Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Cost effectiveness of antimicrobial catheters in the intensive care unit : Addressing uncertainty in the decision

Introduction: Some types of antimicrobial-coated central venous catheters (A-CVC) have been shown to be cost-effective in preventing catheter-related bloodstream infection (CR-BSI). However, not all types have been evaluated, and there are concerns over the quality and usefulness of these earlier studies. There is uncertainty amongst clinicians over which, if any, antimicrobial-coated central venous catheters to use. We re-evaluated the cost-effectiveness of all commercially available antimicrobialcoated central venous catheters for prevention of catheter-related bloodstream infection in adult intensive care unit (ICU) patients. Methods: We used a Markov decision model to compare the cost-effectiveness of antimicrobial-coated central venous catheters relative to uncoated catheters. Four catheter types were evaluated; minocycline and rifampicin (MR)-coated catheters; silver, platinum and carbon (SPC)-impregnated catheters; and two chlorhexidine and silver sulfadiazine-coated catheters, one coated on the external surface (CH/SSD (ext)) and the other coated on both surfaces (CH/SSD (int/ext)). The incremental cost per qualityadjusted life-year gained and the expected net monetary benefits were estimated for each. Uncertainty arising from data estimates, data quality and heterogeneity was explored in sensitivity analyses. Results: The baseline analysis, with no consideration of uncertainty, indicated all four types of antimicrobial-coated central venous catheters were cost-saving relative to uncoated catheters. Minocycline and rifampicin-coated catheters prevented 15 infections per 1,000 catheters and generated the greatest health benefits, 1.6 quality-adjusted life-years, and cost-savings, AUD $130,289. After considering uncertainty in the current evidence, the minocycline and rifampicin-coated catheters returned the highest incremental monetary net benefits of $948 per catheter; but there was a 62% probability of error in this conclusion. Although the minocycline and rifampicin-coated catheters had the highest monetary net benefits across multiple scenarios, the decision was always associated with high uncertainty. Conclusions: Current evidence suggests that the cost-effectiveness of using antimicrobial-coated central venous catheters within the ICU is highly uncertain. Policies to prevent catheter-related bloodstream infection amongst ICU patients should consider the cost-effectiveness of competing interventions in the light of this uncertainty. Decision makers would do well to consider the current gaps in knowledge and the complexity of producing good quality evidence in this area.

Cost-effectiveness of an intervention to reduce emergency re-admissions to hospital among older patients

Background. The objective is to estimate the cost-effectiveness of an intervention that reduces hospital readmission among older people at high risk. A cost-effectiveness model to estimate the costs and health benefits of the intervention was implemented. Methodology/Principal Findings. The model used data from a randomised controlled trial conducted in an Australian tertiary metropolitan hospital. Participants were acute medical admissions aged >65 years with at least one risk factor for readmission: multiple comorbidities, impaired functionality, aged >75 years, 30 recent multiple admissions, poor social support, history of depression. The intervention was a comprehensive nursing and physiotherapy assessment and an individually tailored program of exercise strategies and nurse home visits with telephone follow-up; commencing in hospital and continuing following discharge for 24 weeks. The change to cost outcomes, including the costs of implementing the intervention and all subsequent use of health care services, and, the change to health benefits, represented by quality adjusted life years, were estimated for the intervention as compared to existing practice. The mean change to total costs and quality 38 adjusted life years for an average individual over 24 weeks participating in the intervention were: cost savings of $333 (95% Bayesian credible interval $-1,932:1,282) and 0.118 extra quality adjusted life years (95% Bayesian credible interval 0.1:0.136). The mean net41 monetary-benefit per individual for the intervention group compared to the usual care condition was $7,907 (95% Bayesian credible interval $5,959:$9,995) for the 24 week period. Conclusions/Significance. The estimation model that describes this intervention predicts cost savings and improved health outcomes. A decision to remain with existing practices causes unnecessary costs and reduced health. Decision makers should consider adopting this 46 program for elderly hospitalised patients.

