Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.

Building the toolkit of quality monitoring clinical outcomes as a means of assessing quality in residential care

Residential aged care in Australia does not have a system of quality assessment related to clinical outcomes, creating a significant gap in quality monitoring. Clinical outcomes represent the results of all inputs into care, thus providing an indication of the success of those inputs. To fill this gap, an assessment tool based on resident outcomes (the ResCareQA) was developed and evaluated in collaboration with residential care providers. A useful output of the ResCareQA is a profile of resident clinical status, and this paper will use such outputs to present a snapshot of nine residential facilities. Such comprehensive data has not yet been available within Australia, so this will provide an important insight. ResCareQA data was collected from all residents (N=498) of nine aged care facilities from two major aged care providers. For each facility, numerator–denominator data were calculated to assess the degree of potential clinical problems. Results varied across clinical areas and across facilities, and rank-ordered facility results for selected clinical areas are reviewed and discussed. Use of the ResCareQA to generate clinical outcome data provides a concrete means of monitoring care quality within residential facilities; regular use of the ResCareQA could thus contribute to improved care outcomes within residential aged care.

Characterisation of Ni carbonate-bearing minerals by UV-Vis-NIR spectroscopy

Four nickel carbonate-bearing minerals from Australia have been investigated to study the effect of Ni for Mg substitution. The spectra of nullaginite, zaratite, widgiemoolthalite and takovite show three main features in the range of 26,720–25,855 cm−1 (ν1-band), 15,230–14,740 cm−1 (ν2-band) and 9,200–9,145 cm−1 (ν3-band) which are characteristic of divalent nickel in six-fold coordination. The Crystal Field Stabilization Energy (CFSE) of Ni2+ in the four carbonates is calculated from the observed 3A2g(3F) → 3T2g(3F) transition. CFSE is dependent on mineralogy, crystallinity and chemical composition (Al/Mg-content). The splitting of the ν1- and ν3-bands and non-Gaussian shape of ν3-band in the minerals are the effects of Ni-site distortion from regular octahedral. The effect of structural cation substitutions (Mg2+, Ni2+, Fe2+ and trivalent cations, Al3+, Fe3+) in the carbonate minerals is noticed on band shifts. Thus, electronic bands in the UV–Vis–NIR spectra and the overtones and combination bands of OH and carbonate ion in NIR show shifts to higher wavenumbers, particularly for widgiemoolthalite and takovite.

Use of advanced technology videotapes in the delivery of structural engineering courses

A teaching and learning development project is currently under way at Queensland University of Technology to develop advanced technology videotapes for use with the delivery of structural engineering courses. These tapes consist of integrated computer and laboratory simulations of important concepts, and behaviour of structures and their components for a number of structural engineering subjects. They will be used as part of the regular lectures and thus will not only improve the quality of lectures and learning environment, but also will be able to replace the ever-dwindling laboratory teaching in these subjects. The use of these videotapes, developed using advanced computer graphics, data visualization and video technologies, will enrich the learning process of the current diverse engineering student body. This paper presents the details of this new method, the methodology used, the results and evaluation in relation to one of the structural engineering subjects, steel structures.

Housing supply in Australia : the impact of the availability of development finance

Before the Global Financial Crisis many providers of finance had growth mandates and actively pursued development finance deals as a way of gaining higher returns on funds with regular capital turnover and re-investment possible. This was able to be achieved through high gearing and low presales in a strong market. As asset prices fell, loan covenants breached and memories of the 1990’s returned, banks rapidly adjusted their risk appetite via retraction of gearing and expansion of presale requirements. Early signs of loosening in bank credit policy are emerging, however parties seeking development finance are faced with a severely reduced number of institutions from which to source funding. The few institutions that are lending are filtering out only the best credit risks by way of constrictive credit conditions including: low loan to value ratios, the corresponding requirement to contribute high levels of equity, lack of support in non-prime locations and the requirement for only borrowers with well established track records. In this risk averse and capital constrained environment, the ability of developers to proceed with real estate developments is still being constrained by their inability to obtain project finance. This paper will examine the pre and post GFC development finance environment. It will identify the key lending criteria relevant to real estate development finance and will detail the related changes to credit policies over this period. The associated impact to real estate development projects will be presented, highlighting the significant constraint to supply that the inability to obtain finance poses.

