Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Early intervention music therapy : reporting on a 3-year project to address needs with at-risk families

Sing & Grow is an early intervention music therapy project presented to families with additional needs, or those at risk of experiencing disadvantage due to social and/or economic circumstances that may impact on their parenting experiences. The aim of the project is to provide short term music therapy programs to families in communities where access to such services may be limited. The program is strengths-based and focuses on building upon a parent’s capacity to relate to and respond to their child’s emotional and developmental needs.

The differential recognition of children’s cultural practices in middle primary literacy classrooms

This paper argues that teachers’ recognition of children’s cultural practices is an important positive step in helping socio-economically disadvantaged children engage with school literacies. Based on twenty-one longitudinal case studies of children’s literacy development over a three-year period, the authors demonstrate that when children’s knowledges and practices assembled in home and community spheres are treated as valuable material for school learning, children are more likely to invest in the work of acquiring school literacies. However they show also that whilst some children benefit greatly from being allowed to draw on their knowledge of popular culture, sports and the outdoors, other children’s interests may be ignored or excluded. Some differences in teachers’ valuing of home and community cultures appeared to relate to gender dimensions.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Overview of methods used in cross-cultural comparisons of menopausal symptoms and their determinants : Guidelines for Strengthening the Reporting of Menopause and Aging (STROMA) studies

This paper reviews the methods used in cross-cultural studies of menopausal symptoms with the goal of formulating recommendations to facilitate comparisons of menopausal symptoms across cultures. It provides an overview of existing approaches and serves to introduce four separate reviews of vasomotor, psychological, somatic, and sexual symptoms at midlife. Building on an earlier review of cross-cultural studies of menopause covering time periods until 2004, these reviews are based on searches of Medline, PsycINFO, CINAHL and Google Scholar for English-language articles published from 2004 to 2010 using the terms “cross cultural comparison” and “menopause.” Two major criteria were used: a study had to include more than one culture, country, or ethnic group and to have asked about actual menopausal symptom experience. We found considerable variation across studies in age ranges, symptom lists, reference period for symptom recall, variables included in multivariate analyses, and the measurement of factors (e.g., menopausal status and hormonal factors, demographic, anthropometric, mental/physical health, and lifestyle measures) that influence vasomotor, psychological, somatic and sexual symptoms. Based on these reviews, we make recommendations for future research regarding age range, symptom lists, reference/recall periods, and measurement of menopausal status. Recommendations specific to the cross-cultural study of vasomotor, psychological, somatic, and sexual symptoms are found in the four reviews that follow this introduction.