Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

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.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

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.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

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.

The status of Australian nurse practitioners : the second national census

Objectives. To profile Australian nurse practitioners and their practice in 2009 and compare results with a similar 2007 census. Methods. Self-administered questionnaire. Results. Atotal of 293 nurse practitioners responded (response rate 76.3%). The majority were female (n = 229, 81.2%); mean age was 47.3 years (s.d. = 8.1). As in 2007, emergency nurse practitioners represented the largest clinical specialty (n = 63, 30.3%). A majority practiced in a metropolitan area (n = 133, 64.3%); a decrease from 2007. Consistent with 2007, only 71.5% (n = 208) were employed as a nurse practitioner and 22.8% (n = 46) were awaiting approval for some or all of their clinical protocols. Demographic data, allocations of tasks, and patterns of practice remained consistent with 2007 results. ‘No Medicare provider number’ (n = 182, 91.0%), ‘no authority to prescribe using the Pharmaceutical Benefits Scheme’ (n = 182, 89.6%) and ‘lack of organisational support’ (n = 105, 52.2%) were reported as ‘limiting’ or ‘extremely limiting’ to practice. Conclusions. Our results demonstrate less than satisfactory uptake of the nurse practitioner role despite authorisation. Barriers constraining nurse practitioner practice reduced but remained unacceptably high. Adequate professional and political support is necessary to ensure the efficacy and sustainability of this clinical role.

Resilience of a corrupt police network : the first and second jokes in Queensland

Resilient organised crime groups survive and prosper despite law enforcement activity, criminal competition and market forces. Corrupt police networks, like any other crime network, must contain resiliency characteristics if they are to continue operation and avoid being closed down through detection and arrest of their members. This paper examines the resilience of a large corrupt police network, namely The Joke which operated in the Australian state of Queensland for a number of decades. The paper uses social network analysis tools to determine the resilient characteristics of the network. This paper also assumes that these characteristics will be different to those of mainstream organised crime groups because the police network operates within an established policing agency rather than as an independent entity hiding within the broader community.

Trends in policies, programs and practices in the Australasian First Year Experience literature 2000-2010. The First Year in Higher Education Research Series on Evidence-based Practice. Number 1

This publication is the first in a series of scholarly reports on research-based practice related to the First Year Experience in Higher Education. This report synthesises evidence about practice-based initiatives and pragmatic approaches in Aotearoa (New Zealand) and Australia that aim to enhance the experience of commencing students in the higher education sector. Trends in policies, programs and practices ... examines the first year experience literature from 2000-2010. It acknowledges the uniqueness of the Australasian socio-political context and its influence on the interests and output of researchers. The review surveyed almost 400 empirical reports and conceptual discussions produced over the decade that dealt with the stakeholders, institutions and the higher education sector in Australasia. The literature is examined through two theoretical constructs or “lenses”: first, a set of first year curriculum design principles and second, the generational approach to describing the maturation of initiatives. These outcomes and suggested directions for further research provide the challenges and the opportunities for FYE adherents, both scholars and practitioners, to grapple with in the next decade.