Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Fast exact nearest neighbour matching in high dimensions using d-D Sort

Data structures such as k-D trees and hierarchical k-means trees perform very well in approximate k nearest neighbour matching, but are only marginally more effective than linear search when performing exact matching in high-dimensional image descriptor data. This paper presents several improvements to linear search that allows it to outperform existing methods and recommends two approaches to exact matching. The first method reduces the number of operations by evaluating the distance measure in order of significance of the query dimensions and terminating when the partial distance exceeds the search threshold. This method does not require preprocessing and significantly outperforms existing methods. The second method improves query speed further by presorting the data using a data structure called d-D sort. The order information is used as a priority queue to reduce the time taken to find the exact match and to restrict the range of data searched. Construction of the d-D sort structure is very simple to implement, does not require any parameter tuning, and requires significantly less time than the best-performing tree structure, and data can be added to the structure relatively efficiently.

Standardising radiation therapy undergraduate competency levels

QUT Bachelor of Radiation Therapy students progress from first visiting a radiation therapy department to graduation and progression into the NPDP over a span of three years. Although there are clear guidelines as to expected competency level post-NPDP, there is still a variety of perceived levels prior to this. Staff and students feedback both suggest that different centres and within centres different staff have differing opinions of these levels. Indeed, many staff members object to the use of the word “competency” for a pre-NPODP undergraduate, preferring the term “achievement”. While it is acknowledged that students progress at different rates, it is vitally important for equity that staff expectations of students at different academic levels are identical. Provision of guidelines for different stages of progression are essential for equitable assessment and most assessments, including the NRTAT are complemented by statements to enable level to be determined. For the University-specific competency assessments some level of consensus between clinical staff is required, especially where students are placed at a large number of different placement sites. Aims The main aim of this initial study is to gauge staff opinions of levels of student progression in order to judge cross-centres consistency. A secondary objective is to evaluate the degree of correlation between staff seniority and perception of student levels. Informal feedback suggests that staff at or just post NPDP level have a different perception of student competency expectations than more senior staff. If these perceptions change with level it will make agreement of guidelines statements more challenging. Study Methods A standard evaluation questionnaire was provided to RT staff participating in ongoing updates to clinical assessment. As part of curriculum development staff were asked to provide anonymous and optional answers to further questions in order to audit current practice. This involved assigning level of student progression to different statements relating to tasks or competencies. After data collation, scores were assigned to level and totals used to rank statements according to perceived student level. Descriptive statistical analysis was used to identify which statements were easier to assign to student level and which were more ambiguous. Further sub-analysis was performed for each category of staff seniority to judge differences in perception. Strength of correlation between seniority and expectation was calculated to confirm or contradict the informal feedback. Results By collating different staff perceptions of competencies for different student levels commonly agreed statements can be used to define achievement level. This presentation outlines the results of the audit including statements that most staff perceived as relevant to a specific student group and statements that staff found to be harder to attribute. Strength of correlation between staff perception and seniority will be outlined where statistically significant.

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBD L are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.

Tackling the health burden from household air pollution (HAP) : development and implementation of new WHO Guidelines

Household air pollution (HAP), arising mainly from the combustion of solid and other polluting fuels, is responsible for a very substantial public health burden, most recently estimated as causing 3.5 million premature deaths in 2010. These patterns of household fuel use have also important negative impacts on safety, prospects for poverty reduction and the environment, including climate change. Building on previous air quality guidelines, the WHO is developing new guidelines focused on household fuel combustion, covering cooking, heating and lighting, and although global, the key focus is low and middle income countries reflecting the distribution of disease burden. As discussed in this paper, currently in development, the guidelines will include reviews of a wide range of evidence including fuel use in homes, emissions from stoves and lighting, household air pollution and exposure levels experienced by populations, health risks, impacts of interventions on HAP and exposure, and also key factors influencing sustainable and equitable adoption of improved stoves and cleaner fuels. GRADE, the standard method used for guidelines evidence review may not be well suited to the variety and nature of evidence required for this project, and a modified approach is being developed and tested. Work on the guidelines is being carried out in close collaboration with the UN Foundation Global Alliance on Clean cookstoves, allowing alignment with specific tools including recently developed international voluntary standards for stoves, and the development of country action plans. Following publication, WHO plans to work closely with a number of countries to learn from implementation efforts, in order to further strengthen support and guidance. A case study on the situation and policy actions to date in Bhutan provide an illustration of the challenges and opportunities involved, and the timely importance of the new guidelines and associated research, evaluation and policy development agendas.

