A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Cross-sectional analysis of undergraduate nursing students' perceptions of bioscience

Nursing was one of the last health professions to be established in the higher education sector. A lingering challence is the integration of bioscience into nursing curriculum. Research suggests that students perceive bioscience teaching to be difficult thereby contributing to heightened anxiety. It has been proposed that high content volume, lack of secondary school science, and predominance of science lectureres without clinical practice experience, may lead to a bioscience disconnet with curricula. To ascertain the extent of this problem, we undertook a cross-sectional designed study of commencing, second and third year undergraduate nursing students (n=566). They were surveyed about perceptions, knowledge and approaches to bioscience learning. Preliminary analysis revealed similar findings between the three different cohorts. Generally, sudents perceived bioscience subjects to be difficult, more challenging and requiring more study hours than clinical nursing subjects. Interestingly, the perception of difficulty and associated anxieties were found in both commencing and existing students. Moreover, students with secondary school biology combined with another science subject perceived bioscience teaching more favourably compared to those who had studied one secondary school science subject. University coursework needs to embed strategies to minimise anxieties about learning bioscience by using innovative deliveries and scaffolded assessments that target the learner's needs.

Metabolic and hormonal responses to isoenergetic high-intensity interval exercise and continuous moderate-intensity exercise

This study investigated the effects of high-intensity interval training (HIIT) vs. work-matched moderate-intensity continuous exercise (MOD) on metabolism and counterregulatory stress hormones. In a randomized and counterbalanced order, 10 well-trained male cyclists and triathletes completed a HIIT session [81.6 ± 3.7% maximum oxygen consumption (V̇o2 max); 72.0 ± 3.2% peak power output; 792 ± 95 kJ] and a MOD session (66.7 ± 3.5% V̇o2 max; 48.5 ± 3.1% peak power output; 797 ± 95 kJ). Blood samples were collected before, immediately after, and 1 and 2 h postexercise. Carbohydrate oxidation was higher (P = 0.037; 20%), whereas fat oxidation was lower (P = 0.037; −47%) during HIIT vs. MOD. Immediately after exercise, plasma glucose (P = 0.024; 20%) and lactate (P < 0.01; 5.4×) were higher in HIIT vs. MOD, whereas total serum free fatty acid concentration was not significantly different (P = 0.33). Targeted gas chromatography-mass spectromtery metabolomics analysis identified and quantified 49 metabolites in plasma, among which 11 changed after both HIIT and MOD, 13 changed only after HIIT, and 5 changed only after MOD. Notable changes included substantial increases in tricarboxylic acid intermediates and monounsaturated fatty acids after HIIT and marked decreases in amino acids during recovery from both trials. Plasma adrenocorticotrophic hormone (P = 0.019), cortisol (P < 0.01), and growth hormone (P < 0.01) were all higher immediately after HIIT. Plasma norepinephrine (P = 0.11) and interleukin-6 (P = 0.20) immediately after exercise were not significantly different between trials. Plasma insulin decreased during recovery from both HIIT and MOD (P < 0.01). These data indicate distinct differences in specific metabolites and counterregulatory hormones following HIIT vs. MOD and highlight the value of targeted metabolomic analysis to provide more detailed insights into the metabolic demands of exercise.

Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

Developing young students’ meta-representational competence through integrated mathematics and science investigations

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.

Global, regional, and national age–sex specifi c all-cause and cause-specifi c mortality for 240 causes of death, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