Cost-effectiveness of a telephone-delivered intervention for physical activity and diet

Background: Given escalating rates of chronic disease, broad-reach and cost-effective interventions to increase physical activity and improve dietary intake are needed. The cost-effectiveness of a Telephone Counselling intervention to improve physical activity and diet, targeting adults with established chronic diseases in a low socio-economic area of a major Australian city was examined. Methodology/Principal Findings: A cost-effectiveness modelling study using data collected between February 2005 and November 2007 from a cluster-randomised trial that compared Telephone Counselling with a “Usual Care” (brief intervention) alternative. Economic outcomes were assessed using a state-transition Markov model, which predicted the progress of participants through five health states relating to physical activity and dietary improvement, for ten years after recruitment. The costs and health benefits of Telephone Counselling, Usual Care and an existing practice (Real Control) group were compared. Telephone Counselling compared to Usual Care was not cost-effective ($78,489 per quality adjusted life year gained). However, the Usual Care group did not represent existing practice and is not a useful comparator for decision making. Comparing Telephone Counselling outcomes to existing practice (Real Control), the intervention was found to be cost-effective ($29,375 per quality adjusted life year gained). Usual Care (brief intervention) compared to existing practice (Real Control) was also cost-effective ($12,153 per quality adjusted life year gained). Conclusions/Significance: This modelling study shows that a decision to adopt a Telephone Counselling program over existing practice (Real Control) is likely to be cost-effective. Choosing the ‘Usual Care’ brief intervention over existing practice (Real Control) shows a lower cost per quality adjusted life year, but the lack of supporting evidence for efficacy or sustainability is an important consideration for decision makers. The economics of behavioural approaches to improving health must be made explicit if decision makers are to be convinced that allocating resources toward such programs is worthwhile.

Determining a set of surrogate parameters to evaluate urban stormwater quality

This thesis details methodology to estimate urban stormwater quality based on a set of easy to measure physico-chemical parameters. These parameters can be used as surrogate parameters to estimate other key water quality parameters. The key pollutants considered in this study are nitrogen compounds, phosphorus compounds and solids. The use of surrogate parameter relationships to evaluate urban stormwater quality will reduce the cost of monitoring and so that scientists will have added capability to generate a large amount of data for more rigorous analysis of key urban stormwater quality processes, namely, pollutant build-up and wash-off. This in turn will assist in the development of more stringent stormwater quality mitigation strategies. The research methodology was based on a series of field investigations, laboratory testing and data analysis. Field investigations were conducted to collect pollutant build-up and wash-off samples from residential roads and roof surfaces. Past research has identified that these impervious surfaces are the primary pollutant sources to urban stormwater runoff. A specially designed vacuum system and rainfall simulator were used in the collection of pollutant build-up and wash-off samples. The collected samples were tested for a range of physico-chemical parameters. Data analysis was conducted using both univariate and multivariate data analysis techniques. Analysis of build-up samples showed that pollutant loads accumulated on road surfaces are higher compared to the pollutant loads on roof surfaces. Furthermore, it was found that the fraction of solids smaller than 150 ìm is the most polluted particle size fraction in solids build-up on both roads and roof surfaces. The analysis of wash-off data confirmed that the simulated wash-off process adopted for this research agrees well with the general understanding of the wash-off process on urban impervious surfaces. The observed pollutant concentrations in wash-off from road surfaces were different to pollutant concentrations in wash-off from roof surfaces. Therefore, firstly, the identification of surrogate parameters was undertaken separately for roads and roof surfaces. Secondly, a common set of surrogate parameter relationships were identified for both surfaces together to evaluate urban stormwater quality. Surrogate parameters were identified for nitrogen, phosphorus and solids separately. Electrical conductivity (EC), total organic carbon (TOC), dissolved organic carbon (DOC), total suspended solids (TSS), total dissolved solids (TDS), total solids (TS) and turbidity (TTU) were selected as the relatively easy to measure parameters. Consequently, surrogate parameters for nitrogen and phosphorus were identified from the set of easy to measure parameters for both road surfaces and roof surfaces. Additionally, surrogate parameters for TSS, TDS and TS which are key indicators of solids were obtained from EC and TTU which can be direct field measurements. The regression relationships which were developed for surrogate parameters and key parameter of interest were of a similar format for road and roof surfaces, namely it was in the form of simple linear regression equations. The identified relationships for road surfaces were DTN-TDS:DOC, TP-TS:TOC, TSS-TTU, TDS-EC and TSTTU: EC. The identified relationships for roof surfaces were DTN-TDS and TSTTU: EC. Some of the relationships developed had a higher confidence interval whilst others had a relatively low confidence interval. The relationships obtained for DTN-TDS, DTN-DOC, TP-TS and TS-EC for road surfaces demonstrated good near site portability potential. Currently, best management practices are focussed on providing treatment measures for stormwater runoff at catchment outlets where separation of road and roof runoff is not found. In this context, it is important to find a common set of surrogate parameter relationships for road surfaces and roof surfaces to evaluate urban stormwater quality. Consequently DTN-TDS, TS-EC and TS-TTU relationships were identified as the common relationships which are capable of providing measurements of DTN and TS irrespective of the surface type.

