The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Zernike radial slope polynomials for wavefront reconstruction and refraction

Ophthalmic wavefront sensors typically measure wavefront slope, from which wavefront phase is reconstructed. We show that ophthalmic prescriptions (in power-vector format) can be obtained directly from slope measurements without wavefront reconstruction. This is achieved by fitting the measurement data with a new set of orthonormal basis functions called Zernike radial slope polynomials. Coefficients of this expansion can be used to specify the ophthalmic power vector using explicit formulas derived by a variety of methods. Zernike coefficients for wavefront error can be recovered from the coefficients of radial slope polynomials, thereby offering an alternative way to perform wavefront reconstruction.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Using coloured petri nets to simulate DoS-resistant protocols

In this work, we examine unbalanced computation between an initiator and a responder that leads to resource exhaustion attacks in key exchange protocols. We construct models for two cryp-tographic protocols; one is the well-known Internet protocol named Secure Socket Layer (SSL) protocol, and the other one is the Host Identity Protocol (HIP) which has built-in DoS-resistant mechanisms. To examine such protocols, we develop a formal framework based on Timed Coloured Petri Nets (Timed CPNs) and use a simulation approach provided in CPN Tools to achieve a formal analysis. By adopting the key idea of Meadows' cost-based framework and re¯ning the de¯nition of operational costs during the protocol execution, our simulation provides an accurate cost estimate of protocol execution compar- ing among principals, as well as the percentage of successful connections from legitimate users, under four di®erent strategies of DoS attack.

STRATÉGÉ – Study of Transparent Recognition, Accreditation Tools and Experience in a Global Environment

Engineering graduates of today, face a working environment that assumes global mobility in the labour market. This challenge means, amongst universities worldwide, a demand to increase the globalisation of educational programs, context, and increase and support the mobility of students through mechanisms such as student exchange and double masters degrees. Engineering student mobility from Australia is low with only a few Engineering Faculties encouraging students to go internationally. This comparative study, using universities in Australia and Europe, of feedback from students who have been on exchange or proposing to go on exchange, employers and faculty addresses the motivators and barriers to student mobility and exchange from the perspectives of the university, faculty, students and employers. Recommendations will be presented on how student mobility and exchange can be improved, and mechanisms such as double Masters Degrees, dual accreditation and Erasmus Mundus 2009 – 2013 can be utilised to improve student mobility.

Multi-Outcome Construction Policies : Industry-Focused Research Summary

The Multi-outcomes Construction Policies research project, funded by the Cooperative Research Centre for Construction Innovation (Project 2006-036-A), sought to explore the costs and benefits of leveraging social outcomes on public construction contracts. The context of the research project was the trend towards the contracting out of public construction works and the attempts that have been made to use new contractual arrangements with construction companies to construction achieve a wide range of social outcomes. In federal and state jurisdictions it is now common for governments to impose a range of additional requirements on public works contractors that relate to broad social/community objectives. These requirements include commitments to train apprentices and trainees; to provide local and/or indigenous employment opportunities; to buy local materials; and to include art works. The cost and benefits of using public construction contracts to achieve social/community goals have, to our knowledge, not been thoroughly researched in an Australian context. This is likely to reflect in large part the relatively short history of contracting out public works. As Jensen and Stonecash (2004) explain, most previous empirical studies of contracting out have attempted to measure the cost savings achieved through privatization, as this was the focus of policy debate in the 1980s and 1990s. Relatively few studies have addressed the ability of contracting arrangements to ensure the delivery of desired ‘quality’ outcomes1, or the costs of achieving these outcomes via contracting arrangements. One of the potential costs of attempting to leverage social/community outcomes on public construction projects is a reduction in the amount of competition for these projects, with obvious consequences for average bid prices and choice. In jurisdictions, such as Western Australia and Queensland, where currently construction market conditions are already

Interoperable Standards Development : Final Report

Since 1995 the buildingSMART International Alliance for Interoperability (buildingSMART)has developed a robust standard called the Industry Foundation Classes (IFC). IFC is an object oriented data model with related file format that has facilitated the efficient exchange of data in the development of building information models (BIM). The Cooperative Research Centre for Construction Innovation has contributed to the international effort in the development of the IFC standard and specifically the reinforced concrete part of the latest IFC 2x3 release. Industry Foundation Classes have been endorsed by the International Standards Organisation as a Publicly Available Specification (PAS) under the ISO label ISO/PAS 16739. For more details, go to http://www.tc184- sc4.org/About_TC184-SC4/About_SC4_Standards/ The current IFC model covers the building itself to a useful level of detail. The next stage of development for the IFC standard is where the building meets the ground (terrain) and with civil and external works like pavements, retaining walls, bridges, tunnels etc. With the current focus in Australia on infrastructure projects over the next 20 years a logical extension to this standard was in the area of site and civil works. This proposal recognises that there is an existing body of work on the specification of road representation data. In particular, LandXML is recognised as also is TransXML in the broader context of transportation and CityGML in the common interfacing of city maps, buildings and roads. Examination of interfaces between IFC and these specifications is therefore within the scope of this project. That such interfaces can be developed has already been demonstrated in principle within the IFC for Geographic Information Systems (GIS) project. National road standards that are already in use should be carefully analysed and contacts established in order to gain from this knowledge. The Object Catalogue for the Road Transport Sector (OKSTRA) should be noted as an example. It is also noted that buildingSMART Norway has submitted a proposal

Comparison of methods for processing drinking water samples for the isolation of Myocbacterium avium and intracellulare

Several protocols for isolation of mycobacteria from water exist, but there is no established standard method. This study compared methods of processing potable water samples for the isolation of Mycobacterium avium and Mycobacterium intracellulare using spiked sterilized water and tap water decontaminated using 0.005% cetylpyridinium chloride (CPC). Samples were concentrated by centrifugation or filtration and inoculated onto Middlebrook 7H10 and 7H11 plates and Lowenstein-Jensen slants and into mycobacterial growth indicator tubes with or without polymyxin, azlocillin, nalidixic acid, trimethoprim, and amphotericin B. The solid media were incubated at 32°C, at 35°C, and at 35°C with CO2 and read weekly. The results suggest that filtration of water for the isolation of mycobacteria is a more sensitive method for concentration than centrifugation. The addition of sodium thiosulfate may not be necessary and may reduce the yield. Middlebrook M7H10 and 7H11 were equally sensitive culture media. CPC decontamination, while effective for reducing growth of contaminants, also significantly reduces mycobacterial numbers. There was no difference at 3 weeks between the different incubation temperatures.

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 videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.