Automated symbolic and numeric procedure for manipulator rigid-body dynamic significance analysis and simplification

This paper describes an automated procedure for analysing the significance of each of the many terms in the equations of motion for a serial-link robot manipulator. Significance analysis provides insight into the rigid-body dynamic effects that are significant locally or globally in the manipulator's state space. Deleting those terms that do not contribute significantly to the total joint torque can greatly reduce the computational burden for online control, and a Monte-Carlo style simulation is used to investigate the errors thus introduced. The procedures described are a hybrid of symbolic and numeric techniques, and can be readily implemented using standard computer algebra packages.

Development of rapid and highly resolving combinatorial genotyping schemes for Campylobacter jejuni and Campylobacter coli

Campylobacter jejuni followed by Campylobacter coli contribute substantially to the economic and public health burden attributed to food-borne infections in Australia. Genotypic characterisation of isolates has provided new insights into the epidemiology and pathogenesis of C. jejuni and C. coli. However, currently available methods are not conducive to large scale epidemiological investigations that are necessary to elucidate the global epidemiology of these common food-borne pathogens. This research aims to develop high resolution C. jejuni and C. coli genotyping schemes that are convenient for high throughput applications. Real-time PCR and High Resolution Melt (HRM) analysis are fundamental to the genotyping schemes developed in this study and enable rapid, cost effective, interrogation of a range of different polymorphic sites within the Campylobacter genome. While the sources and routes of transmission of campylobacters are unclear, handling and consumption of poultry meat is frequently associated with human campylobacteriosis in Australia. Therefore, chicken derived C. jejuni and C. coli isolates were used to develop and verify the methods described in this study. The first aim of this study describes the application of MLST-SNP (Multi Locus Sequence Typing Single Nucleotide Polymorphisms) + binary typing to 87 chicken C. jejuni isolates using real-time PCR analysis. These typing schemes were developed previously by our research group using isolates from campylobacteriosis patients. This present study showed that SNP + binary typing alone or in combination are effective at detecting epidemiological linkage between chicken derived Campylobacter isolates and enable data comparisons with other MLST based investigations. SNP + binary types obtained from chicken isolates in this study were compared with a previously SNP + binary and MLST typed set of human isolates. Common genotypes between the two collections of isolates were identified and ST-524 represented a clone that could be worth monitoring in the chicken meat industry. In contrast, ST-48, mainly associated with bovine hosts, was abundant in the human isolates. This genotype was, however, absent in the chicken isolates, indicating the role of non-poultry sources in causing human Campylobacter infections. This demonstrates the potential application of SNP + binary typing for epidemiological investigations and source tracing. While MLST SNPs and binary genes comprise the more stable backbone of the Campylobacter genome and are indicative of long term epidemiological linkage of the isolates, the development of a High Resolution Melt (HRM) based curve analysis method to interrogate the hypervariable Campylobacter flagellin encoding gene (flaA) is described in Aim 2 of this study. The flaA gene product appears to be an important pathogenicity determinant of campylobacters and is therefore a popular target for genotyping, especially for short term epidemiological studies such as outbreak investigations. HRM curve analysis based flaA interrogation is a single-step closed-tube method that provides portable data that can be easily shared and accessed. Critical to the development of flaA HRM was the use of flaA specific primers that did not amplify the flaB gene. HRM curve analysis flaA interrogation was successful at discriminating the 47 sequence variants identified within the 87 C. jejuni and 15 C. coli isolates and correlated to the epidemiological background of the isolates. In the combinatorial format, the resolving power of flaA was additive to that of SNP + binary typing and CRISPR (Clustered regularly spaced short Palindromic repeats) HRM and fits the PHRANA (Progressive hierarchical resolving assays using nucleic acids) approach for genotyping. The use of statistical methods to analyse the HRM data enhanced sophistication of the method. Therefore, flaA HRM is a rapid and cost effective alternative to gel- or sequence-based flaA typing schemes. Aim 3 of this study describes the development of a novel bioinformatics driven method to interrogate Campylobacter MLST gene fragments using HRM, and is called ‘SNP Nucleated Minim MLST’ or ‘Minim typing’. The method involves HRM interrogation of MLST fragments that encompass highly informative “Nucleating SNPS” to ensure high resolution. Selection of fragments potentially suited to HRM analysis was conducted in silico using i) “Minimum SNPs” and ii) the new ’HRMtype’ software packages. Species specific sets of six “Nucleating SNPs” and six HRM fragments were identified for both C. jejuni and C. coli to ensure high typeability and resolution relevant to the MLST database. ‘Minim typing’ was tested empirically by typing 15 C. jejuni and five C. coli isolates. The association of clonal complexes (CC) to each isolate by ‘Minim typing’ and SNP + binary typing were used to compare the two MLST interrogation schemes. The CCs linked with each C. jejuni isolate were consistent for both methods. Thus, ‘Minim typing’ is an efficient and cost effective method to interrogate MLST genes. However, it is not expected to be independent, or meet the resolution of, sequence based MLST gene interrogation. ‘Minim typing’ in combination with flaA HRM is envisaged to comprise a highly resolving combinatorial typing scheme developed around the HRM platform and is amenable to automation and multiplexing. The genotyping techniques described in this thesis involve the combinatorial interrogation of differentially evolving genetic markers on the unified real-time PCR and HRM platform. They provide high resolution and are simple, cost effective and ideally suited to rapid and high throughput genotyping for these common food-borne pathogens.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Long-Duration Solar-powered wireless sensor networks

