Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Models of supervision : from theory to practice

This chapter will address psychodynamic, cognitive-behavioural, and developmental models in supervision by initially considering the historical underpinnings of each and then examining in turn some of the key processes that are evident in the supervisory relationships. Case studies are included where appropriate to highlight the application of theory to practice and several processes are fully elaborated over all models to enable a contemporary view of style and substance in the supervision context.

The effect of language models on phonetic decoding for spoken term detection

Spoken term detection (STD) popularly involves performing word or sub-word level speech recognition and indexing the result. This work challenges the assumption that improved speech recognition accuracy implies better indexing for STD. Using an index derived from phone lattices, this paper examines the effect of language model selection on the relationship between phone recognition accuracy and STD accuracy. Results suggest that language models usually improve phone recognition accuracy but their inclusion does not always translate to improved STD accuracy. The findings suggest that using phone recognition accuracy to measure the quality of an STD index can be problematic, and highlight the need for an alternative that is more closely aligned with the goals of the specific detection task.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Assessing information systems success models : empirical comparison (Research in Progress)

Information System (IS) success may be the most arguable and important dependent variable in the IS field. The purpose of the present study is to address IS success by empirically assess and compare DeLone and McLean’s (1992) and Gable’s et al. (2008) models of IS success in Australian Universities context. The two models have some commonalities and several important distinctions. Both models integrate and interrelate multiple dimensions of IS success. Hence, it would be useful to compare the models to see which is superior; as it is not clear how IS researchers should respond to this controversy.

Multivariate methods to identify cancer-related symptom clusters

Multivariate methods are required to assess the interrelationships among multiple, concurrent symptoms. We examined the conceptual and contextual appropriateness of commonly used multivariate methods for cancer symptom cluster identification. From 178 publications identified in an online database search of Medline, CINAHL, and PsycINFO, limited to articles published in English, 10 years prior to March 2007, 13 cross-sectional studies met the inclusion criteria. Conceptually, common factor analysis (FA) and hierarchical cluster analysis (HCA) are appropriate for symptom cluster identification, not principal component analysis. As a basis for new directions in symptom management, FA methods are more appropriate than HCA. Principal axis factoring or maximum likelihood factoring, the scree plot, oblique rotation, and clinical interpretation are recommended approaches to symptom cluster identification.

Simplified numerical models of LiteSteel Beam floor joists with Web openings for the prediction of section moment capacities

This paper is aimed at investigating the effect of web openings on the plastic bending behaviour and section moment capacity of a new cold-formed steel beam known as LiteSteel beam (LSB) using numerical modelling. Different LSB sections with varying circular hole diameter and spacing were considered. A simplified but appropriate numerical modelling technique was developed for the modelling of monosymmetric sections such as LSBs subject to bending, and was used to simulate a series of section moment capacity tests of LSB flexural members with web openings. The buckling and ultimate strength behaviour was investigated in detail and the modeling technique was further improved through a comparison of numerical and experimental results. This paper describes the simplified finite element modeling technique used in this study that includes all the significant behavioural effects affecting the plastic bending behaviour and section moment capacity of LSB sections with web holes. Numerical and test results and associated findings are also presented.

Vitamin D and sun protection : the impact of mixed public health messages in Australia

Exposure of the skin to sunlight can cause skin cancer and is also necessary for cutaneous vitamin D production. Media reports have highlighted the purported health benefits of vitamin D. Our aim was to examine attitudes and behaviours related to sun protection and vitamin D. A cross-sectional study of 2,001 residents in Queensland, Australia aged 20-70 years was undertaken. Information collected included: skin cancer risk factors; perceptions about levels of sun exposure required to maintain vitamin D; belief that sun protection increases risk of vitamin D deficiency; intention, and actual change in sun protection practices for adults and children. Multivariate models examined predictors of attitudinal and behavioural change. One-third (32%) believed a fair-skinned adult, and 31% thought a child required at least 30 minutes per day in summer sun to maintain vitamin D levels. Reductions in sun protection were reported by 21% of adults and 14% of children. Factors associated with belief that sun protection may result in not obtaining enough vitamin D included aged ≥ 60 years (OR=1.35, 95% CI 1.09-1.66) and having skin that tanned easily (OR=1.96, 95% CI 1.38-2.78). Participants from low income households, and those who frequently used sun protective clothing were more likely to have reduced sun protection practices (OR=1.33, 95% CI 1.10-1.73 and OR=1.73, 95% CI 1.36-2.20, respectively). This study provides evidence of reductions in sun protection practices in a population living in a high UV environment. There is an urgent need to re-focus messages regarding sun exposure and for continued sun protection practices.

