A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems

Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.Comment: 24 pages, 3 figures, submitted to Astronomical Journal; minor errors in equations and one figure correcte

A Hybrid N-body--Coagulation Code for Planet Formation

We describe a hybrid algorithm to calculate the formation of planets from an initial ensemble of planetesimals. The algorithm uses a coagulation code to treat the growth of planetesimals into oligarchs and explicit N-body calculations to follow the evolution of oligarchs into planets. To validate the N-body portion of the algorithm, we use a battery of tests in planetary dynamics. Several complete calculations of terrestrial planet formation with the hybrid code yield good agreement with previously published calculations. These results demonstrate that the hybrid code provides an accurate treatment of the evolution of planetesimals into planets.Comment: Astronomical Journal, accepted; 33 pages + 11 figure

On an asymptotic method for computing the modified energy for symplectic methods

We revisit an algorithm by Skeel et al. [5,16] for computing the modified, or shadow, energy associated with symplectic discretizations of Hamiltonian systems. We amend the algorithm to use Richardson extrapolation in order to obtain arbitrarily high order of accuracy. Error estimates show that the new method captures the exponentially small drift associated with such discretizations. Several numerical examples illustrate the theory

Evaluation of Rehabilitation of Memory in Neurological Disabilities (ReMiND): a randomized controlled trial

OBJECTIVE:The evidence for the effectiveness of memory rehabilitation is inconclusive. The aim was to compare the effectiveness of two group memory rehabilitation programmes with a self-help group control. DESIGN:Single-blind randomized controlled trial. PARTICIPANTS:Participants with memory problems following traumatic brain injury, stroke or multiple sclerosis were recruited from community settings. INTERVENTIONS:Participants were randomly allocated, in cohorts of four, to compensation or restitution group treatment programmes or a self-help group control. All programmes were manual-based and comprised two individual and ten weekly group sessions. MAIN MEASURES:Memory functions, mood, and activities of daily living were assessed at baseline and five and seven months after randomization. RESULTS:There were 72 participants (mean age 47.7, SD 10.2 years; 32 men). There was no significant effect of treatment on the Everyday Memory Questionnaire (P = 0.97). At seven months the mean scores were comparable (restitution 36.6, compensation 41.0, self-help 44.1). However, there was a significant difference between groups on the Internal Memory Aids Questionnaire (P = 0.002). The compensation and restitution groups each used significantly more internal memory aids than the self-help group (P 0.05). CONCLUSIONS:There results show few statistically significant effects of either compensation or restitution memory group treatment as compared with a self-help group control. Further randomized trials of memory rehabilitation are needed

Improving corporate governance in state-owned corporations in China: which way forward?

This article discusses corporate governance in China. It outlines the basic agency problem in Chinese listed companies and questions the effectiveness of the current mechanisms employed to improve their standards of governance. Importantly, it considers alternative means through which corporate practice in China can be brought into line with international expectations and stresses the urgency with which this task must be tackled. It concludes that regulators in China must construct a corporate governance model which is compatible with its domestic setting and not rush to adopt governance initiatives modelled on those in cultures which are fundamentally different in the hope of also reproducing their success

Construction of a Mean Square Error Adaptive Euler--Maruyama Method with Applications in Multilevel Monte Carlo

A formal mean square error expansion (MSE) is derived for Euler--Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise a posteriori adaptive time stepping Euler--Maruyama method for numerical solutions of SDE, and the resulting method is incorporated into a multilevel Monte Carlo (MLMC) method for weak approximations of SDE. This gives an efficient MSE adaptive MLMC method for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC method is shown to outperform the uniform time stepping MLMC method by orders of magnitude, producing output whose error with high probability is bounded by TOL>0 at the near-optimal MLMC cost rate O(TOL^{-2}log(TOL)^4).Comment: 43 pages, 12 figure

Rehabilitation of memory following brain injury (ReMemBrIn): study protocol for a randomised controlled trial

Background Impairments of memory are commonly reported by people with traumatic brain injuries (TBI). Such deficits are persistent, debilitating, and can severely impact quality of life. Currently, many do not routinely receive follow-up appointments for residual memory problems following discharge. Methods/Design This is a multi-centre, randomised controlled trial investigating the clinical and cost-effectiveness of a group-based memory rehabilitation programme. Three hundred and twelve people with a traumatic brain injury will be randomised from four centres. Participants will be eligible if they had a traumatic brain injury more than 3 months prior to recruitment, have memory problems, are 18 to 69 years of age, are able to travel to one of our centres and attend group sessions, and are able to give informed consent. Participants will be randomised in clusters of 4 to 6 to the group rehabilitation intervention or to usual care. Intervention groups will receive 10 weekly sessions of a manualised memory rehabilitation programme, which has been developed in previous pilot studies. The intervention will include restitution strategies to retrain impaired memory functions and compensation strategies to enable participants to cope with their memory problems. All participants will receive a follow-up postal questionnaire and an assessment by a research assistant at 6 and 12 months post-randomisation. The primary outcome is the Everyday Memory Questionnaire at 6 months. Secondary outcomes include the Rivermead Behavioural Memory Test-3, General Health Questionnaire-30, health related quality of life, cost-effectiveness analysis determined by the EQ-5D and a service use questionnaire, individual goal attainment, European Brain Injury Questionnaire (patient and relative versions), and the Everyday Memory Questionnaire-relative version. The primary analysis will be based on intention to treat. A mixed-model regression analysis of the Everyday Memory Questionnaire at 6 months will be used to estimate the effect of the group memory rehabilitation programme. Discussion The study will hopefully provide robust evidence regarding the clinical and cost-effectiveness of a group-based memory rehabilitation intervention for civilians and military personnel following TBI. We discuss our decision-making regarding choice of outcome measures and control group, and the unique challenges to recruiting people with memory problems to trials

Psychosocial interventions for patients with advanced cancer – a systematic review of the literature

Advanced cancer is associated with emotional distress, especially depression and feelings of sadness. To date, it is unclear which is the most effective way to address these problems. This review focuses on the effects of psychosocial interventions on the quality of life (QoL) of patients with advanced cancer. It was hypothesised that patients will benefit from psychosocial interventions by improving QoL, especially in the domain of emotional functioning. The review was conducted using systematic review methodology involving a systematic search of the literature published between 1990 and 2002, quality assessment of included studies, systematic data extraction and narrative data synthesis. In all, 10 randomised controlled studies involving 13 trials were included. Overall interventions and outcome measures across studies were heterogeneous. Outcome measures, pertaining to the QoL dimension of emotional functioning, were most frequently measured. A total of 12 trials evaluating behaviour therapy found positive effects on one or more indicators of QoL, for example, depression. The results of the review support recommendation of behaviour therapy in the care of patients with advanced cancer