This paper discusses hardware design principles for long-term solar-powered wireless sensor networks. We argue that the assumptions and principles appropriate for long-term operation from primary cells are quite different from the solar power case with its abundant energy and regular charging cycles. We present data from a long-term deployment that illustrates the use of solar energy and rechargeable batteries to achieve 24x7 operation for over two years, since March 2005.

Use of advanced technology videotapes in the delivery of structual engineering courses

A teaching and learning development project is currently under way at Queensland University of Technology to develop advanced technology videotapes for use with the delivery of structural engineering courses. These tapes consist of integrated computer and laboratory simulations of important concepts, and behaviour of structures and their components for a number of structural engineering subjects. They will be used as part of the regular lectures and thus will not only improve the quality of lectures and learning environment, but also will be able to replace the ever-dwindling laboratory teaching in these subjects. The use of these videotapes, developed using advanced computer graphics, data visualization and video technologies, will enrich the learning process of the current diverse engineering student body. This paper presents the details of this new method, the methodology used, the results and evaluation in relation to one of the structural engineering subjects, steel structures.

Distance Education and the Integration of E-learning in a Graduate Program

Historically, distance education consisted of a combination of face-to-face blocks of time and surface mailed packages. However, advances in information technology literacy and the abundance of personal computers has placed e-learning in increased demand. The authors describe the planning, implementation, and evaluation of the blending of e-learning with face-to-face education in the postgraduate nursing forum. Experiences of this particular student group are also discussed.

Use of advanced computer graphics and data visualisation technologies in teaching and learning of steel structural design

A teaching and learning development project is currently under way at Queens-land University of Technology to develop advanced technology videotapes for use with the delivery of structural engineering courses. These tapes consist of integrated computer and laboratory simulations of important concepts, and behaviour of structures and their components for a number of structural engineering subjects. They will be used as part of the regular lectures and thus will not only improve the quality of lectures and learning environment, but also will be able to replace the ever-dwindling laboratory teaching in these subjects. The use of these videotapes, developed using advanced computer graphics, data visualization and video technologies, will enrich the learning process of the current diverse engineering student body. This paper presents the details of this new method, the methodology used, the results and evaluation in relation to one of the structural engineering subjects, steel structures.

