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.

Age-related differences in exercise and quality of life among breast cancer survivors

Purpose: Physical activity has become a focus of cancer recovery research as it has the potential to reduce treatment-related burden and optimize health-related quality of life (HRQoL). However, the potential for physical activity to influence recovery may be age-dependent. This paper describes physical activity levels and HRQoL among younger and older women after surgery for breast cancer and explores the correlates of physical inactivity. Methods: A population-based sample of breast cancer patients diagnosed in South-East Queensland, Australia, (n=287) were assessed once every three months, from 6 to 18 months post-surgery. The Functional Assessment of Cancer Therapy-Breast questionnaire (FACTB+4) and items from the Behavioral Risk Factor Surveillance System (BRFSS) questionnaire were used to measure HRQoL and physical activity, respectively. Physical activity was assigned metabolic equivalent task (MET) values, and categorized as < 3, 3 to 17.9 and 18+ MET-hours/weeks. Descriptive statistics, generalized linear models with age stratification (<50 years versus 50+ years), and logistic regression were used for analyses (p=0.05, two-tailed). Results: Younger women who engaged in 3 or more MET-hours/week of physical activity reported a higher HRQoL at 18 months compared to their more sedentary counterparts (p<0.05). Older women reported similar HRQoL irrespective of activity level and consistently reported clinically higher HRQoL than younger women. Increasing age, being overweight or obese, and restricting use of the treated side at six months post-surgery increased the likelihood of sedentary behavior (OR>3, p<0.05). Conclusions: Age influences the potential to observe HRQoL benefits related to physical activity participation. These results also provide relevant information for the design of exercise interventions for breast cancer survivors and highlights that some groups of women are at greater risk of long-term sedentary behavior.

How current pedagogy methods in games teaching in the UK, Australia and the US have been shaped by historical, socio cultural, environmental and political constraints

Crucial to enhancing the status and quality of games teaching in schools is a developed understanding of the teaching strategies adopted by practitioners. In this paper, we will demonstrate that contemporary games‟ teaching is a product of individual, task and environmental constraints (Newell, 1986). More specifically, we will show that current pedagogy in the U.K., Australia and the United States is strongly influenced by historical, socio-cultural environmental and political constraints. In summary, we will aim to answer the question „why do teachers teach games the way they do.‟ In answering this question, we conclude that teacher educators, who are trying to influence pedagogical practice, must understand these potential constraints and provide appropriate pre-service experiences to give future physical education teachers the knowledge, confidence and ability to adopt a range of teaching styles when they become fully fledged teachers. Essential to this process is the need to enable future practitioners to base their pedagogical practice on a sound understanding of contemporary learning theories of skill acquisition.

Increased cardio-metabolic risk is associated with increased TV viewing time

Purpose: Television viewing time, independent of leisure-time physical activity, has cross-sectional relationships with the metabolic syndrome and its individual components. We examined whether baseline and five-year changes in self-reported television viewing time are associated with changes in continuous biomarkers of cardio-metabolic risk (waist circumference, triglycerides, high density lipoprotein cholesterol, systolic and diastolic blood pressure, fasting plasma glucose; and a clustered cardio-metabolic risk score) in Australian adults. Methods: AusDiab is a prospective, population-based cohort study with biological, behavioral, and demographic measures collected in 1999–2000 and 2004–2005. Non-institutionalized adults aged ≥ 25 years were measured at baseline (11,247; 55% of those completing an initial household interview); 6,400 took part in the five-year follow-up biomedical examination, and 3,846 met the inclusion criteria for this analysis. Multiple linear regression analysis was used and unstandardized B coefficients (95% CI) are provided. Results: Baseline television viewing time (10 hours/week unit) was not significantly associated with change in any of the biomarkers of cardio-metabolic risk. Increases in television viewing time over five years (10 hours/week unit) were associated with increases in: waist circumference (cm) (men: 0.43 (0.08, 0.78), P = 0.02; women: 0.68 (0.30, 1.05), P <0.001), diastolic blood pressure (mmHg) (women: 0.47 (0.02, 0.92), P = 0.04), and the clustered cardio-metabolic risk score (women: 0.03 (0.01, 0.05), P = 0.007). These associations were independent of baseline television viewing time and baseline and change in physical activity and other potential confounders. Conclusion: These findings indicate that an increase in television viewing time is associated with adverse cardio-metabolic biomarker changes. Further prospective studies using objective measures of several sedentary behaviors are required to confirm causality of the associations found.