Background Up-to-date evidence on levels and trends for age-sex-specific all-cause and cause-specific mortality is essential for the formation of global, regional, and national health policies. In the Global Burden of Disease Study 2013 (GBD 2013) we estimated yearly deaths for 188 countries between 1990, and 2013. We used the results to assess whether there is epidemiological convergence across countries. Methods We estimated age-sex-specific all-cause mortality using the GBD 2010 methods with some refinements to improve accuracy applied to an updated database of vital registration, survey, and census data. We generally estimated cause of death as in the GBD 2010. Key improvements included the addition of more recent vital registration data for 72 countries, an updated verbal autopsy literature review, two new and detailed data systems for China, and more detail for Mexico, UK, Turkey, and Russia. We improved statistical models for garbage code redistribution. We used six different modelling strategies across the 240 causes; cause of death ensemble modelling (CODEm) was the dominant strategy for causes with sufficient information. Trends for Alzheimer's disease and other dementias were informed by meta-regression of prevalence studies. For pathogen-specific causes of diarrhoea and lower respiratory infections we used a counterfactual approach. We computed two measures of convergence (inequality) across countries: the average relative difference across all pairs of countries (Gini coefficient) and the average absolute difference across countries. To summarise broad findings, we used multiple decrement life-tables to decompose probabilities of death from birth to exact age 15 years, from exact age 15 years to exact age 50 years, and from exact age 50 years to exact age 75 years, and life expectancy at birth into major causes. For all quantities reported, we computed 95% uncertainty intervals (UIs). We constrained cause-specific fractions within each age-sex-country-year group to sum to all-cause mortality based on draws from the uncertainty distributions. Findings Global life expectancy for both sexes increased from 65·3 years (UI 65·0–65·6) in 1990, to 71·5 years (UI 71·0–71·9) in 2013, while the number of deaths increased from 47·5 million (UI 46·8–48·2) to 54·9 million (UI 53·6–56·3) over the same interval. Global progress masked variation by age and sex: for children, average absolute differences between countries decreased but relative differences increased. For women aged 25–39 years and older than 75 years and for men aged 20–49 years and 65 years and older, both absolute and relative differences increased. Decomposition of global and regional life expectancy showed the prominent role of reductions in age-standardised death rates for cardiovascular diseases and cancers in high-income regions, and reductions in child deaths from diarrhoea, lower respiratory infections, and neonatal causes in low-income regions. HIV/AIDS reduced life expectancy in southern sub-Saharan Africa. For most communicable causes of death both numbers of deaths and age-standardised death rates fell whereas for most non-communicable causes, demographic shifts have increased numbers of deaths but decreased age-standardised death rates. Global deaths from injury increased by 10·7%, from 4·3 million deaths in 1990 to 4·8 million in 2013; but age-standardised rates declined over the same period by 21%. For some causes of more than 100 000 deaths per year in 2013, age-standardised death rates increased between 1990 and 2013, including HIV/AIDS, pancreatic cancer, atrial fibrillation and flutter, drug use disorders, diabetes, chronic kidney disease, and sickle-cell anaemias. Diarrhoeal diseases, lower respiratory infections, neonatal causes, and malaria are still in the top five causes of death in children younger than 5 years. The most important pathogens are rotavirus for diarrhoea and pneumococcus for lower respiratory infections. Country-specific probabilities of death over three phases of life were substantially varied between and within regions. Interpretation For most countries, the general pattern of reductions in age-sex specific mortality has been associated with a progressive shift towards a larger share of the remaining deaths caused by non-communicable disease and injuries. Assessing epidemiological convergence across countries depends on whether an absolute or relative measure of inequality is used. Nevertheless, age-standardised death rates for seven substantial causes are increasing, suggesting the potential for reversals in some countries. Important gaps exist in the empirical data for cause of death estimates for some countries; for example, no national data for India are available for the past decade.

Improved Security Analysis of Fugue-256 (Poster)

We present some improved analytical results as part of the ongoing work on the analysis of Fugue-256 hash function, a second round candidate in the NIST’s SHA3 competition. First we improve Aumasson and Phans’ integral distinguisher on the 5.5 rounds of the final transformation of Fugue-256 to 16.5 rounds. Next we improve the designers’ meet-in-the-middle preimage attack on Fugue-256 from 2480 time and memory to 2416. Finally, we comment on possible methods to obtain free-start distinguishers and free-start collisions for Fugue-256.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Weather variability and influenza A (H7N9) transmission in Shanghai, China: A Bayesian spatial analysis