Selective effects of acute exercise and breakfast interventions on mood and motivation to eat

The effects of exercise and breakfast manipulations on mood and motivation to eat were assessed in 11 healthy females who were regular exercisers and habitual breakfast eaters. The study involved a two by two repeated-measures design, with exercise (or no exercise) and a high-energy breakfast (or low-energy breakfast) as the repeated measures. The exercise or no-exercise session (0800 h) was followed by consumption of the low- or high-energy breakfast (0900 h). An ad libitum lunch test meal was provided 4 hours after the beginning of the exercise session (1200 h). Mood and motivation to eat were continuously tracked from 0800 until 1700 h by an electronic appetite ratings system (EARS). In general, morning subjective mood states (e.g., contentment) were significantly lower in the low-energy breakfast condition, but exercise reversed this effect. Exercise also significantly decreased feelings of lethargy, independent of the breakfast condition. Desire-to-eat and fullness ratings were significantly increased in the low-energy breakfast and high-energy breakfast conditions, respectively. Impairments of mood disappeared in the afternoon after consumption of an ad libitum lunch. In these healthy young adults, the condition inducing the largest energy deficit (exercise and low-energy breakfast) was not associated with the lowest mental states.

Improved functional ability and independence in activities of daily living for older adults at high risk of hospital readmission : a randomised controlled trial

Objective: During hospitalisation older people often experience functional decline which impacts on their future independence. The objective of this study was to evaluate a multifaceted transitional care intervention including home-based exercise strategies for at-risk older people on functional status, independence in activities of daily living, and walking ability. Methods: A randomised controlled trial was undertaken in a metropolitan hospital in Australia with 128 patients (64 intervention, 64 control) aged over 65 years with an acute medical admission and at least one risk factor for hospital readmission. The intervention group received an individually tailored program for exercise and follow-up care which was commenced in hospital and included regular visits in hospital by a physiotherapist and a Registered Nurse, a home visit following discharge, and regular telephone follow-up for 24 weeks following discharge. The program was designed to improve health promoting behaviours, strength, stability, endurance and mobility. Data were collected at baseline, then 4, 12 and 24 weeks following discharge using the Index of Activities of Daily Living (ADL), Instrumental Index of Activities of Daily Living (IADL), and the Walking Impairment Questionnaire (Modified). Results: Significant improvements were found in the intervention group in IADL scores (p<.001), ADL scores (p<.001), and WIQ scale scores (p<.001) in comparison to the control group. The greatest improvements were found in the first four weeks following discharge. Conclusions: Early introduction of a transitional model of care incorporating a tailored exercise program and regular telephone follow-up for hospitalised at-risk older adults can improve independence and functional ability.

