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.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

The effect of prolonged reading on visual functions and reading performance in students with low vision

This study is the first to investigate the effect of prolonged reading on reading performance and visual functions in students with low vision. The study focuses on one of the most common modes of achieving adequate magnification for reading by students with low vision, their close reading distance (proximal or relative distance magnification). Close reading distances impose high demands on near visual functions, such as accommodation and convergence. Previous research on accommodation in children with low vision shows that their accommodative responses are reduced compared to normal vision. In addition, there is an increased lag of accommodation for higher stimulus levels as may occur at close reading distance. Reduced accommodative responses in low vision and higher lag of accommodation at close reading distances together could impact on reading performance of students with low vision especially during prolonged reading tasks. The presence of convergence anomalies could further affect reading performance. Therefore, the aims of the present study were 1) To investigate the effect of prolonged reading on reading performance in students with low vision 2) To investigate the effect of prolonged reading on visual functions in students with low vision. This study was conducted as cross-sectional research on 42 students with low vision and a comparison group of 20 students with normal vision, aged 7 to 20 years. The students with low vision had vision impairments arising from a range of causes and represented a typical group of students with low vision, with no significant developmental delays, attending school in Brisbane, Australia. All participants underwent a battery of clinical tests before and after a prolonged reading task. An initial reading-specific history and pre-task measurements that included Bailey-Lovie distance and near visual acuities, Pelli-Robson contrast sensitivity, ocular deviations, sensory fusion, ocular motility, near point of accommodation (pull-away method), accuracy of accommodation (Monocular Estimation Method (MEM)) retinoscopy and Near Point of Convergence (NPC) (push-up method) were recorded for all participants. Reading performance measures were Maximum Oral Reading Rates (MORR), Near Text Visual Acuity (NTVA) and acuity reserves using Bailey-Lovie text charts. Symptoms of visual fatigue were assessed using the Convergence Insufficiency Symptom Survey (CISS) for all participants. Pre-task measurements of reading performance and accuracy of accommodation and NPC were compared with post-task measurements, to test for any effects of prolonged reading. The prolonged reading task involved reading a storybook silently for at least 30 minutes. The task was controlled for print size, contrast, difficulty level and content of the reading material. Silent Reading Rate (SRR) was recorded every 2 minutes during prolonged reading. Symptom scores and visual fatigue scores were also obtained for all participants. A visual fatigue analogue scale (VAS) was used to assess visual fatigue during the task, once at the beginning, once at the middle and once at the end of the task. In addition to the subjective assessments of visual fatigue, tonic accommodation was monitored using a photorefractor (PlusoptiX CR03™) every 6 minutes during the task, as an objective assessment of visual fatigue. Reading measures were done at the habitual reading distance of students with low vision and at 25 cms for students with normal vision. The initial history showed that the students with low vision read for significantly shorter periods at home compared to the students with normal vision. The working distances of participants with low vision ranged from 3-25 cms and half of them were not using any optical devices for magnification. Nearly half of the participants with low vision were able to resolve 8-point print (1M) at 25 cms. Half of the participants in the low vision group had ocular deviations and suppression at near. Reading rates were significantly reduced in students with low vision compared to those of students with normal vision. In addition, there were a significantly larger number of participants in the low vision group who could not sustain the 30-minute task compared to the normal vision group. However, there were no significant changes in reading rates during or following prolonged reading in either the low vision or normal vision groups. Individual changes in reading rates were independent of their baseline reading rates, indicating that the changes in reading rates during prolonged reading cannot be predicted from a typical clinical assessment of reading using brief reading tasks. Contrary to previous reports the silent reading rates of the students with low vision were significantly lower than their oral reading rates, although oral and silent reading was assessed using different methods. Although the visual acuity, contrast sensitivity, near point of convergence and accuracy of accommodation were significantly poorer for the low vision group compared to those of the normal vision group, there were no significant changes in any of these visual functions following prolonged reading in either group. Interestingly, a few students with low vision (n =10) were found to be reading at a distance closer than their near point of accommodation. This suggests a decreased sensitivity to blur. Further evaluation revealed that the equivalent intrinsic refractive errors (an estimate of the spherical dioptirc defocus which would be expected to yield a patient’s visual acuity in normal subjects) were significantly larger for the low vision group compared to those of the normal vision group. As expected, accommodative responses were significantly reduced for the low vision group compared to the expected norms, which is consistent with their close reading distances, reduced visual acuity and contrast sensitivity. For those in the low vision group who had an accommodative error exceeding their equivalent intrinsic refractive errors, a significant decrease in MORR was found following prolonged reading. The silent reading rates however were not significantly affected by accommodative errors in the present study. Suppression also had a significant impact on the changes in reading rates during prolonged reading. The participants who did not have suppression at near showed significant decreases in silent reading rates during and following prolonged reading. This impact of binocular vision at near on prolonged reading was possibly due to the high demands on convergence. The significant predictors of MORR in the low vision group were age, NTVA, reading interest and reading comprehension, accounting for 61.7% of the variances in MORR. SRR was not significantly influenced by any factors, except for the duration of the reading task sustained; participants with higher reading rates were able to sustain a longer reading duration. In students with normal vision, age was the only predictor of MORR. Participants with low vision also reported significantly greater visual fatigue compared to the normal vision group. Measures of tonic accommodation however were little influenced by visual fatigue in the present study. Visual fatigue analogue scores were found to be significantly associated with reading rates in students with low vision and normal vision. However, the patterns of association between visual fatigue and reading rates were different for SRR and MORR. The participants with low vision with higher symptom scores had lower SRRs and participants with higher visual fatigue had lower MORRs. As hypothesized, visual functions such as accuracy of accommodation and convergence did have an impact on prolonged reading in students with low vision, for students whose accommodative errors were greater than their equivalent intrinsic refractive errors, and for those who did not suppress one eye. Those students with low vision who have accommodative errors higher than their equivalent intrinsic refractive errors might significantly benefit from reading glasses. Similarly, considering prisms or occlusion for those without suppression might reduce the convergence demands in these students while using their close reading distances. The impact of these prescriptions on reading rates, reading interest and visual fatigue is an area of promising future research. Most importantly, it is evident from the present study that a combination of factors such as accommodative errors, near point of convergence and suppression should be considered when prescribing reading devices for students with low vision. Considering these factors would also assist rehabilitation specialists in identifying those students who are likely to experience difficulty in prolonged reading, which is otherwise not reflected during typical clinical reading assessments.

Excess deaths during the 2004 heatwave in Brisbane, Australia

The paper examines whether there was an excess of deaths and the relative role of temperature and ozone in a heatwave during 7–26 February 2004 in Brisbane, Australia, a subtropical city accustomed to warm weather. The data on daily counts of deaths from cardiovascular disease and non-external causes, meteorological conditions, and air pollution in Brisbane from 1 January 2001 to 31 October 2004 were supplied by the Australian Bureau of Statistics, Australian Bureau of Meteorology, and Queensland Environmental Protection Agency, respectively. The relationship between temperature and mortality was analysed using a Poisson time series regression model with smoothing splines to control for nonlinear effects of confounding factors. The highest temperature recorded in the 2004 heatwave was 42°C compared with the highest recorded temperature of 34°C during the same periods of 2001–2003. There was a significant relationship between exposure to heat and excess deaths in the 2004 heatwave estimated increase in non-external deaths: 75 [(95% confidence interval, CI: 11–138; cardiovascular deaths: 41 (95% CI: −2 to 84)]. There was no apparent evidence of substantial short-term mortality displacement. The excess deaths were mainly attributed to temperature but exposure to ozone also contributed to these deaths.

Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros