A Minimal Congruence Lattice Representation for ₚ₊₁

Let p be an odd prime. The unary algebra consisting of the dihedral group of order 2p, acting on itself by left translation, is a minimal congruence lattice representation of p+1

Evaluation of an intervention to promote walking during the commute to work: a cluster randomised controlled trial

Background: Opportunities for working adults to accumulate recommended physical activity levels (at least 150min of moderate intensity physical activity in bouts of at least 10 min throughout the week) may include the commute to work. Systematic reviews of interventions to increase active transport suggest studies have tended to be of poor quality, relying on self-report and lacking robust statistical analyses. Methods: We conducted a multi-centre parallel-arm cluster randomised controlled trial, in workplaces in south-west England and south Wales, to assess the effectiveness of a behavioural intervention to increase walking during the commute. Workplace-based Walk to Work promoters were trained to implement a 10-week intervention incorporating key behavioural change techniques: providing information; encouraging intention formation; identifying barriers and solutions; goal setting; self-monitoring; providing general encouragement; identifying social support; reviewing goals, and; relapse prevention. Physical activity outcomes were objectively measured using accelerometers and GPS receivers at baseline and 12-month follow-up. The primary outcome was daily minutes of moderate to vigorous physical activity (MVPA). Secondary outcomes included overall levels of physical activity and modal shift (from private car to walking). Cost-consequences analysis included employer, employee and health service costs and outcomes. Results: Six hundred fifty-four participants were recruited across 87 workplaces: 10 micro (5–9 employees); 35 small(10–49); 22 medium (50–250); 20 large (250+). The majority of participants lived more than two kilometres from their place of work (89%) and travelled to work by car (65%). At 12-month follow-up, 84 workplaces (41 intervention,43 control) and 477 employees (73% of those originally recruited) took part in data collection activities. There was no evidence of an intervention effect on MVPA or overall physical activity at 12-month follow-up. The intervention cost on average £181.97 per workplace and £24.19 per participating employee. Conclusions: The intervention, focusing primarily on individual behaviour change, was insufficient to change travel behaviour. Our findings contribute to the argument that attention should be directed towards a whole systems approach, focusing on interactions between the correlates of travel behaviour. Trial registration: ISRCTN15009100. Prospectively registered. (Date assigned: 10/12/2014). Keywords: Walking, Active travel, Workplace, Behavioural intervention, Randomised controlled trial, Physical activit

Employer schemes to encourage walking to work: feasibility study incorporating an exploratory randomised controlled trial

Background: Physical inactivity increases the risk of many chronic diseases, including coronary heart disease, type 2 diabetes, obesity and some cancers. Increasing physical activity levels, particularly among the most sedentary, is an important aim of current public health policy in the UK. An opportunity for working adults to increase physical activity levels may be through walking during the daily commute. Objectives: To build on existing knowledge and resources to develop an employer-led scheme to increase walking to work; to test the feasibility of implementing and evaluating the intervention; and to explore other requirements of a full-scale trial. Design: Feasibility study incorporating phase 1 resource review, focus groups with employees and interviews with employers in three workplaces (one small, one medium and one large); and phase 2 exploratory cluster randomised controlled trial (RCT) including process and economic evaluations. Setting: Workplaces (eight small, five medium and four large) in Bristol. Participants: One hundred and eighty-seven employees (89 male and 98 female) at baseline. Interventions: Walk to Work promoters were recruited and trained about the health, social, economic and environmental benefits of walking to work and how to identify and promote safe walking routes for employees. They were given resource packs based on nine key behaviour change techniques. The role of the Walk to Work promoter was to encourage participating employees in their workplace to walk to work; to help to identify walking routes; to encourage goal setting; and to provide additional encouragement through four contacts over the following 10 weeks (face to face, e-mail or telephone, as appropriate). Main outcome measures: Recruitment and retention rates; sample size calculation and estimation of the intracluster correlation coefficient (ICC); acceptability of the intervention and evaluation methods; and estimation of costs. Results: Workplace and employee recruitment appeared to be restricted by the initial requirement to identify employees living within 2 miles of the workplace. Once recruited, no workplace withdrew from the study between baseline and 1-year follow-up. It proved feasible to recruit and train workplace Walk to Work promoters. The response rate was 132 (71%) at 1-year follow-up. Although the study was not powered to measure effectiveness, accelerometer data suggest that overall physical activity and moderate to vigorous physical activity (MVPA) were higher in the intervention arm than in the control arm at 1-year follow-up. The ICC was estimated at 0.12 (95% confidence interval 0.00 to 0.30). Based on an average cluster size of eight, an ICC of 0.15 and attrition of 25%, a total sample size of 678 would have 80% power with 5% significance to detect a 15% increase in mean MVPA. The average cost of the intervention was estimated at £441 per workplace. Activity levels were similar in the intervention and control arms at baseline. Conclusions: The intervention and evaluation were feasible, and acceptable to participants. There was sufficient evidence of promise to justify a full-scale trial incorporating lessons learned during the feasibility study. Future work: an application is being submitted for a follow-on full-scale cluster RCT. Trial registration: Current Controlled Trials ISRCTN72882329. Funding: This project was funded by the NIHR Public Health Research programme and will be published in full in Public Health Research; Vol. 3, No. 4. See the NIHR Journals Library website for further project information. The work was undertaken with the support of The Centre for the Development and Evaluation of Complex Interventions for Public Health Improvement (DECIPHer), a UK Clinical Research Collaboration Public Health Research Centre of Excellence. Joint funding (MR/KO232331/1) from the British Heart Foundation, Cancer Research UK, Economic and Social Research Council, Medical Research Council, the Welsh Government and the Wellcome Trust, under the auspices of the UK Clinical Research Collaboration, is gratefully acknowledged