Analysis of distrubances in large interconnected power systems

World economies increasingly demand reliable and economical power supply and distribution. To achieve this aim the majority of power systems are becoming interconnected, with several power utilities supplying the one large network. One problem that occurs in a large interconnected power system is the regular occurrence of system disturbances which can result in the creation of intra-area oscillating modes. These modes can be regarded as the transient responses of the power system to excitation, which are generally characterised as decaying sinusoids. For a power system operating ideally these transient responses would ideally would have a “ring-down” time of 10-15 seconds. Sometimes equipment failures disturb the ideal operation of power systems and oscillating modes with ring-down times greater than 15 seconds arise. The larger settling times associated with such “poorly damped” modes cause substantial power flows between generation nodes, resulting in significant physical stresses on the power distribution system. If these modes are not just poorly damped but “negatively damped”, catastrophic failures of the system can occur. To ensure system stability and security of large power systems, the potentially dangerous oscillating modes generated from disturbances (such as equipment failure) must be quickly identified. The power utility must then apply appropriate damping control strategies. In power system monitoring there exist two facets of critical interest. The first is the estimation of modal parameters for a power system in normal, stable, operation. The second is the rapid detection of any substantial changes to this normal, stable operation (because of equipment breakdown for example). Most work to date has concentrated on the first of these two facets, i.e. on modal parameter estimation. Numerous modal parameter estimation techniques have been proposed and implemented, but all have limitations [1-13]. One of the key limitations of all existing parameter estimation methods is the fact that they require very long data records to provide accurate parameter estimates. This is a particularly significant problem after a sudden detrimental change in damping. One simply cannot afford to wait long enough to collect the large amounts of data required for existing parameter estimators. Motivated by this gap in the current body of knowledge and practice, the research reported in this thesis focuses heavily on rapid detection of changes (i.e. on the second facet mentioned above). This thesis reports on a number of new algorithms which can rapidly flag whether or not there has been a detrimental change to a stable operating system. It will be seen that the new algorithms enable sudden modal changes to be detected within quite short time frames (typically about 1 minute), using data from power systems in normal operation. The new methods reported in this thesis are summarised below. The Energy Based Detector (EBD): The rationale for this method is that the modal disturbance energy is greater for lightly damped modes than it is for heavily damped modes (because the latter decay more rapidly). Sudden changes in modal energy, then, imply sudden changes in modal damping. Because the method relies on data from power systems in normal operation, the modal disturbances are random. Accordingly, the disturbance energy is modelled as a random process (with the parameters of the model being determined from the power system under consideration). A threshold is then set based on the statistical model. The energy method is very simple to implement and is computationally efficient. It is, however, only able to determine whether or not a sudden modal deterioration has occurred; it cannot identify which mode has deteriorated. For this reason the method is particularly well suited to smaller interconnected power systems that involve only a single mode. Optimal Individual Mode Detector (OIMD): As discussed in the previous paragraph, the energy detector can only determine whether or not a change has occurred; it cannot flag which mode is responsible for the deterioration. The OIMD seeks to address this shortcoming. It uses optimal detection theory to test for sudden changes in individual modes. In practice, one can have an OIMD operating for all modes within a system, so that changes in any of the modes can be detected. Like the energy detector, the OIMD is based on a statistical model and a subsequently derived threshold test. The Kalman Innovation Detector (KID): This detector is an alternative to the OIMD. Unlike the OIMD, however, it does not explicitly monitor individual modes. Rather it relies on a key property of a Kalman filter, namely that the Kalman innovation (the difference between the estimated and observed outputs) is white as long as the Kalman filter model is valid. A Kalman filter model is set to represent a particular power system. If some event in the power system (such as equipment failure) causes a sudden change to the power system, the Kalman model will no longer be valid and the innovation will no longer be white. Furthermore, if there is a detrimental system change, the innovation spectrum will display strong peaks in the spectrum at frequency locations associated with changes. Hence the innovation spectrum can be monitored to both set-off an “alarm” when a change occurs and to identify which modal frequency has given rise to the change. The threshold for alarming is based on the simple Chi-Squared PDF for a normalised white noise spectrum [14, 15]. While the method can identify the mode which has deteriorated, it does not necessarily indicate whether there has been a frequency or damping change. The PPM discussed next can monitor frequency changes and so can provide some discrimination in this regard. The Polynomial Phase Method (PPM): In [16] the cubic phase (CP) function was introduced as a tool for revealing frequency related spectral changes. This thesis extends the cubic phase function to a generalised class of polynomial phase functions which can reveal frequency related spectral changes in power systems. A statistical analysis of the technique is performed. When applied to power system analysis, the PPM can provide knowledge of sudden shifts in frequency through both the new frequency estimate and the polynomial phase coefficient information. This knowledge can be then cross-referenced with other detection methods to provide improved detection benchmarks.