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.

Risk of second cancer after lymphohematopoietic neoplasm

People living with lymphohematopoietic neoplasms (LHNs) are known to have increased risks of second cancer; however, the incidence of second cancers after LHNs has not been studied extensively in Australia. The Australian Cancer Database was used to analyze site-specific risk of second primary cancer after LHNs in 127,707 patients diagnosed between 1983 and 2005. Standardized incidence ratios (SIRs) were calculated using population rates. Overall, patients with an LHN had nearly twice the risk of developing a second cancer compared to the Australian population. Among 40,321 patients with non-Hodgkin's lymphoma (NHL), there was over a fourfold significant increase in melanoma, Kaposi sarcoma, cancer of the lip, connective tissue and peripheral nerves, eye, thyroid, Hodgkin's disease (HD) and myeloid leukemia. Among 6,396 patients with HD, there was over a fourfold significant increase in melanoma, Kaposi sarcoma, cancer of the lip, oral cavity and pharynx, female breast, uterine cervix, testis, thyroid, NHL and myeloid leukemia. Among the 33,025 patients with lymphoid and myeloid leukemia, significant excess were seen for cancers of the lip, eye, connective tissue and peripheral nerves, NHL and HD. Among the 13,856 patients with plasma cell tumors, there was over fourfold significant increase for melanoma, cancer of the connective tissue and peripheral nerves and myeloid leukemia. Our findings provide evidence of an increased risk of cancer, particularly ultraviolet radiation- and immunosuppression-related cancers, after an LHN in Australia. Copyright © 2010 UICC.

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.

Entry into Valhalla : contextualising the learning of legal ethics through the use of Second Life machinima

An ability to recognise and resolve ethical dilemmas was identified by the Australian Law Reform Commission as one of the ten fundamental lawyering skills. While the ‘Priestley 11’ list of areas of law required to qualify for legal practice includes ethics and professional responsibility, the commitment to ethics learning in Australian law schools has been far from uniform. The obligation imposed by the Priestley 11 is frequently discharged by a traditional teaching and learning approach involving lectures and/or tutorials and focusing on the content of the formal rules of professional responsibility. However, the effectiveness of such an approach is open to question. Instead, a practical rather than a theoretical approach to the teaching of legal ethics is required. Effective final-year student learning of ethics may be achieved by an approach which engages students, enabling them to appreciate the relevance of what they are learning to the real world and facilitating their transition from study to their working lives. Entry into Valhalla comprises a suite of modules featuring ‘machinima’ (computer-generated imagery) created using the Second Life virtual environment to contextualise otherwise abstract concepts. It provides an engaging learning environment which enables students to obtain an appreciation of ethical responsibility in a real-world context and facilitates understanding and problem-solving ability.

Kinetics of electron recombination of dye-senitized solar cells based on TiO2 nanorod arrays sensitized with different dyes

The performance and electron recombination kinetics of dye-sensitized solar cells based on TiO2 films consisting of one-dimensional nanorod arrays (NR-DSSCs) which are sensitized with dye N719, C218 and D205 respectively have been studied. It has been found that the best efficiency is obtained with the dye C218 based NR-DSSCs, benefiting from a 40% higher short-circuit photocurrent density. However, the open circuit photovoltage of the N719 based cell is 40 mV higher than that of the organic dye C218 and D205 based devices. Investigation of the electron recombination kinetics of the NR-DSSCs has revealed that the effective electron lifetime, τn, of the N719 based NR-DSSC is the lowest whereas the τn of the C218 based NR-DSSC is the highest among the three dyes. The higher Voc with the N719 based NR-DSSC is originated from the more negative energy level of the conduction band of the TiO2 film. In addition, in comparison to the DSSCs with conventional nanocrystalline particles based TiO2 films, the NR-DSSCs have shown over two orders of magnitude higher τn when employing N719 as the sensitizer. Nevertheless, the τn of the DSSCs with the C218 based nanorod arrays is only ten-fold higher than the that of the nanoparticles based devices. The remarkable characteristic of the dye C218 in suppressing the electron recombination of DSSCs is discussed.