Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

The new wave : a Brisbane perspective : La Boite Theatre Company's distinctive contribution

In 1967 Brisbane Repertory Theatre made a decision that was to change the city's cultural landscape in a significant and lasting way. Faced with crippling theatre rental costs, Brisbane Rep. found a realistic solution by converting one of its properties - an old Queenslander - into a unique theatre space. The theatre-in-the box that emerged, aptly called La Boite, opened on 23 June 1967 with a production of John Osborne's Look Back in Anger. This experimental space excited the imagination of a new, younger audience not previously interested in Brisbane Rep's essentially conservative fare. It attracted a new group of directors and actors keen to be part of a changing repertoire that embraced more radical, non-mainstream productions, some of which were of Australian plays. The decade after 1967 was a period of change and development unprecedented in La Boite's history. Since then the company has sustained and grown its commitment to Australian plays and the commissioning of new works. To what extent was this most significance moment in La Boite's transformational journey influenced by southern 'new waves' of change? With the benefit of hindsight, it is now time for a re-consideration of Brisbane's distinctive contribution to the New Wave.

Population-based survival estimates for childhood cancer in Australia during the period 1997–2006

Background: This study provides the latest available relative survival data for Australian childhood cancer patients. Methods: Data from the population-based Australian Paediatric Cancer Registry were used to describe relative survival outcomes using the period method for 11 903 children diagnosed with cancer between 1983 and 2006 and prevalent at any time between 1997 and 2006. Results: The overall relative survival was 90.4% after 1 year, 79.5% after 5 years and 74.7% after 20 years. Where information onstage at diagnosis was available (lymphomas, neuroblastoma, renal tumours and rhabdomyosarcomas), survival was significantly poorer for more-advanced stage. Survival was lower among infants compared with other children for those diagnosed with leukaemia, tumours of the central nervous system and renal tumours but higher for neuroblastoma. Recent improvements in overall childhood cancer survival over time are mainly because of improvements among leukaemia patients. Conclusion: The high and improving survival prognosis for children diagnosed with cancer in Australia is consistent with various international estimates. However, a 5-year survival estimate of 79% still means that many children who are diagnosed with cancer will die within 5 years, whereas others have long-term health morbidities and complications associated with their treatments. It is hoped that continued developments in treatment protocols will result in further improvements in survival.

If Kate voted conservative would you? The role of celebrity endorsements in political party advertising

Purpose – This research has been conducted with the aim of determining if celebrity endorsers in political party advertising have a significant impact on UK voter intentions. The use of celebrity endorsements is commonplace in the USA, but little is known about its effects in the UK. This research also aims to incorporate the use of celebrity endorsements in political party advertising with the political salience construct. Political salience represents how prominent politics and political issues are in the minds of the eligible voter. Design/methodology/approach – A 2 (endorser: celebrity; non-celebrity) £ 2 (political salience: high; low) between-subjects factorial design experiment was used. The results show that celebrity endorsements do play a significant role in attitudes towards the political advert, attitudes towards the endorser and voter intention. However, this effect is significantly moderated by political salience. Findings – The results show that low political salience respondents were significantly more likely to vote for the political party when a celebrity endorser is used. However, the inverse effect is found for high political salience respondents. Practical implications – The results offer significant insights into the effect that celebrity endorsers could have in future elections and the importance that political salience plays in the effectiveness of celebrity endorsement. If political parties are to target those citizens that do not actively engage with politics then the use of celebrity endorsements would make a significant impact, given the results of this research. Originality/value – This research would be of particular interest to political party campaigners as well as academics studying the effects of advertising and identity salience.

A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

Ovine Enzootic Abortion (OEA): a comparison of antibody responses in vaccinated and naturally-infected swiss sheep over a two year period

Background Prevention and control of ovine enzootic abortion (OEA) can be achieved by application of a live vaccine. In this study, five sheep flocks with different vaccination and infection status were serologically tested using a competitive enzyme-linked immunosorbent assay (cELISA) specific for Chlamydophila (Cp.) abortus over a two-year time period. Results Sheep in Flock A with recent OEA history had high antibody values after vaccination similar to Flock C with natural Cp. abortus infections. In contrast, OEA serology negative sheep (Flock E) showed individual animal-specific immunoreactions after vaccination. Antibody levels of vaccinated ewes in Flock B ranged from negative to positive two and three years after vaccination, respectively. Positive antibody values in the negative control Flock D (without OEA or vaccination) are probably due to asymptomatic intestinal infections with Cp. abortus. Excretion of the attenuated strain of Cp. abortus used in the live vaccine through the eye was not observed in vaccinated animals of Flock E. Conclusion The findings of our study indicate that, using serology, no distinction can be made between vaccinated and naturally infected sheep. As a result, confirmation of a negative OEA status in vaccinated animals by serology cannot be determined.

