A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

We propose an alternative crack propagation algo- rithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algo- rithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equa- tions is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algo- rithm, we use five quasi-brittle benchmarks, all successfully solved.

Damage and fracture algorithm using the screened Poisson equation and local remeshing

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the cap- turing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, cir- cumventing the need for a specific direction criterion. Observed phenomena such as mul- tiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests.

Using linear algebra for protein structural comparison and classification.

In this article, we describe a novel methodology to extract semantic characteristics from protein structures using linear algebra in order to compose structural signature vectors which may be used efficiently to compare and classify protein structures into fold families. These signatures are built from the pattern of hydrophobic intrachain interactions using Singular Value Decomposition (SVD) and Latent Semantic Indexing (LSI) techniques. Considering proteins as documents and contacts as terms, we have built a retrieval system which is able to find conserved contacts in samples of myoglobin fold family and to retrieve these proteins among proteins of varied folds with precision of up to 80%. The classifier is a web tool available at our laboratory website. Users can search for similar chains from a specific PDB, view and compare their contact maps and browse their structures using a JMol plug-in.

Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

Space-time variation of malaria incidence in Yunnan province, China

Abstract Background Understanding spatio-temporal variation in malaria incidence provides a basis for effective disease control planning and monitoring. Methods Monthly surveillance data between 1991 and 2006 for Plasmodium vivax and Plasmodium falciparum malaria across 128 counties were assembled for Yunnan, a province of China with one of the highest burdens of malaria. County-level Bayesian Poisson regression models of incidence were constructed, with effects for rainfall, maximum temperature and temporal trend. The model also allowed for spatial variation in county-level incidence and temporal trend, and dependence between incidence in June–September and the preceding January–February. Results Models revealed strong associations between malaria incidence and both rainfall and maximum temperature. There was a significant association between incidence in June–September and the preceding January–February. Raw standardised morbidity ratios showed a high incidence in some counties bordering Myanmar, Laos and Vietnam, and counties in the Red River valley. Clusters of counties in south-western and northern Yunnan were identified that had high incidence not explained by climate. The overall trend in incidence decreased, but there was significant variation between counties. Conclusion Dependence between incidence in summer and the preceding January–February suggests a role of intrinsic host-pathogen dynamics. Incidence during the summer peak might be predictable based on incidence in January–February, facilitating malaria control planning, scaled months in advance to the magnitude of the summer malaria burden. Heterogeneities in county-level temporal trends suggest that reductions in the burden of malaria have been unevenly distributed throughout the province.

Determinants of pre-hospital care non-usage for patients with emergency care needs [including commentary by Snooks H.]

Objective-To establish the demographic, health status and insurance determinants of pre-hospital ambulance non-usage for patients with emergency medical needs. Methods-Triage category, date of birth, sex, marital status, country of origin, method and time of arrival, ambulance insurance status, diagnosis, and disposal were collected for all patients who presented over a four month period (n=10 229) to the emergency department of a major provincial hospital. Data for patients with urgent (n=678) or critical care needs (n=332) who did not use pre-hospital care were analysed using Poisson regression. Results-Only a small percentage (6.6%) of the total sample were triaged as having urgent medical needs or critical care needs (3.2%). Predictors of usage for those with urgent care needs included age greater than 65 years (prevalence ratio (PR)=0.54; 95% confidence interval (CI)= 0.35 to 0.83), being admitted to intensive care or transferred to another hospital (PR=0.62; 95% CI=0.44 to 0.89) or ward (PR=0.72; 95% CI=0.56 to 0.93) and ambulance insurance status (PR=0.67; 95% CI=052 to 0.86). Sex, marital status, time of day and country of origin were not predictive of usage and non-usage. Predictors of usage for those with critical care needs included age 65 years or greater (PR=0.45; 95% CI=0.25 to 0.81) and a diagnosis of trauma (PR=0.49; 95% CI=0.26 to 0.92). A non-English speaking background was predictive of non-usage (PR=1.98; 95% CI=1.06 to 3.70). Sex, marital status, time of day, triage and ambulance insurance status were not predictive of non-usage. Conclusions-Socioeconomic and medical factors variously influence ambulance usage depending on the severity or urgency of the medical condition. Ambulance insurance status was less of an influence as severity of condition increased suggesting that, at a critical level of urgency, patients without insurance are willing to pay for a pre-hospital ambulance service.

