Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Assessment of the health impacts of the 2011 summer floods in Brisbane

Background: During December 2010 and January 2011, torrential rainfall in Queensland resulted in the worst flooding in over 50 years. We carried out a community-based survey to assess the health impacts of this flooding in the city of Brisbane. Methods: A community-based survey was conducted in 12 flood-affected electorates using postal questionnaires. A random sample of residents in these areas was drawn from electoral rolls. Questions examined sociodemographic information, the direct impact of flooding on the household, and perceived flood-related health impacts. Outcome variables included perceived flood-related effects on overall and respiratory health, along with mental health outcomes measured by psychosocial distress, reduced sleep quality and probable post-traumatic stress disorder (PTSD). Multivariable logistic regression was used to examine the association between flooding and health outcome variables, adjusted for current health status and socioeconomic factors. Results: 3000 residents were invited to participate in this survey, with 960 responses (32%). People whose households were directly impacted by flooding had a decrease in perceived overall health (OR 5.3, 95% CI: 2.8–10.2), along with increases in psychological distress (OR 1.9, 1.1–3.5), decreased sleep quality (OR 2.3, 1.2–4.4), and probable PTSD (OR 2.3, 1.2–4.5). Residents were also more likely to increase usage of both tobacco (OR 6.3, 2.4–16.8) and alcohol (OR 7.0, 2.2–22.3) after flooding. Conclusions: There were significant impacts of flood events on residents’ health, in particular psychosocial health. Improved support strategies may need to be integrated into existing disaster management programs to reduce flood-related health impacts.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Accounting for costs

In Golder Associates Pty Ltd v Challen [2012] QDC 11 Samios DCJ recognised a solicitor’s lien over the file for unpaid fees and confirmed that a lien should not be lightly set aside. The decision, which is under appeal, adds to the range of authorities which are now grappling with some of the provisions of the Legal Profession Act 2007 (Qld) (the LPA) relating to costs billing and assessment. These would appear to have been drafted without a great deal of intellectual rigour (cf. Turner v Mitchells Solicitors [2011] QDC 61 at [26]).

A randomised trial of a psychosocial intervention for cancer patients integrated into routine care: The PROMPT study (promoting optimal outcomes in mood through tailored psychosocial therapies)

Background Despite evidence that up to 35% of patients with cancer experience significant distress, access to effective psychosocial care is limited by lack of systematic approaches to assessment, a paucity of psychosocial services, and patient reluctance to accept treatment either because of perceived stigma or difficulties with access to specialist psycho-oncology services due to isolation or disease burden. This paper presents an overview of a randomised study to evaluate the effectiveness of a brief tailored psychosocial Intervention delivered by health professionals in cancer care who undergo focused training and participate in clinical supervision. Methods/design Health professionals from the disciplines of nursing, occupational therapy, speech pathology, dietetics, physiotherapy or radiation therapy will participate in training to deliver the psychosocial Intervention focusing on core concepts of supportive-expressive, cognitive and dignity-conserving care. Health professional training will consist of completion of a self-directed manual and participation in a skills development session. Participating health professionals will be supported through structured clinical supervision whilst delivering the Intervention. In the stepped wedge design each of the 5 participating clinical sites will be allocated in random order from Control condition to Training then delivery of the Intervention. A total of 600 patients will be recruited across all sites. Based on level of distress or risk factors eligible patients will receive up to 4 sessions, each of up to 30 minutes in length, delivered face-to-face or by telephone. Participants will be assessed at baseline and 10-week follow-up. Patient outcome measures include anxiety and depression, quality of life, unmet psychological and supportive care needs. Health professional measures include psychological morbidity, stress and burnout. Process evaluation will be conducted to assess perceptions of participation in the study and the factors that may promote translation of learning into practice. Discussion This study will provide important information about the effectiveness of a brief tailored psychological Intervention for patients with cancer and the potential to prevent development of significant distress in patients considered at risk. It will yield data about the feasibility of this model of care in routine clinical practice and identify enablers and barriers to its systematic implementation in cancer settings.

As trajetorias de carreiras tradicionais estao dando passegem as proteanas? Um estudo com gereentes no setor public Australiano com foco em diferencas quanto ao genero ( Have traditional career paths given way to protean ones?: Evidence from senior managers in the Australian public sector)

Purpose – This mixed-method study aims to determine the extent to which the career paths of senior managers conform with the traditional versus protean elements described in the careers literature and whether these paths vary by gender. Design/methodology/approach – A total of 15 senior managers (seven women and eight men) in a large public sector agency in Australia were interviewed about their career trajectories to date. Data were coded according to four major areas which characterise and distinguish between traditional and protean careers: development, orientation of the employee, definition of success, and organisational environment. A total of 81 managers (34 women and 47 men) from the same organisation were also surveyed. Variables of interest were those that could be triangulated with qualitative data such as the availability of career opportunities. Findings – Results suggest that, contrary to much existing literature which proposes that all careers have been fundamentally altered, the traditional career which relies on length of service, geographic mobility and a steady climb up the corporate ladder, is still the dominant model in some organisations. However, the trend towards protean careers is evident and is more pronounced for women than for men. Research limitations/implications – The specific nature of the organisation (large, male-dominated, public sector) may limit the generalisability of results. Practical implications – The framework used to explore career paths according to traditional/ protean elements in this study may assist human resource practitioners to develop appropriate strategies which maximise the professional development of employees. Originality/value – The results of this research challenge the universality of change in the nature of careers, particularly in public sector environments.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Is the unigram relevance model term independent? Classifying term dependencies in query expansion

This paper develops a framework for classifying term dependencies in query expansion with respect to the role terms play in structural linguistic associations. The framework is used to classify and compare the query expansion terms produced by the unigram and positional relevance models. As the unigram relevance model does not explicitly model term dependencies in its estimation process it is often thought to ignore dependencies that exist between words in natural language. The framework presented in this paper is underpinned by two types of linguistic association, namely syntagmatic and paradigmatic associations. It was found that syntagmatic associations were a more prevalent form of linguistic association used in query expansion. Paradoxically, it was the unigram model that exhibited this association more than the positional relevance model. This surprising finding has two potential implications for information retrieval models: (1) if linguistic associations underpin query expansion, then a probabilistic term dependence assumption based on position is inadequate for capturing them; (2) the unigram relevance model captures more term dependency information than its underlying theoretical model suggests, so its normative position as a baseline that ignores term dependencies should perhaps be reviewed.