Writing representations over proper division subrings

Let �� be a division ring, and G a finite group of automorphisms of E whose elements are distinct modulo inner automorphisms of ��. Let �� = ��G be the division subring of elements of �� fixed by G. Given a representation p : �� →��d×d of an �� -algebra ��, we give necessary and sufficient conditions for p to be writable over ��. (Here ��d×d denotes the algebra of d×d matrices over ��, and a matrix A writes p over �� if A−1p(��)A ⊆ Fd×d.) We give an algorithm for constructing an A, or proving that no A exists. The case of particular interest to us is when �� is a field, and p is absolutely irreducible. The algorithm relies on an explicit formula for A, and a generalization of Hilbert’s Theorem 90 that arises in galois cohomology. The algorithm has applications to the construction of absolutely irreducible group representations (especially for solvable groups), and to the recognition of class C5 in Aschbacher’s matrix group classification scheme [1, 13]

Beyond the Berlin Wall? Investigating joint commissioning and its various meanings using a Q methodology approach

Joint commissioning has been extensively alluded to in English health and social care policy as a way of improving services and outcomes. Yet there is a lack of specificity pertaining to what joint commissioning actually is and what success would look like. In this paper we adopt a Q methodology approach to understand the different meanings of joint commissioning that those involved in these arrangements hold. In doing so we get beyond the more orthodox interpretations of joint commissioning found in the literature although the appeal of joint commissioning as a ‘good thing’ is still prominent across these accounts

Involution centralisers in finite unitary groups of odd characteristic

Funding: Australian Research Council Discovery Project grants DP160102323 and DP190100450.We analyse the complexity of constructing involution centralisers in unitary groups over fields of odd order. In particular, we prove logarithmic bounds on the number of random elements required to generate a subgroup of the centraliser of a strong involution that contains the last term of its derived series. We use this to strengthen previous bounds on the complexity of recognition algorithms for unitary groups in odd characteristic. Our approach generalises and extends two previous papers by the second author and collaborators on strong involutions and regular semisimple elements of linear groups.PostprintPeer reviewe

Health and social care commissioning: an exploration of processes, services and outcomes. Final report.

It is suggested that public sector organisations should work together more effectively to deliver the best services. In recent years this notion of partnership-working has been stressed in terms of the joint commissioning of services. Commissioning is the activity that decides of the services to be provided to local populations and who shall provide and pay for them. The concept of joint commissioning is used here to describe the ways in which health and social care agencies work together to determine this. There is little evidence which describes either the processes or provides clear messages about outcomes it produces. This project proposes an approach which builds on previous experience of evaluating public sector collaborative activities to investigate ways in which joint commissioning operates and the types of outcomes these processes produce for service users. The approach proposed incorporates a range of stakeholders, but in particular front-line staff members and service users within the case-study areas, a factor which has been lacking in previous evaluations. The project aims to produce practical knowledge about the types of joint commissioning activities taking place in England and the outcomes this produces - with the aim that these practical lessons may provide useful learning for other health and social care communities

Micro-enterprises: small enough to care?

This report presents findings of an evaluation of micro-enterprises in social care in England, which ran from 2013 to 2015. Organisations are here classed as micro if they employ five or fewer full-time equivalent staff. The aim of the project was to test the extent to which micro-enterprises deliver services that are personalised, valued, innovative and cost-effective, and how they compare with small, medium and large providers. Working in three parts of the country, researchers compared 27 organisations providing care and support, of which 17 were microenterprises, 2 were small, 4 were medium and 4 were large. The project team interviewed and surveyed 143 people (staff, older people, people with disabilities and carers) who received support from the 27 providers. The findings presented are relevant to people who use services and their families; social care commissioners; regulators and policy makers at a local and national level; people who provide care services; and social entrepreneurs who are considering setting up micro forms of support. The research was based at the University of Birmingham. It was funded by the Economic and Social Research Council (ESRC), as part of a project entitled Does Smaller mean Better? Evaluating Micro-enterprises in Adult Social Care (ESRC Standard Grant ES/ K002317/1)

Writing projective representations over subfields

Let G=〈X〉be an absolutely irreducible subgroup of GL(d, K), and let F be a proper subfield of the finite field K. We present a practical algorithm to decide constructively whether or not G is conjugate to a subgroup of GL(d, F).K×, where K× denotes the centre of GL(d, K). If the derived group of G also acts absolutely irreducibly, then the algorithm is Las Vegas and costs O(|X|d3+d2log|F|) arithmetic operations in K. This work forms part of a recognition project based on Aschbacher’s classification of maximal subgroups of GL(d, K)

Effects of ocean sprawl on ecological connectivity: impacts and solutions

The growing number of artificial structures in estuarine, coastal and marine environments is causing “ocean sprawl”. Artificial structures do not only modify marine and coastal ecosystems at the sites of their placement, but may also produce larger-scale impacts through their alteration of ecological connectivity - the movement of organisms, materials and energy between habitat units within seascapes. Despite the growing awareness of the capacity of ocean sprawl to influence ecological connectivity, we lack a comprehensive understanding of how artificial structures modify ecological connectivity in near- and off-shore environments, and when and where their effects on connectivity are greatest. We review the mechanisms by which ocean sprawl may modify ecological connectivity, including trophic connectivity associated with the flow of nutrients and resources. We also review demonstrated, inferred and likely ecological impacts of such changes to connectivity, at scales from genes to ecosystems, and potential strategies of management for mitigating these effects. Ocean sprawl may alter connectivity by: (1) creating barriers to the movement of some organisms and resources - by adding physical barriers or by modifying and fragmenting habitats; (2) introducing new structural material that acts as a conduit for the movement of other organisms or resources across the landscape; and (3) altering trophic connectivity. Changes to connectivity may, in turn, influence the genetic structure and size of populations, the distribution of species, and community structure and ecological functioning. Two main approaches to the assessment of ecological connectivity have been taken: (1) measurement of structural connectivity - the configuration of the landscape and habitat patches and their dynamics; and (2) measurement of functional connectivity - the response of organisms or particles to the landscape. Our review reveals the paucity of studies directly addressing the effects of artificial structures on ecological connectivity in the marine environment, particularly at large spatial and temporal scales. With the ongoing development of estuarine and marine environments, there is a pressing need for additional studies that quantify the effects of ocean sprawl on ecological connectivity. Understanding the mechanisms by which structures modify connectivity is essential if marine spatial planning and eco-engineering are to be effectively utilised to minimise impacts

A cross-sectional study exploring the relationship between regulator quality ratings and care home residents' quality of life in England

Background: The quality of life of people receiving health and social care is an important indicator of service quality, but the relationship between patient experience and outcomes and regulator quality ratings in England is unknown. In 2013, the health and social care regulator in England, the Care Quality Commission (CQC), introduced a new ratings system and by February 2017, all social care services were inspected and awarded new quality ratings (outstanding, good, requires improvement and inadequate). This study aimed to explore whether quality ratings were associated with residents’ quality of life, controlling for confounding variables