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Vision, functional and cognitive determinants of motor vehicle incidents in older drivers

Background: The proportion of older individuals in the driving population is predicted to increase in the next 50 years. This has important implications for driving safety as abilities which are important for safe driving, such as vision (which accounts for the majority of the sensory input required for driving), processing ability and cognition have been shown to decline with age. The current methods employed for screening older drivers upon re-licensure are also vision based. This study, which investigated social, behavioural and professional aspects involved with older drivers, aimed to determine: (i) if the current visual standards in place for testing upon re-licensure are effective in reducing the older driver fatality rate in Australia; (ii) if the recommended visual standards are actually implemented as part of the testing procedures by Australian optometrists; and (iii) if there are other non-standardised tests which may be better at predicting the on-road incident-risk (including near misses and minor incidents) in older drivers than those tests recommended in the standards. Methods: For the first phase of the study, state-based age- and gender-stratified numbers of older driver fatalities for 2000-2003 were obtained from the Australian Transportation Safety Bureau database. Poisson regression analyses of fatality rates were considered by renewal frequency and jurisdiction (as separate models), adjusting for possible confounding variables of age, gender and year. For the second phase, all practising optometrists in Australia were surveyed on the vision tests they conduct in consultations relating to driving and their knowledge of vision requirements for older drivers. Finally, for the third phase of the study to investigate determinants of on-road incident risk, a stratified random sample of 600 Brisbane residents aged 60 years and were selected and invited to participate using an introductory letter explaining the project requirements. In order to capture the number and type of road incidents which occurred for each participant over 12 months (including near misses and minor incidents), an important component of the prospective research study was the development and validation of a driving diary. The diary was a tool in which incidents that occurred could be logged at that time (or very close in time to which they occurred) and thus, in comparison with relying on participant memory over time, recall bias of incident occurrence was minimised. Association between all visual tests, cognition and scores obtained for non-standard functional tests with retrospective and prospective incident occurrence was investigated. Results: In the first phase,rivers aged 60-69 years had a 33% lower fatality risk (Rate Ratio [RR] = 0.75, 95% CI 0.32-1.77) in states with vision testing upon re-licensure compared with states with no vision testing upon re-licensure, however, because the CIs are wide, crossing 1.00, this result should be regarded with caution. However, overall fatality rates and fatality rates for those aged 70 years and older (RR=1.17, CI 0.64-2.13) did not differ between states with and without license renewal procedures, indicating no apparent benefit in vision testing legislation. For the second phase of the study, nearly all optometrists measured visual acuity (VA) as part of a vision assessment for re-licensing, however, 20% of optometrists did not perform any visual field (VF) testing and only 20% routinely performed automated VF on older drivers, despite the standards for licensing advocating automated VF as part of the vision standard. This demonstrates the need for more effective communication between the policy makers and those responsible for carrying out the standards. It may also indicate that the overall higher driver fatality rate in jurisdictions with vision testing