A cost-based optimization of a fiberboard pressing plant using Monte-Carlo simulation (a reliability program)

In this research the reliability and availability of fiberboard pressing plant is assessed and a cost-based optimization of the system using the Monte- Carlo simulation method is performed. The woodchip and pulp or engineered wood industry in Australia and around the world is a lucrative industry. One such industry is hardboard. The pressing system is the main system, as it converts the wet pulp to fiberboard. The assessment identified the pressing system has the highest downtime throughout the plant plus it represents the bottleneck in the process. A survey in the late nineties revealed there are over one thousand plants around the world, with the pressing system being a common system among these plants. No work has been done to assess or estimate the reliability of such a pressing system; therefore this assessment can be used for assessing any plant of this type.

Closed-form design equations for decoupling networks of small arrays

Small element spacing in compact arrays results in strong mutual coupling between the array elements. A decoupling network consisting of reactive cross-coupling elements can alleviate problems associated with the coupling. Closed-form design equations for the decoupling networks of symmetrical arrays with two or three elements are presented.

Holding cost model for Greenfield Housing developments

Presentation provided to a PhD Colloquium between two Australian and one Malaysian University providing the opportunity to inform and critique progress of students concerning their selected topic. This presentation essentially involves "The conceptualisation, sensitivity and measurement of holding costs and other selected elements impacting housing affordability" as provided by Gary Owen Garner of QUT, with research objectives thus: 1. To establish the nature and composition of holding costs over time, as related to residential property in Australia, and internationally. 2. To examine the linkages that may exist between various planning instruments, the length of regulatory assessment periods, and housing affordability. 3. To develop a model that quantifies the impact of holding costs on housing affordability in Australia, with a particular focus on the consequences of extended assessment periods as a component of holding costs. Thus, provide clarification as to the impact of holding costs on overall housing affordability.

A summary view of government cost recovery policies in Australia and New Zealand relating to the supply of public sector information

Researching administrative history is problematical. A trail of authoritative documents is often hard to find; and useful summaries can be difficult to organise, especially if source material is in paper formats in geographically dispersed locations. In the absence of documents, the reasons for particular decisions and the rationale underpinning particular policies can be confounded as key personnel advance in their professions and retire. The rationale for past decisions may be lost for practical purposes; and if an organisation’s memory of events is diminished, its learning through experience is also diminished. Publishing this document tries to avoid unnecessary duplication of effort by other researchers that need to venture into how policies of charging for public sector information have been justified. The author compiled this work within a somewhat limited time period and the work does not pretend to be a complete or comprehensive analysis of the issues.----- A significant part of the role of government is to provide a framework of legally-enforceable rights and obligations that can support individuals and non-government organisations in their lawful activities. Accordingly, claims that governments should be more ‘business-like’ need careful scrutiny. A significant supply of goods and services occurs as non-market activity where neither benefits nor costs are quantified within conventional accounting systems or in terms of money. Where a government decides to provide information as a service; and information from land registries is archetypical, the transactions occur as a political decision made under a direct or a clearly delegated authority of a parliament with the requisite constitutional powers. This is not a market transaction and the language of the market confuses attempts to describe a number of aspects of how governments allocate resources.----- Cost recovery can be construed as an aspect of taxation that is a sole prerogative of a parliament. The issues are fundamental to political constitutions; but they become more complicated where states cede some taxing powers to a central government as part of a federal system. Nor should the absence of markets be construed necessarily as ‘market failure’ or even ‘government failure’. The absence is often attributable to particular technical, economic and political constraints that preclude the operation of markets. Arguably, greater care is needed in distinguishing between the polity and markets in raising revenues and allocating resources; and that needs to start by removing unhelpful references to ‘business’ in the context of government decision-making.