Abstract Background A novel avian influenza A (H7N9) virus was first found in humans in Shanghai, and infected over 433 patients in China. To date, very little is known about the spatiotemporal variability or environmental drivers of the risk of H7N9 infection. This study explored the spatial and temporal variation of H7N9 infection and assessed the effects of temperature and rainfall on H7N9 incidence. Methods A Bayesian spatial conditional autoregressive (CAR) model was used to assess the spatiotemporal distribution of the risk of H7N9 infection in Shanghai, by district and fortnight for the period 19th February–14th April 2013. Data on daily laboratory-confirmed H7N9 cases, and weather variability including temperature (°C) and rainfall (mm) were obtained from the Chinese Information System for Diseases Control and Prevention and Chinese Meteorological Data Sharing Service System, respectively, and aggregated by fortnight. Results High spatial variations in the H7N9 risk were mainly observed in the east and centre of Shanghai municipality. H7N9 incidence rate was significantly associated with fortnightly mean temperature (Relative Risk (RR): 1.54; 95% credible interval (CI): 1.22–1.94) and fortnightly mean rainfall (RR: 2.86; 95% CI: 1.47–5.56). Conclusion There was a substantial variation in the spatiotemporal distribution of H7N9 infection across different districts in Shanghai. Optimal temperature and rainfall may be one of the driving forces for H7N9.

Socio-environmental drivers and suicide in Australia: Bayesian spatial analysis

Background The impact of socio-environmental factors on suicide has been examined in many studies. Few of them, however, have explored these associations from a spatial perspective, especially in assessing the association between meteorological factors and suicide. This study examined the association of meteorological and socio-demographic factors with suicide across small areas over different time periods. Methods Suicide, population and socio-demographic data (e.g., population of Aboriginal and Torres Strait Islanders (ATSI), and unemployment rate (UNE) at the Local Government Area (LGA) level were obtained from the Australian Bureau of Statistics for the period of 1986 to 2005. Information on meteorological factors (rainfall, temperature and humidity) was supplied by Australian Bureau of Meteorology. A Bayesian Conditional Autoregressive (CAR) Model was applied to explore the association of socio-demographic and meteorological factors with suicide across LGAs. Results In Model I (socio-demographic factors), proportion of ATSI and UNE were positively associated with suicide from 1996 to 2000 (Relative Risk (RR)ATSI = 1.0107, 95% Credible Interval (CI): 1.0062-1.0151; RRUNE = 1.0187, 95% CI: 1.0060-1.0315), and from 2001 to 2005 (RRATSI = 1.0126, 95% CI: 1.0076-1.0176; RRUNE = 1.0198, 95% CI: 1.0041-1.0354). Socio-Economic Index for Area (SEIFA) and IND, however, had negative associations with suicide between 1986 and 1990 (RRSEIFA = 0.9983, 95% CI: 0.9971-0.9995; RRATSI = 0.9914, 95% CI: 0.9848-0.9980). Model II (meteorological factors): a 1°C higher yearly mean temperature across LGAs increased the suicide rate by an average by 2.27% (95% CI: 0.73%, 3.82%) in 1996–2000, and 3.24% (95% CI: 1.26%, 5.21%) in 2001–2005. The associations between socio-demographic factors and suicide in Model III (socio-demographic and meteorological factors) were similar to those in Model I; but, there is no substantive association between climate and suicide in Model III. Conclusions Proportion of Aboriginal and Torres Strait Islanders, unemployment and temperature appeared to be statistically associated with of suicide incidence across LGAs among all selected variables, especially in recent years. The results indicated that socio-demographic factors played more important roles than meteorological factors in the spatial pattern of suicide incidence.

Analysis of moderation practices in a large STEM-focused faculty

Moderation of assessment constitutes a crucial element of the learning and teaching process at the university. Yet, despite its importance, many academics have confusing beliefs and attitudes towards moderation practices, processes and procedures. This paper reports on a qualitative study conducted in a Science, Technology, Engineering and Mathematics (STEM)-focused faculty at a large Australian higher education institution. The findings of the study revealed a strong need for further investigation on the ways moderation is understood and enacted by academics within a STEM-specific context and informed redevelopment of the faculty’s internal moderation policy.