requirements is resultant as the tests recommended by the standards are only partially being conducted by optometrists. Hence a standardised protocol for the screening of older drivers for re-licensure across the nation must be established. The opinions of Australian optometrists with regard to the responsibility of reporting older drivers who fail to meet the licensing standards highlighted the conflict between maintaining patient confidentiality or upholding public safety. Mandatory reporting requirements of those drivers who fail to reach the standards necessary for driving would minimise potential conflict between the patient and their practitioner, and help maintain patient trust and goodwill. The final phase of the PhD program investigated the efficacy of vision, functional and cognitive tests to discriminate between at-risk and safe older drivers. Nearly 80% of the participants experienced an incident of some form over the prospective 12 months, with the total incident rate being 4.65/10 000 km. Sixty-three percent reported having a near miss and 28% had a minor incident. The results from the prospective diary study indicate that the current vision screening tests (VA and VF) used for re-licensure do not accurately predict older drivers who are at increased odds of having an on-road incident. However, the variation in visual measurements of the cohort was narrow, also affecting the results seen with the visual functon questionnaires. Hence a larger cohort with greater variability should be considered for a future study. A slightly lower cognitive level (as measured with the Mini-Mental State Examination [MMSE]) did show an association with incident involvement as did slower reaction time (RT), however the Useful-Field-of-View (UFOV) provided the most compelling results of the study. Cut-off values of UFOV processing (>23.3ms), divided attention (>113ms), selective attention (>258ms) and overall score (moderate/ high/ very high risk) were effective in determining older drivers at increased odds of having any on-road incident and the occurrence of minor incidents. Discussion: The results have shown that for the 60-69 year age-group, there is a potential benefit in testing vision upon licence renewal. However, overall fatality rates and fatality rates for those aged 70 years and older indicated no benefit in vision testing legislation and suggests a need for inclusion of screening tests which better predict on-road incidents. Although VA is routinely performed by Australian optometrists on older drivers renewing their licence, VF is not. Therefore there is a need for a protocol to be developed and administered which would result in standardised methods conducted throughout the nation for the screening of older drivers upon re-licensure. Communication between the community, policy makers and those conducting the protocol should be maximised. By implementing a standardised screening protocol which incorporates a level of mandatory reporting by the practitioner, the ethical dilemma of breaching patient confidentiality would also be resolved. The tests which should be included in this screening protocol, however, cannot solely be ones which have been implemented in the past. In this investigation, RT, MMSE and UFOV were shown to be better determinants of on-road incidents in older drivers than VA and VF, however, as previously mentioned, there was a lack of variability in visual status within the cohort. Nevertheless, it is the recommendation from this investigation, that subject to appropriate sensitivity and specificity being demonstrated in the future using a cohort with wider variation in vision, functional performance and cognition, these tests of cognition and information processing should be added to the current protocol for the screening of older drivers which may be conducted at licensing centres across the nation.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Socio-environmental factors and suicide in Queensland, Australia

