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.

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.

From classroom resistance to school reform

In the project described in this chapter, a group of educationally disengaged high school students investigated their peers' perspectives of factors related to low aspiration for and access to university. On the basis of their findings, they created an informative DVD to address the student needs.

p53-independent NOXA induction overcomes apoptotic resistance of malignant melanomas

Once melanoma metastasizes, no effective treatment modalities prolong survival in most patients. This notorious refractoriness to therapy challenges investigators to identify agents that overcome melanoma resistance to apoptosis. Whereas many survival pathways contribute to the death-defying phenotype in melanoma, a defect in apoptotic machinery previously highlighted inactivation of Apaf-1, an apoptosome component engaged after mitochondrial damage. During studies involving Notch signaling in melanoma, we observed a gamma-secretase tripeptide inhibitor (GSI; z-Leu-Leu-Nle-CHO), selected from a group of compounds originally used in Alzheimer's disease, induced apoptosis in nine of nine melanoma lines. GSI only induced G2-M growth arrest (but not killing) in five of five normal melanocyte cultures tested. Effective killing of melanoma cells by GSI involved new protein synthesis and a mitochondrial-based pathway mediated by up-regulation of BH3-only members (Bim and NOXA). p53 activation was not necessary for up-regulation of NOXA in melanoma cells. Blocking GSI-induced NOXA using an antisense (but not control) oligonucleotide significantly reduced the apoptotic response. GSI also killed melanoma cell lines with low Apaf-1 levels. We conclude that GSI is highly effective in killing melanoma cells while sparing normal melanocytes. Direct enhancement of BH3-only proteins executes an apoptotic program overcoming resistance of this lethal tumor. Identification of a p53-independent apoptotic pathway in melanoma cells, including cells with low Apaf-1, bypasses an impediment to current cytotoxic therapy and provides new targets for future therapeutic trials involving chemoresistant tumors.