A comparative risk assessment of burden of disease and injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990–2010: A systematic analysis for the Global Burden of Disease Study 2010

BACKGROUND Quantification of the disease burden caused by different risks informs prevention by providing an account of health loss different to that provided by a disease-by-disease analysis. No complete revision of global disease burden caused by risk factors has been done since a comparative risk assessment in 2000, and no previous analysis has assessed changes in burden attributable to risk factors over time. METHODS We estimated deaths and disability-adjusted life years (DALYs; sum of years lived with disability [YLD] and years of life lost [YLL]) attributable to the independent effects of 67 risk factors and clusters of risk factors for 21 regions in 1990 and 2010. We estimated exposure distributions for each year, region, sex, and age group, and relative risks per unit of exposure by systematically reviewing and synthesising published and unpublished data. We used these estimates, together with estimates of cause-specific deaths and DALYs from the Global Burden of Disease Study 2010, to calculate the burden attributable to each risk factor exposure compared with the theoretical-minimum-risk exposure. We incorporated uncertainty in disease burden, relative risks, and exposures into our estimates of attributable burden. FINDINGS In 2010, the three leading risk factors for global disease burden were high blood pressure (7·0% [95% uncertainty interval 6·2-7·7] of global DALYs), tobacco smoking including second-hand smoke (6·3% [5·5-7·0]), and alcohol use (5·5% [5·0-5·9]). In 1990, the leading risks were childhood underweight (7·9% [6·8-9·4]), household air pollution from solid fuels (HAP; 7·0% [5·6-8·3]), and tobacco smoking including second-hand smoke (6·1% [5·4-6·8]). Dietary risk factors and physical inactivity collectively accounted for 10·0% (95% UI 9·2-10·8) of global DALYs in 2010, with the most prominent dietary risks being diets low in fruits and those high in sodium. Several risks that primarily affect childhood communicable diseases, including unimproved water and sanitation and childhood micronutrient deficiencies, fell in rank between 1990 and 2010, with unimproved water and sanitation accounting for 0·9% (0·4-1·6) of global DALYs in 2010. However, in most of sub-Saharan Africa childhood underweight, HAP, and non-exclusive and discontinued breastfeeding were the leading risks in 2010, while HAP was the leading risk in south Asia. The leading risk factor in Eastern Europe, most of Latin America, and southern sub-Saharan Africa in 2010 was alcohol use; in most of Asia, North Africa and Middle East, and central Europe it was high blood pressure. Despite declines, tobacco smoking including second-hand smoke remained the leading risk in high-income north America and western Europe. High body-mass index has increased globally and it is the leading risk in Australasia and southern Latin America, and also ranks high in other high-income regions, North Africa and Middle East, and Oceania. INTERPRETATION Worldwide, the contribution of different risk factors to disease burden has changed substantially, with a shift away from risks for communicable diseases in children towards those for non-communicable diseases in adults. These changes are related to the ageing population, decreased mortality among children younger than 5 years, changes in cause-of-death composition, and changes in risk factor exposures. New evidence has led to changes in the magnitude of key risks including unimproved water and sanitation, vitamin A and zinc deficiencies, and ambient particulate matter pollution. The extent to which the epidemiological shift has occurred and what the leading risks currently are varies greatly across regions. In much of sub-Saharan Africa, the leading risks are still those associated with poverty and those that affect children.

Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.

Stochastic analysis of a radial-inflow turbine in the presence of parametric uncertainties

This paper presents an uncertainty quantification study of the performance analysis of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multi-purpose Small Power Unit. A deterministic 3D volume-averaged Computational Fluid Dynamics (CFD) solver is coupled with a non-statistical generalized Polynomial Chaos (gPC) representation based on a pseudo-spectral projection method. One of the advantages of this approach is that it does not require any modification of the CFD code for the propagation of random disturbances in the aerodynamic and geometric fields. The stochastic results highlight the importance of the blade thickness and trailing edge tip radius on the total-to-static efficiency of the turbine compared to the angular velocity and trailing edge tip length. From a theoretical point of view, the use of the gPC representation on an arbitrary grid also allows the investigation of the sensitivity of the blade thickness profiles on the turbine efficiency. The gPC approach is also applied to coupled random parameters. The results show that the most influential coupled random variables are trailing edge tip radius coupled with the angular velocity.

Handbook of International Research in Mathematics Education [3rd Ed.]

"This third edition ofthe Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field."--Publisher website