A framework for a dense matching algorithm : Results using matching metrics and order statistic filters

An algorithm for computing dense correspondences between images of a stereo pair or image sequence is presented. The algorithm can make use of both standard matching metrics and the rank and census filters, two filters based on order statistics which have been applied to the image matching problem. Their advantages include robustness to radiometric distortion and amenability to hardware implementation. Results obtained using both real stereo pairs and a synthetic stereo pair with ground truth were compared. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Order statistic filters for image matching

The rank and census are two filters based on order statistics which have been applied to the image matching problem for stereo pairs. Advantages of these filters include their robustness to radiometric distortion and small amounts of random noise, and their amenability to hardware implementation. In this paper, a new matching algorithm is presented, which provides an overall framework for matching, and is used to compare the rank and census techniques with standard matching metrics. The algorithm was tested using both real stereo pairs and a synthetic pair with ground truth. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

The deep trauma of secondary victimisation : parents of sex offenders

The publication of the fourth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV; American Psychiatric Association, 1994) introduced the notion that a life-threatening illness can be a stressor and catalyst for Posttraumatic Stress Disorder (PTSD). Since then a solid body of research has been established investigating the post-diagnosis experience of cancer. These studies have identified a number of short and long-term life changes resulting from a diagnosis of cancer and associated treatments. In this chapter, we discuss the psychosocial response to the cancer experience and the potential for cancer-related distress. Cancer can represent a life-threatening diagnosis that may be associated with aggressive treatments and result in physical and psychological changes. The potential for future trauma through the lasting effects of the disease and treatment, and the possibility of recurrence, can be a source of continued psychological distress. In addition to the documented adverse repercussions of cancer, we also outline the recent shift that has occurred in the psycho-oncology literature regarding positive life change or posttraumatic growth that is commonly reported after a diagnosis of cancer. Adopting a salutogenic framework acknowledges that the cancer experience is a dynamic psychosocial process with both negative and positive repercussions. Next, we describe the situational and individual factors that are associated with posttraumatic growth and the types of positive life change that are prevalent in this context. Finally, we discuss the implications of this research in a therapeutic context and the directions of future posttraumatic growth research with cancer survivors. This chapter will present both quantitative and qualitative research that indicates the potential for personal growth from adversity rather than just mere survival and return to pre-diagnosis functioning. It is important to emphasise however, that the presence of growth and prevalence of resilience does not negate the extremely distressing nature of a cancer diagnosis for the patient and their families and the suffering that can accompany treatment regimes. Indeed, it will be explained that for growth to occur, the experience must be one that quite literally shatters previously held schemas in order to act as a catalyst for change.

Depression among Holocaust survivors : a meta-analytic review

The publication of the fourth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV; American Psychiatric Association, 1994) introduced the notion that a life-threatening illness can be a stressor and catalyst for Posttraumatic Stress Disorder (PTSD). Since then a solid body of research has been established investigating the post-diagnosis experience of cancer. These studies have identified a number of short and long-term life changes resulting from a diagnosis of cancer and associated treatments. In this chapter, we discuss the psychosocial response to the cancer experience and the potential for cancer-related distress. Cancer can represent a life-threatening diagnosis that may be associated with aggressive treatments and result in physical and psychological changes. The potential for future trauma through the lasting effects of the disease and treatment, and the possibility of recurrence, can be a source of continued psychological distress. In addition to the documented adverse repercussions of cancer, we also outline the recent shift that has occurred in the psycho-oncology literature regarding positive life change or posttraumatic growth that is commonly reported after a diagnosis of cancer. Adopting a salutogenic framework acknowledges that the cancer experience is a dynamic psychosocial process with both negative and positive repercussions. Next, we describe the situational and individual factors that are associated with posttraumatic growth and the types of positive life change that are prevalent in this context. Finally, we discuss the implications of this research in a therapeutic context and the directions of future posttraumatic growth research with cancer survivors. This chapter will present both quantitative and qualitative research that indicates the potential for personal growth from adversity rather than just mere survival and return to pre-diagnosis functioning. It is important to emphasise however, that the presence of growth and prevalence of resilience does not negate the extremely distressing nature of a cancer diagnosis for the patient and their families and the suffering that can accompany treatment regimes. Indeed, it will be explained that for growth to occur, the experience must be one that quite literally shatters previously held schemas in order to act as a catalyst for change.

Supreme Court Act 1995 (Qld) s 253 – whether refusal to stay execution of costs is an order “as to costs only”

In Virgtel Ltd v Zabusky [2009] QCA 92 the Queensland Court of Appeal considered the scope of an order “as to costs only” within the meaning of s 253 of the Supreme Court Act 1995 (Qld) (‘the Act”). The Court also declined to accept submissions from one of the parties after oral hearing, and made some useful comments which serve as a reminder to practitioners of their obligations in that regard.

