Cohen-Macaulay Circulant Graphs

Let G be the circulant graph C_n(S) with S a subset of {1,2,...,\lfloor n/2 \rfloor}, and let I(G) denote its the edge ideal in the ring R = k[x_1,...,x_n]. We consider the problem of determining when G is Cohen-Macaulay, i.e, R/I(G) is a Cohen-Macaulay ring. Because a Cohen-Macaulay graph G must be well-covered, we focus on known families of well-covered circulant graphs of the form C_n(1,2,...,d). We also characterize which cubic circulant graphs are Cohen-Macaulay. We end with the observation that even though the well-covered property is preserved under lexicographical products of graphs, this is not true of the Cohen-Macaulay property.Comment: 14 page

Obtaining evidence from child witnesses: the advantage of VIPER parades.

In the UK there have been an increasing number of children being asked to give evidence as witnesses in criminal cases and view video lineups to identify perpetrators, however little research has investigated how well children perform using this type of identification procedure. In this study children aged 6-8 and 13-14 years witnessed a staged event where an unfamiliar man interrupted a classroom or assembly and several days later were asked to identify the man from either a video or photographic lineup. For some lineups the target was present (target present) whereas for others the target was not (target absent). The results found an advantage for the target absent video lineups over the photographic lineups, but only for adolescents

A field evaluation of the VIPER system: A new technique for eliciting eyewitness identification evidence

Advances in technology have led to a new system for gathering facial identification evidence from eyewitnesses with accompanying changes in legislation in the UK. The current paper presents the responses of 1718 real witnesses and victims who attempted an identification from a video parade in Scotland in 2008. The witnesses comprised a large subset who were classified as ‘vulnerable’ due to their age, ability or the nature of the incident. Suspect identifications averaged 44%, a figure comparable to the rate reported in other field studies conducted in the UK. The foil identification rate at 42% is higher than other field data. The paper discusses the effects of witness age, vulnerability, perceived emotional state, crime type, delay and procedural aspects of the video procedure on suspect identifications

General Practitioners at the Deep End: The Experience and Views of General Practitioners Working in the Most Severely Deprived Areas of Scotland

General Practitioners at the Deep End, by Prof. Graham Watt, is the latest in the College's Occasional Papers series. This important paper looks at the work of front-line GPs in the 100 most deprived practice populations in Scotland. Although offering no short-term solutions to the problem of health inequality in deprived areas, the paper gives a raft of measures to break through the barriers created by, first, the inverse care law and, second, the dysfunctional links between practices and other services. <p></p> This seminal paper has vital messages for primary care in the UK and globally, and should form the basis of discussion of the future of primary care for primary care teams, Associates-in-Training and politicians