A generative design system based on evolutionary and mathematical functions

Previous work by Professor John Frazer on Evolutionary Architecture provides a basis for the development of a system evolving architectural envelopes in a generic and abstract manner. Recent research by the authors has focused on the implementation of a virtual environment for the automatic generation and exploration of complex forms and architectural envelopes based on solid modelling techniques and the integration of evolutionary algorithms, enhanced computational and mathematical models. Abstract data types are introduced for genotypes in a genetic algorithm order to develop complex models using generative and evolutionary computing techniques. Multi-objective optimisation techniques are employed for defining the fitness function in the evaluation process.

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.

Heart versus mind : the functions of emotional and cognitive loyalty

While there is substantial research on attitudinal and behavioral loyalty, the deconstruction of attitudinal loyalty into its two key components – emotional and cognitive loyalty – has been largely ignored. Despite the existence of managerial strategies aimed at increasing each of these two components, there is little academic research to support these managerial efforts. This paper seeks to advance the understanding of emotional and cognitive brand loyalty by examining the psychological function that these dimensions of brand loyalty perform for the consumer. We employ Katz’s (1960) four functions of attitudes (utilitarian, knowledge, value-expression, ego-defence) to investigate this question. Surveys using a convenience sample were completed by 268 consumers in two metropolitan cities on a variety of goods, services and durable products. The relationship between the functions and dimensions of loyalty were examined using MANOVA. The results show that both the utilitarian and knowledge functions of loyalty are significantly positively related to cognitive loyalty while the ego-defensive function of loyalty is significantly positively related to emotional loyalty. The results for the value-expressive function of loyalty were nonsignificant.

Vitamin D in health and disease : an insight into traditional functions and new roles for the 'sunshine vitamin'

Vitamin D is unique among the vitamins in that humans can synthesize it via the action of UV radiation upon the skin. This combined with its ability to act on specific target tissues via Vitamin D Receptor’s (VDR) make its classification as a steroid hormone more appropriate. While Vitamin D deficiency is a recognized problem in some northern latitude countries, recent studies have shown even in sunny countries such as Australia, vitamin D deficiency may be more prevalent than first thought. Vitamin D is most well known for its role in bone health, however, the discovery of VDR’s on a wide variety of tissue types has also opened up roles for vitamin D far beyond traditional bone health. These include possible associations with autoimmune diseases such as multiple sclerosis and inflammatory bowel diseases, cancer, cardiovascular diseases and muscle strength. Firstly, this paper presents an overview of the two sources of vitamin D: exposure to ultraviolet-B radiation and food sources of vitamin D, with particular focus on both Australian and international studies on dietary vitamin D intake and national fortification strategies. Secondly, the paper reviews recent epidemiological and experimental evidence linking vitamin D and its role in health and disease for the major conditions linked to suboptimal vitamin D, while identifying significant gaps in the research and possible future directions for research.

Discovery and characterization of IGFBP-mediated endocytosis in the human retinal pigment epithelial cell line ARPE-19

Insulin-like growth factor binding proteins (IGFBPs) are prime regulators of IGF-action in numerous cell types including the retinal pigment epithelium (RPE). The RPE performs several functions essential for vision, including growth factor secretion and waste removal via a phagocytic process mediated in part by vitronectin (Vn). In the course of studying the effects of IGFBPs on IGF-mediated VEGF secretion and Vn-mediated phagocytosis in the RPE cell line ARPE-19, we have discovered that these cells avidly ingest synthetic microspheres (2.0 μm diameter) coated with IGFBPs. Given the novelty of this finding and the established role for endocytosis in mediating IGFBP actions in other cell types, we have explored the potential role of candidate cell surface receptors. Moreover, we have examined the role of key IGFBP structural motifs, by comparing responses to three members of the IGFBP family (IGFBP-3, IGFBP-4 and IGFBP-5) which display overlapping variations in primary structure and glycosylation status. Coating of microspheres (FluoSpheres®, sulfate modified polystyrene filled with a fluorophore) was conducted at 37 °C for 1 h using 20 μg/mL of test protein, followed by extensive washing. Binding of proteins was confirmed using a microBCA assay. The negative control consisted of microspheres treated with 0.1% bovine serum albumin (BSA), and all test samples were post-treated with BSA in an effort to coat any remaining free protein binding sites, which might otherwise encourage non-specific interactions with the cell surface. Serum-starved cultures of ARPE-19 cells were incubated with microspheres for 24 h, using a ratio of approximately 100 microspheres per cell. Uptake of microspheres was quantified using a fluorometer and was confirmed visually by confocal fluorescence microscopy. The ARPE-19 cells displayed little affinity for BSA-treated microspheres, but avidly ingested large quantities of those pre-treated with Vn (ANOVA; p < 0.001). Strong responses were also observed towards recombinant formulations of non-glycosylated IGFBP-3, glycosylated IGFBP-3 and glycosylated IGFBP-5 (all p < 0.001), while glycosylated IGFBP-4 induced a relatively minor response (p < 0.05). The response to IGFBP-3 was unaffected in the presence of excess soluble IGFBP-3, IGF-I or Vn. Likewise, soluble IGFBP-3 did not induce uptake of BSA-treated microspheres. Antibodies to either the transferrin receptor or type 1 IGF-receptor displayed slight inhibitory effects on responses to IGFBPs and Vn. Heparin abolished responses to Vn, IGFBP-5 and non-glycosylated IGFBP-3, but only partially inhibited the response to glycosylated IGFBP-3. Our results demonstrate for the first time IGFBP-mediated endocytosis in ARPE-19 cells and suggest roles for the IGFBP-heparin-binding domain and glycosylation status. These findings have important implications for understanding the mechanisms of IGFBP actions on the RPE, and in particular suggest a role for IGFBP-endocytosis.