Disclosure obligations on ex parte application for freezing order - duty of practitioners to the court - failure to comply with duty - serious dereliction of duty to court - supplemental order for costs against solicitors personally

The decision of Applegarth J in Heartwood Architectural & Joinery Pty Ltd v Redchip Lawyers [2009] QSC 195 (27 July 2009) involved a costs order against solicitors personally. This decision is but one of several recent decisions in which the court has been persuaded that the circumstances justified costs orders against legal practitioners on the indemnity basis. These decisions serve as a reminder to practitioners of their disclosure obligations when seeking any interlocutory relief in an ex parte application. These obligations are now clearly set out in r 14.4 of the Legal Profession (Solicitors) Rule 2007 and r 25 of 2007 Barristers Rule. Inexperience or ignorance will not excuse breaches of the duties owed to the court.

Analysis of higher-order aberrations in a large clinical population

Purpose: To use a large wavefront database of a clinical population to investigate relationships between refractions and higher order aberrations and between aberrations of right and left eyes. Methods: Third and fourth-order aberration coefficients and higher-order root-mean-squared aberrations (HO RMS), scaled to a pupil size of 4.5 mm diameter, were analysed in a population of about 24,000 patients from Carl Zeiss Vision's European wavefront database. Correlations were determined between the aberrations and the variables of refraction, near addition and cylinder. Results: Most aberration coefficients were significantly dependent upon these variables, but the proportions of aberrations that could be explained by these factors were less than 2% except for spherical aberration (12%), horizontal coma (9%) and HO RMS (7%). Near addition was the major contributor for horizontal coma (8.5% out of 9.5%) and spherical equivalent was the major contributor for spherical aberration (7.7% out of 11.6%). Interocular correlations were highly significant for all aberration coefficients, varying between 0.16 and 0.81. Anisometropia was a variable of significance for three aberrations (vertical coma, secondary astigmatism and tetrafoil), but little importance can be placed on this because of the small proportions of aberrations that can be explained by refraction (all less than 1.0 %). Conclusions: Most third- and fourth-order aberration coefficients were significantly dependent upon spherical equivalent, near addition and cylinder, but only horizontal coma (9%) and spherical aberration (12%) showed dependencies of greater than 2%. Interocular correlations were highly significant for all aberration coefficients, but anisometropia had little influence on aberration coefficients.

Scaffold percolative efficiency : in vitro evaluation of the structural criterion for electrospun mats

Fibrous scaffolds of engineered structures can be chosen as promising porous environments when an approved criterion validates their applicability for a specific medical purpose. For such biomaterials, this paper sought to investigate various structural characteristics in order to determine whether they are appropriate descriptors. A number of poly(3-hydroxybutyrate) scaffolds were electrospun; each of which possessed a distinguished architecture when their material and processing conditions were altered. Subsequent culture of mouse fibroblast cells (L929) was carried out to evaluate the cells viability on each scaffold after their attachment for 24 h and proliferation for 48 and 72 h. The scaffolds’ porosity, pores number, pores size and distribution were quantified and none could establish a relationship with the viability results. Virtual reconstruction of the mats introduced an authentic criterion, “Scaffold Percolative Efficiency” (SPE), with which the above descriptors were addressed collectively. It was hypothesized to be able to quantify the efficacy of fibrous scaffolds by considering the integration of porosity and interconnectivity of the pores. There was a correlation of 80% as a good agreement between the SPE values and the spectrophotometer absorbance of viable cells; a viability of more than 350% in comparison to that of the controls.

Character in the workplace : self directedness mediates harm avoidance in the prediction of job performance

The purpose of this study was to test a model of the relationship between temperament, character and job performance, in order to better understand the cause of stable individual differences in job performance. Personality was conceptualized in terms of Cloninger, Svrakic and Przybeck’s (1993) theoretical framework of personality. It was expected that Self Directedness (character) would mediate Harm Avoidance and Persistence (temperament) in the prediction of job performance. In order to test the hypotheses, a sample of 94 employee/supervisor pairs was recruited from several organizations across Australia. Participants completed a number of questionnaires online, regarding their personality traits (completed by employees) and Job Performance (completed by Supervisors). Consistent with the hypothesis, Self Directedness was found to be a moderate, direct predictor of job performance. Also consistent with the hypothesis, Self Directedness mediated Harm Avoidance in the prediction of job performance. Results show that character (Self Directedness) is important in the prediction of job performance, and also suggests that fearful, avoidant individuals are less likely to perform well in the workplace, based on their low level of character development.