Test architecture for prototyping automated dynamic airspace control

The automation of various aspects of air traffic management has many wide-reaching benefits including: reducing the workload for Air Traffic Controllers; increasing the flexibility of operations (both civil and military) within the airspace system through facilitating automated dynamic changes to en-route flight plans; ensuring safe aircraft separation for a complex mix of airspace users within a highly complex and dynamic airspace management system architecture. These benefits accumulate to increase the efficiency and flexibility of airspace use(1). Such functions are critical for the anticipated increase in volume of manned and unmanned aircraft traffic. One significant challenge facing the advancement of airspace automation lies in convincing air traffic regulatory authorities that the level of safety achievable through the use of automation concepts is comparable to, or exceeds, the accepted safety performance of the current system.

Dancing between diversity and consistency : refining assessment in postgraduate degrees in dance

This publication is the culmination of a 2 year Australian Learning and Teaching Council's Project Priority Programs Research Grant which investigates key issues and challenges in developing flexible guidelines lines for best practice in Australian Doctoral and Masters by Research Examination, encompassing the two modes of investigation, written and multi-modal (practice-led/based) theses, their distinctiveness and their potential interplay. The aims of the project were to address issues of assessment legitimacy raised by the entry of practice-orientated dance studies into Australian higher degrees; examine literal embodiment and presence, as opposed to cultural studies about states of embodiment; foreground the validity of questions around subjectivity and corporeal intelligence/s and the reliability of artistic/aesthetic communications, and finally to celebrate ‘performance mastery’(Melrose 2003) as a rigorous and legitimate mode of higher research. The project began with questions which centred around: the functions of higher degree dance research; concepts of 'master-ness’ and ‘doctorateness’; the kinds of languages, structures and processes which may guide candidates, supervisors, examiners and research personnel; the purpose of evaluation/examination; addressing positive and negative attributes of examination. Finally the study examined ways in which academic/professional, writing/dancing, tradition/creation and diversity/consistency relationships might be fostered to embrace change. Over two years, the authors undertook a qualitative national study encompassing a triangulation of semi-structured face to face interviews and industry forums to gather views from the profession, together with an analysis of existing guidelines, and recent literature in the field. The most significant primary data emerged from 74 qualitative interviews with supervisors, examiners, research deans and administrators, and candidates in dance and more broadly across the creative arts. Qualitative data gathered from the two primary sources, was coded and analysed using the NVivo software program. Further perspectives were drawn from international consultant and dance researcher Susan Melrose, as well as publications in the field, and initial feedback from a draft document circulated at the World Dance Alliance Global Summit in July 2008 in Brisbane. Refinement of data occurred in a continual sifting process until the final publication was produced. This process resulted in a set of guidelines in the form of a complex dynamic system for both product and process oriented outcomes of multi-modal theses, along with short position papers on issues which arose from the research such as contested definitions, embodiment and ephemerality, ‘liveness’ in performance research higher degrees, dissolving theory/practice binaries, the relationship between academe and industry, documenting practices and a re-consideration of the viva voce.

Getting creative in health care

Health care accounts for a substantial and growing share of national expenditures, and Australia’s health-care system faces some unprecedented pressures. This paper examines the contribution of creative expertise and services to Australian health care. They are found to be making a range of contributions to the development and delivery of health-care goods and services, the initial training and ongoing professionalism of doctors and nurses, and the effective functioning of health-care buildings. Creative activities within health-care services are also undertaken by medical professionals and patients. Key functions that creative activities address are innovation and service delivery in information management and analysis, and making complex information comprehensible or more useful, assisting communication and reducing psycho-social and distance-mediated barriers, and improving the efficiency and effectiveness of services.