Characterisation of soils with the use of instrumental techniques : a multivariate forensic study

The value of soil evidence in the forensic discipline is well known. However, it would be advantageous if an in-situ method was available that could record responses from tyre or shoe impressions in ground soil at the crime scene. The development of optical fibres and emerging portable NIR instruments has unveiled a potential methodology which could permit such a proposal. The NIR spectral region contains rich chemical information in the form of overtone and combination bands of the fundamental infrared absorptions and low-energy electronic transitions. This region has in the past, been perceived as being too complex for interpretation and consequently was scarcely utilized. The application of NIR in the forensic discipline is virtually non-existent creating a vacancy for research in this area. NIR spectroscopy has great potential in the forensic discipline as it is simple, nondestructive and capable of rapidly providing information relating to chemical composition. The objective of this study is to investigate the ability of NIR spectroscopy combined with Chemometrics to discriminate between individual soils. A further objective is to apply the NIR process to a simulated forensic scenario where soil transfer occurs. NIR spectra were recorded from twenty-seven soils sampled from the Logan region in South-East Queensland, Australia. A series of three high quartz soils were mixed with three different kaolinites in varying ratios and NIR spectra collected. Spectra were also collected from six soils as the temperature of the soils was ramped from room temperature up to 6000C. Finally, a forensic scenario was simulated where the transferral of ground soil to shoe soles was investigated. Chemometrics methods such as the commonly known Principal Component Analysis (PCA), the less well known fuzzy clustering (FC) and ranking by means of multicriteria decision making (MCDM) methodology were employed to interpret the spectral results. All soils were characterised using Inductively Coupled Plasma Optical Emission Spectroscopy and X-Ray Diffractometry. Results were promising revealing NIR combined with Chemometrics is capable of discriminating between the various soils. Peak assignments were established by comparing the spectra of known minerals with the spectra collected from the soil samples. The temperature dependent NIR analysis confirmed the assignments of the absorptions due to adsorbed and molecular bound water. The relative intensities of the identified NIR absorptions reflected the quantitative XRD and ICP characterisation results. PCA and FC analysis of the raw soils in the initial NIR investigation revealed that the soils were primarily distinguished on the basis of their relative quartz and kaolinte contents, and to a lesser extent on the horizon from which they originated. Furthermore, PCA could distinguish between the three kaolinites used in the study, suggesting that the NIR spectral region was sensitive enough to contain information describing variation within kaolinite itself. The forensic scenario simulation PCA successfully discriminated between the ‘Backyard Soil’ and ‘Melcann® Sand’, as well as the two sampling methods employed. Further PCA exploration revealed that it was possible to distinguish between the various shoes used in the simulation. In addition, it was possible to establish association between specific sampling sites on the shoe with the corresponding site remaining in the impression. The forensic application revealed some limitations of the process relating to moisture content and homogeneity of the soil. These limitations can both be overcome by simple sampling practices and maintaining the original integrity of the soil. The results from the forensic scenario simulation proved that the concept shows great promise in the forensic discipline.

Development of lifetime warranty policies and models for estimating costs

In today's fiercely competitive products market, product warranty has started playing an important role. The warranty period offered by the manufacturer/dealer has been progressively increasing since the beginning of the 20th Century. Currently, a large number of products are being sold with long-term warranty policies in the form of extended warranty, warranty for used products, service contracts and lifetime warranty policies. Lifetime warranties are relatively a new concept. The modelling of failures during the warranty period and the costs for such policies are complex since the lifespan in these policies are not defined well and it is often difficult to tell about life measures for the longer period of coverage due to usage pattern/maintenance activities undertaken and uncertainties of costs over the period. This paper focuses on defining lifetime, developing lifetime warranty policies and models for predicting failures and estimating costs for lifetime warranty policies.