Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Confirmatory factor analysis of the Way of Coping Checklist-Revised (WCCL-R) in the Asian context

Industrial employment growth has been one of the most dynamic areas of expansion in Asia; however, current trends in industrialised working environments have resulted in greater employee stress. Despite research showing that cultural values affect the way people cope with stress, there is a dearth of psychometrically established tools for use in non-Western countries to measure these constructs. Studies of the "Way of Coping Checklist-Revised" (WCCL-R) in the West suggest that the WCCL-R has good psychometric properties, but its applicability in the East is still understudied. A confirmatory factor analysis (CFA) is used to validate the WCCL-R constructs in an Asian population. This study used 1,314 participants from Indonesia, Sri Lanka, Singapore, and Thailand. An initial exploratory factor analysis revealed that original structures were not confirmed; however, a subsequent EFA and CFA showed that a 38-item, five-factor structure model was confirmed. The revised WCCL-R in the Asian sample was also found to have good reliability and sound construct and concurrent validity. The 38-item structure of the WCCL-R has considerable potential in future occupational stress-related research in Asian countries.

Constraints on the complete optimization of human motion

In sport and exercise biomechanics, forward dynamics analyses or simulations have frequently been used in attempts to establish optimal techniques for performance of a wide range of motor activities. However, the accuracy and validity of these simulations is largely dependent on the complexity of the mathematical model used to represent the neuromusculoskeletal system. It could be argued that complex mathematical models are superior to simple mathematical models as they enable basic mechanical insights to be made and individual-specific optimal movement solutions to be identified. Contrary to some claims in the literature, however, we suggest that it is currently not possible to identify the complete optimal solution for a given motor activity. For a complete optimization of human motion, dynamical systems theory implies that mathematical models must incorporate a much wider range of organismic, environmental and task constraints. These ideas encapsulate why sports medicine specialists need to adopt more individualized clinical assessment procedures in interpreting why performers' movement patterns may differ.

A nested real-time PCR assay has an increased sensitivity suitable for detection of viruses in aerosol studies

Aims: Influenza is commonly spread by infectious aerosols; however, detection of viruses in aerosols is not sensitive enough to confirm the characteristics of virus aerosols. The aim of this study was to develop an assay for respiratory viruses sufficiently sensitive to be used in epidemiological studies. Method: A two-step, nested real-time PCR assay was developed for MS2 bacteriophage, and for influenza A and B, parainfluenza 1 and human respiratory syncytial virus. Outer primer pairs were designed to nest each existing real-time PCR assay. The sensitivities of the nested real-time PCR assays were compared to those of existing real-time PCR assays. Both assays were applied in an aerosol study to compare their detection limits in air samples. Conclusions: The nested real-time PCR assays were found to be several logs more sensitive than the real-time PCR assays, with lower levels of virus detected at lower Ct values. The nested real-time PCR assay successfully detected MS2 in air samples, whereas the real-time assay did not. Significance and Impact of the Study: The sensitive assays for respiratory viruses will permit further research using air samples from naturally generated virus aerosols. This will inform current knowledge regarding the risks associated with the spread of viruses through aerosol transmission.

Seasonal activity and abundance of Orosius orientalis (Hemiptera : Cicadellidae) at agricultural sites in Southeastern Australia

Orosius orientalis is a leafhopper vector of several viruses and phytoplasmas affecting a broad range of agricultural crops. Sweep net, yellow pan trap and yellow sticky trap collection techniques were evaluated. Seasonal distribution of O. orientalis was surveyed over two successive growing seasons around the borders of commercially grown tobacco crops. Orosius orientalis seasonal activity as assessed using pan and sticky traps was characterised by a trimodal peak and relative abundance as assessed using sweep nets differed between field sites with peak activity occurring in spring and summer months. Yellow pan traps consistently trapped a higher number of O. orientalis than yellow sticky traps.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabiesPetrogale penicillata

1. Species' distribution modelling relies on adequate data sets to build reliable statistical models with high predictive ability. However, the money spent collecting empirical data might be better spent on management. A less expensive source of species' distribution information is expert opinion. This study evaluates expert knowledge and its source. In particular, we determine whether models built on expert knowledge apply over multiple regions or only within the region where the knowledge was derived. 2. The case study focuses on the distribution of the brush-tailed rock-wallaby Petrogale penicillata in eastern Australia. We brought together from two biogeographically different regions substantial and well-designed field data and knowledge from nine experts. We used a novel elicitation tool within a geographical information system to systematically collect expert opinions. The tool utilized an indirect approach to elicitation, asking experts simpler questions about observable rather than abstract quantities, with measures in place to identify uncertainty and offer feedback. Bayesian analysis was used to combine field data and expert knowledge in each region to determine: (i) how expert opinion affected models based on field data and (ii) how similar expert-informed models were within regions and across regions. 3. The elicitation tool effectively captured the experts' opinions and their uncertainties. Experts were comfortable with the map-based elicitation approach used, especially with graphical feedback. Experts tended to predict lower values of species occurrence compared with field data. 4. Across experts, consensus on effect sizes occurred for several habitat variables. Expert opinion generally influenced predictions from field data. However, south-east Queensland and north-east New South Wales experts had different opinions on the influence of elevation and geology, with these differences attributable to geological differences between these regions. 5. Synthesis and applications. When formulated as priors in Bayesian analysis, expert opinion is useful for modifying or strengthening patterns exhibited by empirical data sets that are limited in size or scope. Nevertheless, the ability of an expert to extrapolate beyond their region of knowledge may be poor. Hence there is significant merit in obtaining information from local experts when compiling species' distribution models across several regions.