What's in the Numbers? Child Welfare Statistics and the Children (NI) Order

This article draws attention to the importance of routinely collected administrative data as an important source for understanding the characteristics of the Northern Ireland child welfare system as it has developed since the Children (Northern Ireland) Order 1995 became its legislative base. The article argues that the availability of such data is a strength of the Northern Ireland child welfare system and urges local politicians, lobbyists, researchers, policy-makers, operational managers, practitioners and service user groups to make more use of them. The main sources of administrative data are identified. Illustration of how these can be used to understand and to ask questions about the system is provided by considering some of the trends since the Children Order was enacted. The “protection” principle of the Children Order provides the focus for the illustration. The statistical trends considered relate to child protection referrals, investigations and registrations and to children and young people looked after under a range of court orders available to ensure their protection and well-being.

The relationship between adipokines and the onset of type 2 diabetes in middle-aged men: The PRIME study

Aims: Epidemiological evidence suggests that adipokines may be associated with the onset of type 2 diabetes, but the evidence to date is limited and inconclusive. This study examined the association between adiponectin and leptin and the subsequent diagnosis of type 2 diabetes in a UK population based cohort of non-diabetic middle-aged men.
Methods: Baseline serum levels of leptin and adiponectin were measured in 1839 nondiabetic men aged 50–60 years who were participating in the prospective populationbased PRIME study. Over a mean follow-up of 14.7 years, new cases of type 2 diabetes were determined from self-reported clinical information with subsequent validation by general practitioners.
Results: 151 Participants developed type 2 diabetes during follow-up. In Cox regression models adjusted for age, men in the top third of the leptin distribution were at increased risk (hazard ratio (HR) 4.27, 95% CI 2.67–6.83) and men in the top third of the adiponectin
distribution at reduced risk (HR 0.24, 95% CI 0.14–0.42) relative to men in the bottom third. However, significance was lost for leptin after additional adjustment for BMI, waist to hip ratio, lifestyle factors and biological risk factors, including C-reactive protein (CRP). Further adjustment for HOMA-IR also resulted in loss of significance for adiponectin.
Conclusions: This study provides evidence that adipokines are associated with men’s future type 2 diabetes risk but not independently of other risk factors.

Estimating quantum chromatic numbers

We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. We describe the tracial rank, the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number, the quantum chromatic number and the classical chromatic number, respectively. Finally, we present a new SDP algorithm that yields a parameter larger than the Lovász number and is yet a lower bound for the tracial rank of the graph. We determine the precise value of the tracial rank of an odd cycle.