The outflow ranking method for weighted directed graphs

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity – meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node’s outflow does not increase – and order preservation – meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the ‘sum’ weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.

Compact Toffoli gate using weighted graph states

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven, or eight qubits, we show that success probabilities of 1/4, 1/2, and 1, respectively, can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup independent, they could be realized in a variety of systems, including linear optics and ion traps.

Unconditional constants and polynomial inequalities

If P is a polynomial on Rm of degree at most n then we define the polynomial |P|. Now if B is a convex compact set in Rm, we define the norm ||P||B of P as the maximum of P on B, and then we investigate the inequality || |P| ||B

Overcoming health inequalities: A participative evaluation framework fit for the task

Aims: Healthcare providers are confronted with the claim that the distribution of health and healthcare provision is inherently unfair. There is also a growing awareness that the tools and methodologies applied in tackling health inequalities require further development. Evaluations as well as interventions usually focus on population-based indicators, but do not always provide guidance for frontline service evaluation and delivery. That is why the evaluation framework presented here focuses on facilitating local service development, service provider and user involvement, and the adequate representation of different population groups. Methods: A participative evaluation framework was constructed by drawing on six common success characteristics extrapolated from the published literature and policies on health inequalities. This framework was then applied to an intervention addressing women’s psychosocial health needs in order to demonstrate its utility in practice. Results: The framework provides healthcare professionals with an evidence-based tool for evaluating projects or programmes targeting health inequalities in ways that are responsive to local contexts and stakeholders. Conclusion: This participative evaluation framework supports the identification of meaningful psychosocial and contextual indicators for assessing the diverse health and social needs of service users. It uses multi-dimensional indicators to assess health and social care needs, to inform local service development, and to facilitate the exchange of knowledge between researchers, service providers, and service users. The inherent responsiveness enables rigorous yet flexible action on local health inequalities.

Socio-economic inequalities in cerebral palsy prevalence in the United Kingdom: a register-based study

Evidence is unclear as to whether there is a socio-economic gradient in cerebral palsy (CP) prevalence beyond what would be expected from the socio-economic gradient for low birthweight, a strong risk factor for CP. We conducted a population-based study in five regions of the UK with CP registers, to investigate the relationship between CP prevalence and socio-economic deprivation, and how it varies by region, by birthweight and by severity and type of CP. The total study population was 1 657 569 livebirths, born between 1984 and 1997. Wards of residence were classified into five quintiles according to a census-based deprivation index, from Q1 (least deprived) to Q5 (most deprived). Socio-economic gradients were modelled by Poisson regression, and region-specific estimates combined by meta-analysis.

The prevalence of postneonatally acquired CP was 0.14 per 1000 livebirths overall. The mean deprivation gradient, expressed as the relative risk in the most deprived vs. the least deprived quintile, was 1.86 (95% confidence interval [95% CI 1.19, 2.88]). The prevalence of non-acquired CP was 2.22 per 1000 livebirths. For non-acquired CP the gradient was 1.16 [95% CI 1.00, 1.35]. Evidence for a socio-economic gradient was strongest for spastic bilateral cases (1.32 [95% CI 1.09, 1.59]) and cases with severe intellectual impairment (1.59 [95% CI 1.06, 2.39]). There was evidence for differences in gradient between regions. The gradient of risk of CP among normal birthweight births was not statistically significant overall (1.21 [95% CI 0.95, 1.54]), but was significant in two regions. There was non-significant evidence of a reduction in gradients over time.

The reduction of the higher rates of postneonatally acquired CP in the more socioeconomically deprived areas is a clear goal for prevention. While we found evidence for a socio-economic gradient for non-acquired CP of antenatal or perinatal origin, the picture was not consistent across regions, and there was some evidence of a decline in inequalities over time. The steeper gradients in some regions for normal birthweight cases and cases with severe intellectual impairment require further investigation.