of America and data was gathered from faculty members involved in decision making at the department level and higher. A positivist epistemological and objective ontological stance was adopted and a deductive approach was used. The research model was tested using the data collected from 485 valid responses to a survey questionnaire. Linear regression was the primary analysis approach and supplemented by path analysis. Results from the regression analysis showed that decision importance exerts influence on decision effectiveness through the mediators, rationality in decision making, intuition and decentralization in decision making. However, the outcome of path analysis showed that only rationality in decision making and intuition are important while decentalisation was not found to be statistically significant. Similarly environmental factors exerted pressure only on the relationship between rationality in decision making and decision effectiveness. The contradicting SDMP factors rationality in decision making and intuition were both found to be necessary to SDMP in the HEI context. This research has contributed to knowledge in terms of establishing a relationship between decision importance and decision process effectiveness mediated by rationality in decision making and intuition and development of the model. Theoretically the findings of this research show that the modification imposed on the model developed by Elbanna and Child was found to be statistically significant and found support from the literature. Environmental factors affected the relationship between rationality in decision making and decision effectiveness. This research has provided a model that can be used to help decision makers in HEIs to implement SDMP practically in the organization, to guide the process towards more robust decisions. The findings of this research find application in supporting policy makers to increase the likelihood of more effective decisions so that the decisions taken more effective.