Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats

In this article we describe an efficient approximation of the stochastic Galerkin matrix which stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed to be a log-normal random field with given covariance and mean functions. The approximation is done in the canonical tensor format and then compared numerically with the tensor train and hierarchical tensor formats. It will be shown that under additional assumptions the approximation error depends only on smoothness of the covariance function and does not depend either on the number of random variables nor the degree of the multivariate Hermite polynomials

Developing an acceptable peer support intervention that enables clients, attending a weight management programme, to cascade their learning within their social network

Impacting on health and well-being, obesity creates an unmanageable burden on the health service and economy, yet is preventable and treatable. Establishing peer support as a tool for weight management could extend the reach of interventions and enhance their efficacy. A Narrative Systematic literature review highlights valuable peer support, yet also evidences that some peers are unhelpful. The aim of this research was to develop an intervention enabling clients of a weight management programme to cascade their learnings and experiential knowledge to those they know. Introducing a peer support intervention to clients and clients offering this to peers requires behaviour changes by lead facilitators and clients. Guided by the theoretical Behaviour Change Wheel (BCW) for designing behaviour change interventions, with Capability, Opportunity, Motivation for Behaviour (COM-B) at its centre, an iterative qualitative approach was undertaken. Using a prospective longitudinal design and maximum diversity sampling within the population attending three programmes, 21 clients attended semi-structured and some serial interviews; four focus groups were conducted with nine Leads. Thematic and interpretive analysis identified key themes. Motivated by altruistic benefits and seeing their peers’ readiness to change, Participants perceived they would be able to indirectly offer support without formal training or role however cues for these offers could be missed. These findings add new knowledge to the field of peer support. Acceptable support was praise, inclusion into and demonstration of weight-related activities, and encouragement. Practical dietary advice was welcomed but ‘norms’ of their social network take precedence over healthy goals. Giving time to peers and stress from hearing their problems, were barriers to offering support. Leads perceived the topic of peer support could be introduced once clients showed readiness to change. Based on theory and findings, an intervention manual, was developed using TIDieR guidance which requires further testing in the future