The genetic basis of human height : the role of estrogen

Height is a complex physical trait that displays strong heritability. Adult height is related to length of the long bones, which is determined by growth at the epiphyseal growth plate. Longitudinal bone growth occurs via the process of endochondral ossification, where bone forms over the differentiating cartilage template at the growth plate. Estrogen plays a major role in regulating longitudinal bone growth and is responsible for inducing the pubertal growth spurt and fusion of the epiphyseal growth plate. However, the mechanism by which estrogen promotes epiphyseal fusion is poorly understood. It has been hypothesised that estrogen functions to regulate growth plate fusion by stimulating chondrocyte apoptosis, angiogenesis and bone cell invasion in the growth plate. Another theory has suggested that estrogen exposure exhausts the proliferative capacity of growth plate chondrocytes, which accelerates the process of chondrocyte senescence, leading to growth plate fusion. The overall objective of this study was to gain a greater understanding of the molecular mechanisms behind estrogen-mediated growth and height attainment by examining gene regulation in chondrocytes and the role of some of these genes in normal height inheritance. With the heritability of height so well established, the initial hypothesis was that genetic variation in candidate genes associated with longitudinal bone growth would be involved in normal adult height variation. The height-related genes FGFR3, CBFA1, ER and CBFA1 were screened for novel polymorphisms using denaturing HPLC and RFLP analysis. In total, 24 polymorphisms were identified. Two SNPs in ER (rs3757323 C>T and rs1801132 G>C) were strongly associated with adult male height and displayed an 8 cm and 9 cm height difference between homozygous genotypes, respectively. The TC haplotype of these SNPs was associated with a 6 cm decrease in height and remarkably, no homozygous carriers of the TC haplotype were identified in tall subjects. No significant associations with height were found for polymorphisms in the FGFR3, CBFA1 or VDR genes. In the epiphyseal growth plate, chondrocyte proliferation, matrix synthesis and chondrocyte hypertrophy are all major contributors to long bone growth. As estrogen plays such a significant role in both growth and final height attainment, another hypothesis of this study was that estrogen exerted its effects in the growth plate by influencing chondrocyte proliferation and mediating the expression of chondrocyte marker genes. The examination of genes regulated by estrogen in chondrocyte-like cells aimed to identify potential regulators of growth plate fusion, which may further elucidate mechanisms involved in the cessation of linear growth. While estrogen did not dramatically alter the proliferation of the SW1353 cell line, gene expression experiments identified several estrogen regulated genes. Sixteen chondrocyte marker genes were examined in response to estrogen concentrations ranging from 10-12 M to 10-8 M over varying time points. Of the genes analysed, IHH, FGFR3, collagen II and collagen X were not readily detectable and PTHrP, GHR, ER, BMP6, SOX9 and TGF1 mRNAs showed no significant response to estrogen treatments. However, the expression of MMP13, CBFA1, BCL-2 and BAX genes were significantly decreased. Interestingly, the majority of estrogen regulated genes in SW1353 cells are expressed in the hypertrophic zone of the growth plate. Estrogen is also known to regulate systemic GH secretion and local GH action. At the molecular level, estrogen functions to inhibit GH action by negatively regulating GH signalling. GH treated SW1353 cells displayed increases in MMP9 mRNA expression (4.4-fold) and MMP13 mRNA expression (64-fold) in SW1353 cells. Increases were also detected in their respective proteins. Treatment with AG490, an established JAK2 inhibitor, blocked the GH mediated stimulation of both MMP9 and MMP13 mRNA expression. The application of estrogen and GH to SW1353 cells attenuated GH-stimulated MMP13 levels, but did not affect MMP9 levels. Investigation of GH signalling revealed that SW1353 cells have high levels of activated JAK2 and exposure to GH, estrogen, AG490 and other signalling inhibitors did not affect JAK2 phosphorylation. Interestingly, AG490 treatment dramatically decreased ERK2 signalling, although GH did stimulate ERK2 phosphorylation above control levels. AG490 also decreased CBFA1 expression, a transcription factor known to activate MMP9 and MMP13. Finally, GH and estrogen treatment increased expression of SOCS3 mRNA, suggesting that SOCS3 may regulate JAK/STAT signalling in SW1353 cells. The modulation of GH-mediated MMP expression by estrogen in SW1353 cells represents a potentially novel mechanism by which estrogen may regulate longitudinal bone growth. However, further investigation is required in order to elucidate the precise mechanisms behind estrogen and GH regulation of MMP13 expression in SW1353 cells. This study has provided additional evidence that estrogen and the ER gene are major factors in the regulation of growth and the determination of adult height. Newly identified polymorphisms in the ER gene not only contribute to our understanding of the genetic basis of human height, but may also be useful in association studies examining other complex traits. This study also identified several estrogen regulated genes and indicated that estrogen modifies the expression of genes which are primarily expressed in the hypertrophic region of the epiphyseal growth plate. Furthermore, synergistic studies incorporating GH and estrogen have revealed the ability of estrogen to attenuate the effects of GH on MMP13 expression, revealing potential pathways by which estrogen may modulate growth plate fusion, longitudinal bone growth and even arthritis.

