Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Issues in Australian Foreign Policy: January to June 2002

No abstract

Remitting behaviour of Nepalese rural-to-urban migrants: Implications for theory and policy

This article uses data for Nepal to test contemporary hypotheses about the remitting behaviour and associated motives of rural-to-urban migrants and to consider the likely impact of such remittances on rural development. Possibilities for inheritance, degree of family attachment, likelihood of eventual return to place of origin and family investment in the education of the migrants are found to be significant influences on levels of remittances by Nepalese migrants. However, in Nepal, remittances do not seem to result in long-term capital investment in rural areas and so may not promote long-term development of these areas.

Evaluating Australia's National Medicines Policy using geographical mapping

Background: There has been a proliferation of quality use of medicines activities in Australia since the 1990s. However, knowledge of the nature and extent of these activities was lacking. A mechanism was required to map the activities to enable their coordination. Aims: To develop a geographical mapping facility as an evaluative tool to assist the planning and implementation of Australia's policy on the quality use of medicines. Methods: A web-based database incorporating geographical mapping software was developed. Quality use of medicines projects implemented across the country was identified from project listings funded by the Quality Use of Medicines Evaluation Program, the National Health and Medical Research Council, Mental Health Strategy, Rural Health Support, Education and Training Program, the Healthy Seniors Initiative, the General Practice Evaluation Program and the Drug Utilisation Evaluation Network. In addition, projects were identified through direct mail to persons working in the field. Results: The Quality Use of Medicines Mapping Project (QUMMP) was developed, providing a Web-based database that can be continuously updated. This database showed the distribution of quality use of medicines activities by: (i) geographical region, (ii) project type, (iii) target group, (iv) stakeholder involvement, (v) funding body and (vi) evaluation method. At September 2001, the database included 901 projects. Sixty-two per cent of projects had been conducted in Australian capital cities, where approximately 63% of the population reside. Distribution of projects varied between States. In Western Australia and Queensland, 36 and 73 projects had been conducted, respectively, representing approximately two projects per 100 000 people. By comparison, in South Australia and Tasmania approximately seven projects per 100 000 people were recorded, with six per 100 000 people in Victoria and three per 100 000 people in New South Wales. Rural and remote areas of the country had more limited project activity. Conclusions: The mapping of projects by geographical location enabled easy identification of high and low activity areas. Analysis of the types of projects undertaken in each region enabled identification of target groups that had not been involved or services that had not yet been developed. This served as a powerful tool for policy planning and implementation and will be used to support the continued implementation of Australia's policy on the quality use of medicines.

Impact numbers in health policy decisions

Objective: To outline the major methodological issues appropriate to the use of the population impact number (PIN) and the disease impact number (DIN) in health policy decision making. Design: Review of literature and calculation of PIN and DIN statistics in different settings. Setting: Previously proposed extensions to the number needed to treat (NNT): the DIN and the PIN, which give a population perspective to this measure. Main results: The PIN and DIN allow us to compare the population impact of different interventions either within the same disease or in different diseases or conditions. The primary studies used for relative risk estimates should have outcomes, time periods and comparison groups that are congruent and relevant to the local setting. These need to be combined with local data on disease rates and population size. Depending on the particular problem, the target may be disease incidence or prevalence and the effects of interest may be either the incremental impact or the total impact of each intervention. For practical application, it will be important to use sensitivity analyses to determine plausible intervals for the impact numbers. Conclusions: Attention to various methodological issues will permit the DIN and PIN to be used to assist health policy makers assign a population perspective to measures of risk.

Public policy and the prevention of substance-use disorders

Drug prevention has traditionally focused on influencing individual attitudes and behaviours. In particular, efforts have been directed towards adolescents in the school setting. However, evaluations of school-based drug education have identified limited success. There is increasing recognition that drug abuse is one of a number of risk behaviours, including truancy, delinquency and mental health problems, which share common antecedents that begin in the early years of childhood. Furthermore, these behaviours are shaped by macroenvironmental influences including the economic, social, cultural, and physical environment. Drug prevention needs to adopt a broader perspective: with greater collaboration in related programmes such as crime prevention and suicide prevention; with greater attention to the macroenvironmental influences on problem behaviours; and with greater attention to healthy development in the first years of childhood. (C) 2002 Lippincott Williams Wilkins.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Initial effects of elbow taping on pain-free grip strength and pressure pain threshold

Study design: Single-blind, placebo control, randomized, crossover, experimental Study with repeated measures, Objective: To determine the initial effects of a taping technique on grip strength and pain in individuals with lateral epicondylalgia. Background: Taping techniques are advocated for chronic musculoskeletal conditions such as lateral epicondylalgia, a prevalent disorder with significant impact on the individual and community. Little evidence exists supporting the effects of taping techniques on musculoskeletal pain. Methods and Measures: Sixteen participants (mean age +/- SD, 45.8 +/- 10.2 years) with chronic lateral epicondylalgia (rnean duration +/- SD, 13.1 +/- 9.9 months) participated in a placebo control study of an elbow taping technique. Outcome measures were pain-free grip strength and pressure pain threshold taken before, immediately after, and 30 minutes after application of tape. Results: The taping technique significantly improved pain-free grip strength by 24% from baseline (P = .028). The treatment effect was greater than that for placebo and control conditions. Changes in pressure pain threshold (19%), although positive, were not statistically significant. Conclusion: This preliminary study demonstrated an initial ameliorative effect of a taping technique for lateral epicondylalgia and suggests that it should be considered as an adjunct in the management of this condition.