Ticagrelor, a platelet aggregation inhibitor for the potential prevention and treatment of arterial thrombosis and acute coronary syndromes

Ticagrelor is an orally active ADP P2Y12 receptor antagonist in development by AstraZeneca plc for the reduction of recurrent ischemic events in patients with acute coronary syndromes (ACS). Prior to the development of ticagrelor, thienopyridine compounds, such as clopidogrel, were the focus of research into therapies for ACS. Although the thienopyridines are effective platelet aggregation inhibitors, they are prodrugs and, consequently, exert a slow onset of action. In addition, the variability in inter-individual metabolism of thienopyridine prodrugs has been associated with reduced efficacy in some patients. Ticagrelor is not a prodrug and exhibits a more rapid onset of action than the thienopyridine prodrugs. In clinical trials conducted to date, ticagrelor was a potent inhibitor of ADP-induced platelet aggregation and demonstrated effects that were comparable to clopidogrel. In a phase II, short-term trial, the bleeding profile of participants treated with ticagrelor was similar to that obtained with clopidogrel; however, an increased incidence of dyspnea was observed - an effect that has not been reported with the thienopyridines. Considering the occurrence of dyspnea, and the apparent non-superiority of ticagrelor to clopidogrel, it is difficult to justify a clear benefit to the continued development of ticagrelor. Outcomes from an ongoing phase III trial comparing ticagrelor with clopidogrel in 18,000 patients with ACS are likely to impact on the future development of ticagrelor.

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.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Modeling the impact of potential vaccines on epidemics of sexually transmitted chlamydia trachomatis infection

Background. We investigated the likely impact of vaccines on the prevalence of and morbidity due to Chlamydia trachomatis (chlamydia) infections in heterosexual populations. Methods.An individual‐based mathematical model of chlamydia transmission was developed and linked to the infection course in chlamydia‐infected individuals. The model describes the impact of a vaccine through its effect on the chlamydial load required to infect susceptible individuals (the “critical load”), the load in infected individuals, and their subsequent infectiousness. The model was calibrated using behavioral, biological, and clinical data. Results.A fully protective chlamydia vaccine administered before sexual debut can theoretically eliminate chlamydia epidemics within 20 years. Partially effective vaccines can still greatly reduce the incidence of chlamydia infection. Vaccines should aim primarily to increase the critical load in susceptible individuals and secondarily to decrease the peak load and/or the duration of infection in vaccinated individuals who become infected. Vaccinating both sexes has a beneficial impact on chlamydia‐related morbidity, but targeting women is more effective than targeting men. Conclusions.Our findings can be used in laboratory settings to evaluate vaccine candidates in animal models, by regulatory bodies in the promotion of candidates for clinical trials, and by public health authorities in deciding on optimal intervention strategies.