The organisation of action in complex neurobiological systems

This chapter elucidates key ideas behind neurocomputational and ecological dynamics and perspectives of understanding the organisation of action in complex neurobiological systems. The need to study the close link between neurobiological systems and their environments (particularly their sensory and movement subsystems and the surrounding energy sources) is advocated. It is proposed how degeneracy in complex neurobiological systems provides the basis for functional variability in organisation of action. In such systems processes of cognition and action facilitate the specific interactions of each performer with particular task and environmental constraints.

Increasing stochastic perturbations enhances acquisition and learning of complex sport movements

Traditionally, the aquisition of skills and sport movement has been characterised by numerous repetitions of presumed model movement pattern to be acquired by learners. This approach has been questioned by research identifying the presence of individualised movement patterns and the low probability of occurrence of two identical movements within and between individuals. In contrast, the differential learning approach claims advantage for incurring variability in the learning process by adding stochastic perturbations during practice. These ideas are exemplified by data from a high jump experiment which compared the effectiveness of classical and a differential training approach with pre-post test design. Results showed clear advantages for the group with additional stochastic perturbation during the aquisition phase in comparison to classically trained athletes. Analogies to similar phenomenological effects in the neurobiological literature are discussed.

Biochemical characterization of Aprataxin, the protein deficient in Ataxia with Oculomotor Apraxia type 1

