A method is proposed for the numerical solution of Ito stochastic differential equations by means of a second-order Runge-Kutta iterative scheme rather than the less efficient Euler iterative scheme. It requires the Runge-Kutta iterative scheme to be applied to a different stochastic differential equation obtained by subtraction of a correction term from the given one.It was observed by Wright [8] that different iterative schemes for the numerical solution of stochastic differential equationswhere £, is a Wiener process, converge to different solutions for the same noise sample and initial condition. This is in contrast to their deterministic counterparts for ordinary differential equations, which converge to the same solution.Strictly speaking stochastic differentia] equations (1) are really integral equationsx t = x 0 +\ a(s,x s )ds+\ b(s,x s )d£ s ,[2]Stochastic differential equations 9

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IntroductionPeople with mobility limitations can benefit from rehabilitation programmes that provide a high dose of exercise. However, since providing a high dose of exercise is logistically challenging and resource-intensive, people in rehabilitation spend most of the day inactive. This trial aims to evaluate the effect of the addition of affordable technology to usual care on physical activity and mobility in people with mobility limitations admitted to inpatient aged and neurological rehabilitation units compared to usual care alone.Methods and analysisA pragmatic, assessor blinded, parallel-group randomised trial recruiting 300 consenting rehabilitation patients with reduced mobility will be conducted. Participants will be individually randomised to intervention or control groups. The intervention group will receive technology-based exercise to target mobility and physical activity problems for 6 months. The technology will include the use of video and computer games/exercises and tablet applications as well as activity monitors. The control group will not receive any additional intervention and both groups will receive usual inpatient and outpatient rehabilitation care over the 6-month study period. The coprimary outcomes will be objectively assessed physical activity (proportion of the day spent upright) and mobility (Short Physical Performance Battery) at 6 months after randomisation. Secondary outcomes will include: self-reported and objectively assessed physical activity, mobility, cognition, activity performance and participation, utility-based quality of life, balance confidence, technology self-efficacy, falls and service utilisation. Linear models will assess the effect of group allocation for each continuously scored outcome measure with baseline scores entered as a covariate. Fall rates between groups will be compared using negative binomial regression. Primary analyses will be preplanned, conducted while masked to group allocation and use an intention-to-treat approach.Ethics and disseminationThe protocol has been approved by the relevant Human Research Ethics Committees and the results will be disseminated widely through peer-reviewed publication and conference presentations.Trial registration numberACTRN12614000936628. Pre-results.

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In many complex, real-world situations, problem solving and decision making require effective reasoning about causation and uncertainty. However, human reasoning in these cases is prone to confusion and error. Bayesian networks (BNs) are an artificial intelligence technology that models uncertain situations, supporting better probabilistic and causal reasoning and decision making. However, to date, BN methodologies and software require (but do not include) substantial upfront training, do not provide much guidance on either the model building process or on using the model for reasoning and reporting, and provide no support for building BNs collaboratively. Here, we contribute a detailed description and motivation for our new methodology and application, Bayesian ARgumentation via Delphi (BARD). BARD utilizes BNs and addresses these shortcomings by integrating (1) short, high-quality e-courses, tips, and help on demand; (2) a stepwise, iterative, and incremental BN construction process; (3) report templates and an automated explanation tool; and (4) a multiuser web-based software platform and Delphi-style social processes. The result is an end-to-end online platform, with associated online training, for groups without prior BN expertise to understand and analyze a problem, build a model of its underlying probabilistic causal structure, validate and reason with the causal model, and (optionally) use it to produce a written analytic report. Initial experiments demonstrate that, for suitable problems, BARD aids in reasoning and reporting. Comparing their effect sizes also suggests BARD's BN-building and collaboration combine beneficially and cumulatively.

As replications of individual studies are resource intensive, techniques for predicting the replicability are required. We introduce the repliCATS (Collaborative Assessments for Trustworthy Science) process, a new method for eliciting expert predictions about the replicability of research. This process is a structured expert elicitation approach based on a modified Delphi technique applied to the evaluation of research claims in social and behavioural sciences. The utility of processes to predict replicability is their capacity to test scientific claims without the costs of full replication. Experimental data supports the validity of this process, with a validation study producing a classification accuracy of 84% and an Area Under the Curve of 0.94, meeting or exceeding the accuracy of other techniques used to predict replicability. The repliCATS process provides other benefits. It is highly scalable, able to be deployed for both rapid assessment of small numbers of claims, and assessment of high volumes of claims over an extended period through an online elicitation platform, having been used to assess 3000 research claims over an 18 month period. It is available to be implemented in a range of ways and we describe one such implementation. An important advantage of the repliCATS process is that it collects qualitative data that has the potential to provide insight in understanding the limits of generalizability of scientific claims. The primary limitation of the repliCATS process is its reliance on human-derived predictions with consequent costs in terms of participant fatigue although careful design can minimise these costs. The repliCATS process has potential applications in alternative peer review and in the allocation of effort for replication studies.

SUMMARYA quasi-geostrophic mean flow can form the basic state upon which a sea breeze is superimposed; a model is described. With a mean flow perpendicular to the coast the speed of the sea breeze front is shown to be a linear function of the onshore component of the mean flow. When a constant mean flow is introduced the general structure of the sea breeze is unchanged. In particular, for a constant energy input the intensity is also unaltered. In contrast, a shear changes the general qualitative structure but leaves the speed of the front and the intensity of the sea breeze unchanged. These features are consistent with the available potential energy of the system and a constant transfer, per unit area, of this into kinetic energy. Model results and other studies are discussed.