Caring for women suffering depression in the postnatal period

The research and theoretical perspectives that underpin knowledge of depression in the postnatal period have tended to rely on standardized measures and 'objective' data which combine to disempower women's individual experiences. From a feminist perspective, contradictions exist between women's accounts of the early days and months following childbirth and the diagnosis of postnatal depression made by some health professionals. A framework for nursing care that uses the strengths of feminist and cognitive therapies is suggested. From this feminist-cognitive perspective, mental health nursing care will provide opportunities for women suffering depression to debrief the experience of birth and pregnancy, manage conflicts about identity, gain a sense of survival, and develop a new perspective.

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of autocorrelated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.

Mothers' sleep and driving in the postpartum period

Introduction: Previous studies investigating mothers’ sleep in the postpartum period commonly demonstrated elevated levels of sleepiness in this population. A Karolinska Sleepiness Scale (KSS) rating of 5 or above is associated with an exponential increase in vehicle crash risk. To date, no studies have investigated the relationship between mothers’ sleep in the postpartum period and their driving behaviour. Methods: Sleep-wake diary data was collected from 14 mother-infant dyads during two 7-day assessment periods when the infants were 6 and 12 weeks old. The mothers’ indicated all driving episodes during these weeks and their respective sleepiness level using the KSS. Semi-structured interviews were conducted with the mothers when their infant was 12 weeks old. Results: The infants slept significantly more than their mothers at 6 weeks and 12 weeks of age. During both time points, mothers and infants had a similar number of night awakenings (waking between 22:00 and 06:00), with some mothers experiencing greater than 19 awakenings over 7 nights. Notably, 36% of the mothers did not experience a continuous sleep period longer than 4.5 hours when their infant was 6 weeks old. A total of 141 driving episodes were reported during the 7 day assessment period when the infants were 6 weeks old. Over 50% of the driving episodes were denoted with a KSS score of 5 or above. Strategies mothers cited they employed during this period included only driving when feeling alert, postponing driving until another person is present, and driving in the morning when less sleepy. Conclusion: Mothers are experiencing disrupted sleep at night and some mothers do not obtain more than 4.5 hours of continuous sleep during the early postpartum weeks. In this sample, some mothers reported self-regulating driving behaviour, however over half of the driving episodes were undertaken with a sleepiness rating linked with elevated crash risk.

Were regulatory changes in reporting "abnormal items" justified? : evidence of intra-period classificatory earnings management practices in Australia

Purpose Managers generally have discretion in determining how components of earnings are presented in financial statements in distinguishing between ‘normal’ earnings and items classified as unusual, special, significant, exceptional or abnormal. Prior research has found that such intra-period classificatory choice is used as a form of earnings management. Prior to 2001, Australian accounting standards mandated that unusually large items of revenue and expense be classified as ‘abnormal items’ for financial reporting, but this classification was removed from accounting standards from 2001. This move by the regulators was partly in response to concerns that the abnormal classification was being used opportunistically to manage reported pre-abnormal earnings. This study extends the earnings management literature by examining the reporting of abnormal items for evidence of intra-period classificatory earnings management in the unique Australian setting. Design/methodology/approach This study investigates associations between reporting of abnormal items and incentives in the form of analyst following and the earnings benchmarks of analysts’ forecasts, earnings levels, and earnings changes, for a sample of Australian top-500 firms for the seven-year period from 1994 to 2000. Findings The findings suggest there are systematic differences between firms reporting abnormal items and those with no abnormal items. Results show evidence that, on average, firms shifted expense items from pre-abnormal earnings to bottom line net income through reclassification as abnormal losses. Originality/value These findings suggest that the standard setters were justified in removing the ‘abnormal’ classification from the accounting standard. However, it cannot be assumed that all firms acted opportunistically in the classification of items as abnormal. With the removal of the standardised classification of items outside normal operations as ‘abnormal’, firms lost the opportunity to use such disclosures as a signalling device, with the consequential effect of limiting the scope of effectively communicating information about the nature of items presented in financial reports.