Neurodegenerative disorders are heterogenous in nature and include a range of ataxias with oculomotor apraxia, which are characterised by a wide variety of neurological and ophthalmological features. This family includes recessive and dominant disorders. A subfamily of autosomal recessive cerebellar ataxias are characterised by defects in the cellular response to DNA damage. These include the well characterised disorders Ataxia-Telangiectasia (A-T) and Ataxia-Telangiectasia Like Disorder (A-TLD) as well as the recently identified diseases Spinocerebellar ataxia with axonal neuropathy Type 1 (SCAN1), Ataxia with Oculomotor Apraxia Type 2 (AOA2), as well as the subject of this thesis, Ataxia with Oculomotor Apraxia Type 1 (AOA1). AOA1 is caused by mutations in the APTX gene, which is located at chromosomal locus 9p13. This gene codes for the 342 amino acid protein Aprataxin. Mutations in APTX cause destabilization of Aprataxin, thus AOA1 is a result of Aprataxin deficiency. Aprataxin has three functional domains, an N-terminal Forkhead Associated (FHA) phosphoprotein interaction domain, a central Histidine Triad (HIT) nucleotide hydrolase domain and a C-terminal C2H2 zinc finger. Aprataxins FHA domain has homology to FHA domain of the DNA repair protein 5’ polynucleotide kinase 3’ phosphatase (PNKP). PNKP interacts with a range of DNA repair proteins via its FHA domain and plays a critical role in processing damaged DNA termini. The presence of this domain with a nucleotide hydrolase domain and a DNA binding motif implicated that Aprataxin may be involved in DNA repair and that AOA1 may be caused by a DNA repair deficit. This was substantiated by the interaction of Aprataxin with proteins involved in the repair of both single and double strand DNA breaks (XRay Cross-Complementing 1, XRCC4 and Poly-ADP Ribose Polymerase-1) and the hypersensitivity of AOA1 patient cell lines to single and double strand break inducing agents. At the commencement of this study little was known about the in vitro and in vivo properties of Aprataxin. Initially this study focused on generation of recombinant Aprataxin proteins to facilitate examination of the in vitro properties of Aprataxin. Using recombinant Aprataxin proteins I found that Aprataxin binds to double stranded DNA. Consistent with a role for Aprataxin as a DNA repair enzyme, this binding is not sequence specific. I also report that the HIT domain of Aprataxin hydrolyses adenosine derivatives and interestingly found that this activity is competitively inhibited by DNA. This provided initial evidence that DNA binds to the HIT domain of Aprataxin. The interaction of DNA with the nucleotide hydrolase domain of Aprataxin provided initial evidence that Aprataxin may be a DNA-processing factor. Following these studies, Aprataxin was found to hydrolyse 5’adenylated DNA, which can be generated by unscheduled ligation at DNA breaks with non-standard termini. I found that cell extracts from AOA1 patients do not have DNA-adenylate hydrolase activity indicating that Aprataxin is the only DNA-adenylate hydrolase in mammalian cells. I further characterised this activity by examining the contribution of the zinc finger and FHA domains to DNA-adenylate hydrolysis by the HIT domain. I found that deletion of the zinc finger ablated the activity of the HIT domain against adenylated DNA, indicating that the zinc finger may be required for the formation of a stable enzyme-substrate complex. Deletion of the FHA domain stimulated DNA-adenylate hydrolysis, which indicated that the activity of the HIT domain may be regulated by the FHA domain. Given that the FHA domain is involved in protein-protein interactions I propose that the activity of Aprataxins HIT domain may be regulated by proteins which interact with its FHA domain. We examined this possibility by measuring the DNA-adenylate hydrolase activity of extracts from cells deficient for the Aprataxin-interacting DNA repair proteins XRCC1 and PARP-1. XRCC1 deficiency did not affect Aprataxin activity but I found that Aprataxin is destabilized in the absence of PARP-1, resulting in a deficiency of DNA-adenylate hydrolase activity in PARP-1 knockout cells. This implies a critical role for PARP-1 in the stabilization of Aprataxin. Conversely I found that PARP-1 is destabilized in the absence of Aprataxin. PARP-1 is a central player in a number of DNA repair mechanisms and this implies that not only do AOA1 cells lack Aprataxin, they may also have defects in PARP-1 dependant cellular functions. Based on this I identified a defect in a PARP-1 dependant DNA repair mechanism in AOA1 cells. Additionally, I identified elevated levels of oxidized DNA in AOA1 cells, which is indicative of a defect in Base Excision Repair (BER). I attribute this to the reduced level of the BER protein Apurinic Endonuclease 1 (APE1) I identified in Aprataxin deficient cells. This study has identified and characterised multiple DNA repair defects in AOA1 cells, indicating that Aprataxin deficiency has far-reaching cellular consequences. Consistent with the literature, I show that Aprataxin is a nuclear protein with nucleoplasmic and nucleolar distribution. Previous studies have shown that Aprataxin interacts with the nucleolar rRNA processing factor nucleolin and that AOA1 cells appear to have a mild defect in rRNA synthesis. Given the nucleolar localization of Aprataxin I examined the protein-protein interactions of Aprataxin and found that Aprataxin interacts with a number of rRNA transcription and processing factors. Based on this and the nucleolar localization of Aprataxin I proposed that Aprataxin may have an alternative role in the nucleolus. I therefore examined the transcriptional activity of Aprataxin deficient cells using nucleotide analogue incorporation. I found that AOA1 cells do not display a defect in basal levels of RNA synthesis, however they display defective transcriptional responses to DNA damage. In summary, this thesis demonstrates that Aprataxin is a DNA repair enzyme responsible for the repair of adenylated DNA termini and that it is required for stabilization of at least two other DNA repair proteins. Thus not only do AOA1 cells have no Aprataxin protein or activity, they have additional deficiencies in PolyADP Ribose Polymerase-1 and Apurinic Endonuclease 1 dependant DNA repair mechanisms. I additionally demonstrate DNA-damage inducible transcriptional defects in AOA1 cells, indicating that Aprataxin deficiency confers a broad range of cellular defects and highlighting the complexity of the cellular response to DNA damage and the multiple defects which result from Aprataxin deficiency. My detailed characterization of the cellular consequences of Aprataxin deficiency provides an important contribution to our understanding of interlinking DNA repair processes.