Suicide has drawn much attention from both the scientific community and the public. Examining the impact of socio-environmental factors on suicide is essential in developing suicide prevention strategies and interventions, because it will provide health authorities with important information for their decision-making. However, previous studies did not examine the impact of socio-environmental factors on suicide using a spatial analysis approach. The purpose of this study was to identify the patterns of suicide and to examine how socio-environmental factors impact on suicide over time and space at the Local Governmental Area (LGA) level in Queensland. The suicide data between 1999 and 2003 were collected from the Australian Bureau of Statistics (ABS). Socio-environmental variables at the LGA level included climate (rainfall, maximum and minimum temperature), Socioeconomic Indexes for Areas (SEIFA) and demographic variables (proportion of Indigenous population, unemployment rate, proportion of population with low income and low education level). Climate data were obtained from Australian Bureau of Meteorology. SEIFA and demographic variables were acquired from ABS. A series of statistical and geographical information system (GIS) approaches were applied in the analysis. This study included two stages. The first stage used average annual data to view the spatial pattern of suicide and to examine the association between socio-environmental factors and suicide over space. The second stage examined the spatiotemporal pattern of suicide and assessed the socio-environmental determinants of suicide, using more detailed seasonal data. In this research, 2,445 suicide cases were included, with 1,957 males (80.0%) and 488 females (20.0%). In the first stage, we examined the spatial pattern and the determinants of suicide using 5-year aggregated data. Spearman correlations were used to assess associations between variables. Then a Poisson regression model was applied in the multivariable analysis, as the occurrence of suicide is a small probability event and this model fitted the data quite well. Suicide mortality varied across LGAs and was associated with a range of socio-environmental factors. The multivariable analysis showed that maximum temperature was significantly and positively associated with male suicide (relative risk [RR] = 1.03, 95% CI: 1.00 to 1.07). Higher proportion of Indigenous population was accompanied with more suicide in male population (male: RR = 1.02, 95% CI: 1.01 to 1.03). There was a positive association between unemployment rate and suicide in both genders (male: RR = 1.04, 95% CI: 1.02 to 1.06; female: RR = 1.07, 95% CI: 1.00 to 1.16). No significant association was observed for rainfall, minimum temperature, SEIFA, proportion of population with low individual income and low educational attainment. In the second stage of this study, we undertook a preliminary spatiotemporal analysis of suicide using seasonal data. Firstly, we assessed the interrelations between variables. Secondly, a generalised estimating equations (GEE) model was used to examine the socio-environmental impact on suicide over time and space, as this model is well suited to analyze repeated longitudinal data (e.g., seasonal suicide mortality in a certain LGA) and it fitted the data better than other models (e.g., Poisson model). The suicide pattern varied with season and LGA. The north of Queensland had the highest suicide mortality rate in all the seasons, while there was no suicide case occurred in the southwest. Northwest had consistently higher suicide mortality in spring, autumn and winter. In other areas, suicide mortality varied between seasons. This analysis showed that maximum temperature was positively associated with suicide among male population (RR = 1.24, 95% CI: 1.04 to 1.47) and total population (RR = 1.15, 95% CI: 1.00 to 1.32). Higher proportion of Indigenous population was accompanied with more suicide among total population (RR = 1.16, 95% CI: 1.13 to 1.19) and by gender (male: RR = 1.07, 95% CI: 1.01 to 1.13; female: RR = 1.23, 95% CI: 1.03 to 1.48). Unemployment rate was positively associated with total (RR = 1.40, 95% CI: 1.24 to 1.59) and female (RR=1.09, 95% CI: 1.01 to 1.18) suicide. There was also a positive association between proportion of population with low individual income and suicide in total (RR = 1.28, 95% CI: 1.10 to 1.48) and male (RR = 1.45, 95% CI: 1.23 to 1.72) population. Rainfall was only positively associated with suicide in total population (RR = 1.11, 95% CI: 1.04 to 1.19). There was no significant association for rainfall, minimum temperature, SEIFA, proportion of population with low educational attainment. The second stage is the extension of the first stage. Different spatial scales of dataset were used between the two stages (i.e., mean yearly data in the first stage, and seasonal data in the second stage), but the results are generally consistent with each other. Compared with other studies, this research explored the variety of the impact of a wide range of socio-environmental factors on suicide in different geographical units. Maximum temperature, proportion of Indigenous population, unemployment rate and proportion of population with low individual income were among the major determinants of suicide in Queensland. However, the influence from other factors (e.g. socio-culture background, alcohol and drug use) influencing suicide cannot be ignored. An in-depth understanding of these factors is vital in planning and implementing suicide prevention strategies. Five recommendations for future research are derived from this study: (1) It is vital to acquire detailed personal information on each suicide case and relevant information among the population in assessing the key socio-environmental determinants of suicide; (2) Bayesian model could be applied to compare mortality rates and their socio-environmental determinants across LGAs in future research; (3) In the LGAs with warm weather, high proportion of Indigenous population and/or unemployment rate, concerted efforts need to be made to control and prevent suicide and other mental health problems; (4) The current surveillance, forecasting and early warning system needs to be strengthened, to trace the climate and socioeconomic change over time and space and its impact on population health; (5) It is necessary to evaluate and improve the facilities of mental health care, psychological consultation, suicide prevention and control programs; especially in the areas with low socio-economic status, high unemployment rate, extreme weather events and natural disasters.