Determining a set of surrogate parameters to evaluate urban stormwater quality

This thesis details methodology to estimate urban stormwater quality based on a set of easy to measure physico-chemical parameters. These parameters can be used as surrogate parameters to estimate other key water quality parameters. The key pollutants considered in this study are nitrogen compounds, phosphorus compounds and solids. The use of surrogate parameter relationships to evaluate urban stormwater quality will reduce the cost of monitoring and so that scientists will have added capability to generate a large amount of data for more rigorous analysis of key urban stormwater quality processes, namely, pollutant build-up and wash-off. This in turn will assist in the development of more stringent stormwater quality mitigation strategies. The research methodology was based on a series of field investigations, laboratory testing and data analysis. Field investigations were conducted to collect pollutant build-up and wash-off samples from residential roads and roof surfaces. Past research has identified that these impervious surfaces are the primary pollutant sources to urban stormwater runoff. A specially designed vacuum system and rainfall simulator were used in the collection of pollutant build-up and wash-off samples. The collected samples were tested for a range of physico-chemical parameters. Data analysis was conducted using both univariate and multivariate data analysis techniques. Analysis of build-up samples showed that pollutant loads accumulated on road surfaces are higher compared to the pollutant loads on roof surfaces. Furthermore, it was found that the fraction of solids smaller than 150 ìm is the most polluted particle size fraction in solids build-up on both roads and roof surfaces. The analysis of wash-off data confirmed that the simulated wash-off process adopted for this research agrees well with the general understanding of the wash-off process on urban impervious surfaces. The observed pollutant concentrations in wash-off from road surfaces were different to pollutant concentrations in wash-off from roof surfaces. Therefore, firstly, the identification of surrogate parameters was undertaken separately for roads and roof surfaces. Secondly, a common set of surrogate parameter relationships were identified for both surfaces together to evaluate urban stormwater quality. Surrogate parameters were identified for nitrogen, phosphorus and solids separately. Electrical conductivity (EC), total organic carbon (TOC), dissolved organic carbon (DOC), total suspended solids (TSS), total dissolved solids (TDS), total solids (TS) and turbidity (TTU) were selected as the relatively easy to measure parameters. Consequently, surrogate parameters for nitrogen and phosphorus were identified from the set of easy to measure parameters for both road surfaces and roof surfaces. Additionally, surrogate parameters for TSS, TDS and TS which are key indicators of solids were obtained from EC and TTU which can be direct field measurements. The regression relationships which were developed for surrogate parameters and key parameter of interest were of a similar format for road and roof surfaces, namely it was in the form of simple linear regression equations. The identified relationships for road surfaces were DTN-TDS:DOC, TP-TS:TOC, TSS-TTU, TDS-EC and TSTTU: EC. The identified relationships for roof surfaces were DTN-TDS and TSTTU: EC. Some of the relationships developed had a higher confidence interval whilst others had a relatively low confidence interval. The relationships obtained for DTN-TDS, DTN-DOC, TP-TS and TS-EC for road surfaces demonstrated good near site portability potential. Currently, best management practices are focussed on providing treatment measures for stormwater runoff at catchment outlets where separation of road and roof runoff is not found. In this context, it is important to find a common set of surrogate parameter relationships for road surfaces and roof surfaces to evaluate urban stormwater quality. Consequently DTN-TDS, TS-EC and TS-TTU relationships were identified as the common relationships which are capable of providing measurements of DTN and TS irrespective of the surface type.

Biomechanical aspects of bone microstructure in vertebrates : potential approach to paleontological investigations

The biomechanical or biophysical principles can be applied to study biological structures in their modern or fossil form. Bone is an important tissue in paleontological studies as it is a commonly preserved element in most fossil vertebrates, and can often allow its microstructures such as lacuna and canaliculi to be studied in detail. In this context, the principles of Fluid Mechanics and Scaling Laws have been previously applied to enhance the understanding of bone microarchitecture and their implications for the evolution of hydraulic structures to transport fluid. It has been shown that the microstructure of bone has evolved to maintain efficient transport between the nutrient supply and cells, the living components of the tissue. Application of the principle of minimal expenditure of energy to this analysis shows that the path distance comprising five or six lamellar regions represents an effective limit for fluid and solute transport between the nutrient supply and cells; beyond this threshold, hydraulic resistance in the network increases and additional energy expenditure is necessary for further transportation. This suggests an optimization of the size of bone’s building blocks (such as osteon or trabecular thickness) to meet the metabolic demand concomitant to minimal expenditure of energy. This biomechanical aspect of bone microstructure is corroborated from the ratio of osteon to Haversian canal diameters and scaling constants of several mammals considered in this study. This aspect of vertebrate bone microstructure and physiology may provide a basis of understanding of the form and function relationship in both extinct and extant taxa.

The impact of delayed blood centrifuging, choice of collection tube, and type of assay on 25-hydroxyvitamin D concentrations

Studies have examined the associations between cancers and circulating 25-hydroxyvitamin D [25(OH)D], but little is known about the impact of different laboratory practices on 25(OH)D concentrations. We examined the potential impact of delayed blood centrifuging, choice of collection tube, and type of assay on 25(OH)D concentrations. Blood samples from 20 healthy volunteers underwent alternative laboratory procedures: four centrifuging times (2, 24, 72, and 96 h after blood draw); three types of collection tubes (red top serum tube, two different plasma anticoagulant tubes containing heparin or EDTA); and two types of assays (DiaSorin radioimmunoassay [RIA] and chemiluminescence immunoassay [CLIA/LIAISON®]). Log-transformed 25(OH)D concentrations were analyzed using the generalized estimating equations (GEE) linear regression models. We found no difference in 25(OH)D concentrations by centrifuging times or type of assay. There was some indication of a difference in 25(OH)D concentrations by tube type in CLIA/LIAISON®-assayed samples, with concentrations in heparinized plasma (geometric mean, 16.1 ng ml−1) higher than those in serum (geometric mean, 15.3 ng ml−1) (p = 0.01), but the difference was significant only after substantial centrifuging delays (96 h). Our study suggests no necessity for requiring immediate processing of blood samples after collection or for the choice of a tube type or assay.