Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis

Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the single-particle Gaussian wave packets through an integral transformation, thereby facilitating fully analytical calculations of the matrix elements. The nonlinear parameters of the trial function are chosen by a stochastic technique. The method has proved very efficient, virtually exact, and it seems feasible for any few-body bound-state problems emerging in nuclear or atomic physics.Comment: 39 pages (revtex) + 3 figures (appended as compressed uuencoded .ps files

Early Emergence of Ethnic Differences in Type 2 Diabetes Precursors in the UK: The Child Heart and Health Study in England (CHASE Study)

Peter Whincup and colleagues carry out a cross-sectional study examining ethnic differences in precursors of of type 2 diabetes among children aged 9–10 living in three UK cities

Salivary Testosterone Levels and Health Status in Men and Women in the British General Population: Findings from the Third National Survey of Sexual Attitudes and Lifestyles (Natsal-3)

Context: Salivary T (Sal-T) measurement by liquid chromatography–tandem mass spectroscopy resents the opportunity to examine health correlates of Sal-T in a large-scale population survey. Objective: This study sought to examine associations between Sal-T and health-related factors in men and women age 18 –74 years. Design and Setting: Morning saliva samples were obtained from participants in a cross-sectional probability-sample survey of the general British population (Natsal-3). Self-reported health and lifestyle questions were administered as part of a wider sexual health interview. Participants: Study participants included 1599 men and 2123 women. Methods: Sal-T was measured using liquid chromatography–tandem mass spectroscopy. Linear regression was used to examine associations between health factors and mean Sal-T. Results: In men, mean Sal-T was associated with a range of health factors after age adjustment, and showed a strong independent negative association with body mass index (BMI) in multivariable analysis. Men reporting cardiovascular disease or currently taking medication for depression had lower age-adjusted Sal-T, although there was no association with cardiovascular disease after adjustment for BMI. The decline in Sal-T with increasing age remained after adjustment for healthrelated factors. In women, Sal-T declined with increasing age; however, there were no age-independent associations with health-related factors or specific heath conditions with the exception of higher Sal-T in smokers. Conclusions: Sal-T levels were associated, independently of age, with a range of self-reported health markers, particularly BMI, in men but not women. The findings support the view that there is an age-related decline in Sal-T in men and women, which cannot be explained by an increase in ill health. Our results demonstrate the potential of Sal-T as a convenient measure of tissue androgen exposure for population research

Competences of Mathematics Teachers in Diagnosing Teaching Situations and Offering Feedback to Students:Specificity, Consistency and Reification of Pedagogical and Mathematical Discourses

In the study we report in this chapter, we investigate the competences of mathematics pre- and in-service teachers in diagnosing situations pertaining to mathematics teaching and in offering feedback to the students at the heart of said situations. To this aim we deploy a research design that involves engaging teachers with situation-specific tasks in which we invite participants to: solve a mathematical problem; examine a (fictional yet research-informed) solution proposed by a student in class and a (fictional yet research-informed) teacher response to the student; and, describe the approach they themselves would adopt in this classroom situation. Participants were 23 mathematics graduates enrolled in a post-graduate mathematics education programme, many already in-service teachers. They responded to a task that involved debating the identification of a tangent line at an inflection point of a cubic function through resorting to the formal definition of tangency or the function graph. Analysis of their written responses to the task revealed a great variation in the participants’ diagnosing and addressing of teaching issues – in this case involving the role of visualisation in mathematical reasoning. We describe this variation in terms of a typology of four interrelated characteristics that emerged from the data analysis: consistency between stated beliefs/knowledge and intended practice, specificity of the response to the given classroom situation, reification of pedagogical discourses, and reification of mathematical discourses. We propose that deploying the theoretical construct of these characteristics in tandem with our situation-specific task design can contribute towards the identification – as well as reflection upon and development – of mathematics teachers’ diagnostic competences in teacher education and professional development programmes

Hierarchical related regression for combining aggregate and individual data in studies of socio-economic disease risk factors

To obtain information about the contribution of individual and area level factors to population health, it is desirable to use both data collected on areas, such as censuses, and on individuals, e.g. survey and cohort data. Recently developed models allow us to carry out simultaneous regressions on related data at the individual and aggregate levels. These can reduce 'ecological bias' that is caused by confounding, model misspecification or lack of information and increase power compared with analysing the data sets singly. We use these methods in an application investigating individual and area level sociodemographic predictors of the risk of hospital admissions for heart and circulatory disease in London. We discuss the practical issues that are encountered in this kind of data synthesis and demonstrate that this modelling framework is sufficiently flexible to incorporate a wide range of sources of data and to answer substantive questions. Our analysis shows that the variations that are observed are mainly attributable to individual level factors rather than the contextual effect of deprivation. Copyright 2008 Royal Statistical Society.