Virtually abelian K\"ahler and projective groups

We characterise the virtually abelian groups which are fundamental groups of compact K\"ahler manifolds and of smooth projective varieties. We show that a virtually abelian group is K\"ahler if and only if it is projective. In particular, this allows to describe the K\"ahler condition for such groups in terms of integral symplectic representations

A development study and randomised feasibility trial of a tailored intervention to improve activity and reduce falls in older adults with mild cognitive impairment and mild dementia

Background: People with dementia progressively lose abilities and are prone to falling. Exercise- and activity-based interventions hold the prospect of increasing abilities, reducing falls, and slowing decline in cognition. Current falls prevention approaches are poorly suited to people with dementia, however, and are of uncertain effectiveness. We used multiple sources, and a co-production approach, to develop a new intervention, which we will evaluate in a feasibility randomised controlled trial (RCT), with embedded adherence, process and economic analyses. Methods: We will recruit people with mild cognitive impairment or mild dementia from memory assessment clinics, and a family member or carer. We will randomise participants between a therapy programme with high intensity supervision over 12 months, a therapy programme with moderate intensity supervision over 3 months, and brief falls assessment and advice as a control intervention. The therapy programmes will be delivered at home by mental health specialist therapists and therapy assistants. We will measure activities of daily living, falls and a battery of intermediate and distal health status outcomes, including activity, balance, cognition, mood and quality of life. The main aim is to test recruitment and retention, intervention delivery, data collection and other trial processes in advance of a planned definitive RCT. We will also study motivation and adherence, and conduct a process evaluation to help understand why results occurred using mixed methods, including a qualitative interview study and scales measuring psychological, motivation and communication variables. We will undertake an economic study, including modelling of future impact and cost to end-of-life, and a social return on investment analysis. Discussion: In this study, we aim to better understand the practicalities of both intervention and research delivery, and to generate substantial new knowledge on motivation, adherence and the approach to economic analysis. This will enable us to refine a novel intervention to promote activity and safety after a diagnosis of dementia, which will be evaluated in a definitive randomised controlled trial.\ud Trial registration: ClinicalTrials.gov: NCT02874300; ISRCTN 10550694

A randomised controlled trial comparing the effectiveness of Tai Chi alongside usual care with usual care alone on the postural balance of community-dwelling people with dementia: Protocol for The TACIT Trial (TAi ChI for people with dementia).

Background: Falls are a public health issue for the older adult population and more so for people with dementia (PWD). Compared with their cognitively intact peers, PWD are at higher risk of falls and injurious falls. This randomised controlled trial aims to test the clinical and cost effectiveness of Tai Chi to improve postural balance among community-dwelling PWD and to assess the feasibility of conducting a larger definitive trial to reduce the incidence of falls among PWD. Methods: A 3-centre parallel group randomised controlled trial with embedded process evaluation. One hundred and fifty community-dwelling dyads of a person with dementia and their informal carer will be recruited and assessed at baseline and at six-month follow-up. Dyads will be randomised in a 1:1 ratio to either usual care or usual care plus a Tai Chi intervention for 20 weeks. The Tai Chi intervention will consist of weekly classes (45 minutes’ Tai Chi plus up to 45 minutes for informal discussion, with up to 10 dyads per class) and home-based exercises (20 minutes per day to be facilitated by the carer). Home practice of Tai Chi will be supported by the use of behaviour change techniques with the Tai Chi instructor at a home visit in week 3-4 of the intervention (action planning, coping planning, self-monitoring, and alarm clock reminder) and at the end of each class (feedback on home practice). The primary outcome is dynamic balance measured using the Timed Up and Go test, coinciding with the end of the 20-week intervention phase for participants in the Tai Chi arm. Secondary outcomes for PWD include functional balance, static balance, fear of falling, global cognitive functioning, visual-spatial cognitive functioning, quality of life, and falls. Secondary outcomes for carers include dynamic balance, static balance, quality of life, costs, and carer burden. Discussion: This trial is the first in the UK to test the effectiveness of Tai Chi to improve balance among PWD. The trial will inform a future study that will be the first in the world to use Tai Chi in a trial to prevent falls among PWD. Trial registration: NCT02864056

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