The problem of measurement indeterminacy in complex neurobiological movement systems

In the study of complex neurobiological movement systems, measurement indeterminacy has typically been overcome by imposing artificial modelling constraints to reduce the number of unknowns (e.g., reducing all muscle, bone and ligament forces crossing a joint to a single vector). However, this approach prevents human movement scientists from investigating more fully the role, functionality and ubiquity of coordinative structures or functional motor synergies. Advancements in measurement methods and analysis techniques are required if the contribution of individual component parts or degrees of freedom of these task-specific structural units is to be established, thereby effectively solving the indeterminacy problem by reducing the number of unknowns. A further benefit of establishing more of the unknowns is that human movement scientists will be able to gain greater insight into ubiquitous processes of physical self-organising that underpin the formation of coordinative structures and the confluence of organismic, environmental and task constraints that determine the exact morphology of these special-purpose devices.

Monitoring the Performance of Complex Projects from Multiple Perspectives over Multiple Time Frames

When complex projects go wrong they can go horribly wrong with severe financial consequences. We are undertaking research to develop leading performance indicators for complex projects, metrics to provide early warning of potential difficulties. The assessment of success of complex projects can be made by a range of stakeholders over different time scales, against different levels of project results: the project’s outputs at the end of the project; the project’s outcomes in the months following project completion; and the project’s impact in the years following completion. We aim to identify leading performance indicators, which may include both success criteria and success factors, and which can be measured by the project team during project delivery to forecast success as assessed by key stakeholders in the days, months and years following the project. The hope is the leading performance indicators will act as alarm bells to show if a project is diverting from plan so early corrective action can be taken. It may be that different combinations of the leading performance indicators will be appropriate depending on the nature of project complexity. In this paper we develop a new model of project success, whereby success is assessed by different stakeholders over different time frames against different levels of project results. We then relate this to measurements that can be taken during project delivery. A methodology is described to evaluate the early parts of this model. Its implications and limitations are described. This paper describes work in progress.

Fingerprinting of complex mixtures with the use of high performance liquid chromatography, inductively coupled plasma atomic emission spectroscopy and chemometrics

The molecular and metal profile fingerprints were obtained from a complex substance, Atractylis chinensis DC—a traditional Chinese medicine (TCM), with the use of the high performance liquid chromatography (HPLC) and inductively coupled plasma atomic emission spectroscopy (ICP-AES) techniques. This substance was used in this work as an example of a complex biological material, which has found application as a TCM. Such TCM samples are traditionally processed by the Bran, Cut, Fried and Swill methods, and were collected from five provinces in China. The data matrices obtained from the two types of analysis produced two principal component biplots, which showed that the HPLC fingerprint data were discriminated on the basis of the methods for processing the raw TCM, while the metal analysis grouped according to the geographical origin. When the two data matrices were combined into a one two-way matrix, the resulting biplot showed a clear separation on the basis of the HPLC fingerprints. Importantly, within each different grouping the objects separated according to their geographical origin, and they ranked approximately in the same order in each group. This result suggested that by using such an approach, it is possible to derive improved characterisation of the complex TCM materials on the basis of the two kinds of analytical data. In addition, two supervised pattern recognition methods, K-nearest neighbors (KNNs) method, and linear discriminant analysis (LDA), were successfully applied to the individual data matrices—thus, supporting the PCA approach.

Identifying with an avatar : a multidisciplinary perspective

Avatars perform a complex range of inter-related functions. They not only allow us to express a digital identity, they facilitate the expression of physical motility and, through non-verbal expression, help to mediate social interaction in networked environments. When well designed, they can contribute to a sense of “presence” (a sense of being there) and a sense of “co-presence” (a sense of being there with others) in digital space. Because of this complexity, the study of avatars can be enriched by theoretical insights from a range of disciplines. This paper considers avatars from the perspectives of critical theory, visual communication, and art theory (on portraiture) to help elucidate the role of avatars as an expression of identity. It goes on to argue that identification with an avatar is also produced through their expression of motility and discusses the benefits of film theory for explaining this process. Conceding the limits of this approach, the paper draws on philosophies of body image, Human Computer Interaction (HCI) theory on embodied interaction, and fields as diverse as dance to explain the sense of identification, immersion, presence and co-presence that avatars can produce.

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.

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.