A unifying framework for teaching probability event types

The concepts and mathematics of mutually exclusive, dependent and independent events are developed in a unifying framework of event association

Lagrange multipliers, adjoint equations, the Pontryagin maximum principle and heuristic proofs

Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to a constrained static optimization problem

Volunteering among Christian church attendees 1991-2006

Although volunteering is a strongly held value in many Christian churches, there may be important denominational differences in the extent to which this volunteering is encouraged as a church activity or whether attendees volunteer in the wider community. Some information about the voluntary activities of church attendees across Australia was collected as part of the National Church Life Surveys in 1991, 1996, 2001 and 2006. This analysis examined denominational differences in volunteering within and beyond the congregation to identify whether the patterns have changed or remained stable over time. Involvement in social welfare and social justice volunteering also showed a fairly stable denominational pattern across the four years for both congregational-based and community-based involvement. Information on the total hours of volunteering was collected in 2001 and 2006 only. After demographic differences were taken into account, Pentecostals volunteered more hours within the congregation and Catholics volunteered fewer; however, there were no denominational differences in hours of volunteering beyond the congregation. The number of hours volunteered in each congregation was stable across 2001 and 2006. The strongest finding was that volunteering within the congregation was strongly related to volunteering beyond the congregation with many people volunteering in both the congregation and the community

Analysis of long-term water quality for effective river health monitoring in peri-urban landscapes : a case study of the Hawkesbury-Nepean river system in NSW, Australia

The Hawkesbury-Nepean River (HNR) system in South-Eastern Australia is the main source of water supply for the Sydney Metropolitan area and is one of the more complex river systems due to the influence of urbanisation and other activities in the peri-urban landscape through which it flows. The long-term monitoring of river water quality is likely to suffer from data gaps due to funding cuts, changes in priority and related reasons. Nevertheless, we need to assess river health based on the available information. In this study, we demonstrated how the Factor Analysis (FA), Hierarchical Agglomerative Cluster Analysis (HACA) and Trend Analysis (TA) can be applied to evaluate long-term historic data sets. Six water quality parameters, viz., temperature, chlorophyll-a, dissolved oxygen, oxides of nitrogen, suspended solids and reactive silicates, measured at weekly intervals between 1985 and 2008 at 12 monitoring stations located along the 300 km length of the HNR system were evaluated to understand the human and natural influences on the river system in a peri-urban landscape. The application of FA extracted three latent factors which explained more than 70% of the total variance of the data and related to the ‘bio-geographical’, ‘natural’ and ‘nutrient pollutant’ dimensions of the HNR system. The bio-geographical and nutrient pollution factors more likely related to the direct influence of changes and activities of peri-urban natures and accounted for approximately 50% of variability in water quality. The application of HACA indicated two major clusters representing clean and polluted zones of the river. On the spatial scale, one cluster was represented by the upper and lower sections of the river (clean zone) and accounted for approximately 158 km of the river. The other cluster was represented by the middle section (polluted zone) with a length of approximately 98 km. Trend Analysis indicated how the point sources influence river water quality on spatio-temporal scales, taking into account the various effects of nutrient and other pollutant loads from sewerage effluents, agriculture and other point and non-point sources along the river and major tributaries of the HNR. Over the past 26 years, water temperature has significantly increased while suspended solids have significantly decreased (p<0.05). The analysis of water quality data through FA, HACA and TA helped to characterise the key sections and cluster the key water quality variables of the HNR system. The insights gained from this study have the potential to improve the effectiveness of river health-monitoring programs in terms of cost, time and effort, particularly in a peri-urban context

Some combinatorial and recurrence relations for shapes in a trellis

The first author in 2002 (when aged 10) raised a number of non-trivial questions, namely, in any representation of a trellis fence of a specified size: how many squares are there? How many symmetric crosses are there? How many rectangles are there? How many crosses, symmetric or asymmetric, are there? This paper outlines the salient features of the sub-problems in order to bring out the interplay of the combinatorial and number theoretic relations and to open up further related research

Disaster medical assistance teams : what psychosocial support is needed?

