Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Formalised peer mentoring pilot evaluation

Over the past ten years, mentoring of children and young people has become an increasingly important feature of social policy in the UK. This has been mirrored in the rapid growth in the number of mentoring schemes operating. However, it is widely acknowledged that no one single definition or model of mentoring exists; rather there are a number of different models providing support to young people in a range of settings. This research was undertaken during the autumn term of 2006 and the summer term of 2007. The methodology comprised an analysis of mentoring models in the 180 participating schools; questionnaires sent to all co-ordinators and to mentors/proteges in 40 schools; interviews with co-ordinators, pupils and support agents in 8 case study schools. Includes: •Introduction •Evaluation methodology •Analysis of school pilot application forms •Evaluation results •Conclusions •Recommendations •Bibliography •Appendices