Objective: The objective of this preliminary study was to evaluate the perceptions of internationally deployed Disaster Medical Assistance Team (DMAT) personnel regarding the psychosocial support needs of these teams.Methods: The DMAT questionnaire was sent to 34 members of Australian medical teams involved in deployments to the 2004 Southeast Asian tsunami and the 2006 Java earthquake. Twenty personnel (59%) completed this survey, which reviewed key deployment stressors, specific support strategies, and the support needs of team members, their families, and team leaders. A key aspect of the survey was to determine whether the perceived psychosocial needs would be supported best within with existing provisions and structures, or if they would be enhanced by further provisions, including the deployment of mental health specialists.Results: There was strong support for brief reviews of stress management strategies as part of the pre-deployment briefing, and access to written stress management information for both team members and their families. However, more comprehensive provisions, including pre-deployment, stressmanagement training programs for personnel and intra-deployment family support programs, received lower levels of support. The availability of mental health-related training for the team leader role and access to consultation with mental health specialists was supported, but this did not extend to the actual deployment of mental health specialists.Conclusions: In this preliminary study, clear trends toward the maintenance of current mental health support provisions and the role of the DMAT leader were evident. A follow-up study will examine the relationship between teamleader, psychosocial support strategies and team functioning

Drama therapy with older people with dementia : does it improve quality of life?

This article describes a pilot study that aimed to evaluate the effect of drama therapy on the quality of life (QoL) of elderly people with mild to moderate dementia, using a mixed method (quantitative and qualitative) approach.Study participants (N=13; age range 61-88 years; 1 female) were Australians of European descent, principally with Alzheimer's disease, living in the community in an east-coast Australian context. The drama therapy group (N=4) was compared with a group of participants (N=9) who watched movies over a four-month period. All participants were assessed for QoL using the quantitative Quality of Life Alzheimer's Disease (QoL-AD) scale of Logsdon, Gibbons, McCurry, & Teri (1999, Journal of Mental Health and Aging 5, 21) prior to and following 16 group meetings. Qualitative data were generated and examined using phenomenological methods including recording and transcribing body language and dialogue, as well as narrative, ethnography, group themes and metaphor.Although not statistically significantly different, the average QoL-AD score increased for the drama therapy group while it decreased for the movie group. Qualitative findings established an unambiguous participant ability to express ideas and feelings through drama therapy as well as an unveiling of conscious awareness of participants' own wellbeing and QoL. The findings also indicate the potential worth of a future larger study along the lines exemplified here

The acute haemodynamic effect of nebulised frusemide in stable, advanced heart failure

Purpose: To assess the acute haemodynamic effects of nebulised frusemide in a stable advanced heart failure population. Procedure: In this randomised, double blind, placebo controlled trial, people with stable, advanced heart failure undergoing right heart catheterisation were randomised to receive either 40mg (4ml) of nebulised frusemide or 4ml of normal saline. Following inhalation of the study medication, subjects' pulmonary pressures were recorded every 15 min for 1h. Findings: There were no significant changes in the weighted average time course data of the subjects (n= 32) in either group over the study period, in particular no differences were observed in haemodynamic parameters between the two groups. Weighted average pulmonary capillary wedge pressure after 60. min in the frusemide group was 22.5 (SD 6.5) mmHg (n= 14) compared to the placebo group's 24.0 (SD 7.3) mmHg (n= 18), p= 0.55. The frusemide group had a significantly greater change in the median volume of urine in the bladder over the study period (186ml IQR 137.8-260.8) compared to the placebo group (76ml IQR 39.0-148.0) p= 0.02. Conclusion: This study showed that nebulised frusemide had no significant clinical effect on the haemodynamic characteristics of the subjects

Influence of body weight on the performance of glomerular filtration rate estimators in subjects with type 2 diabetes

The American Diabetes Association recommends estimation of glomerular filtration rate (GFR) (1) by either the Cockcroft-Gault (2) or the Modification of Diet in Renal Disease (MDRD) (3) equation in all patients with diabetes. The implication is that these equations provide similar results. Body weight is a numerator in the Cockcroft- Gault equation; however, it is absent from the MDRD equation. This may explain some of the difference in the ability of these equations to estimate GFR in patients with type 2 diabetes, over 80% of whom are obese (4), and may lead to discrepancies in reporting of chronic kidney disease stage (5). Our study was designed to identify whether body weight may explain variability in performance between the Cockcroft-Gault and MDRD equations in patients newly diagnosed with type 2 diabetes