The Borwein brothers, Pi and the AGM

We consider some of Jonathan and Peter Borweins' contributions to the high-precision computation of $\pi$ and the elementary functions, with particular reference to their book "Pi and the AGM" (Wiley, 1987). Here "AGM" is the arithmetic-geometric mean of Gauss and Legendre. Because the AGM converges quadratically, it can be combined with fast multiplication algorithms to give fast algorithms for the $n$-bit computation of $\pi$, and more generally the elementary functions. These algorithms run in almost linear time $O(M(n)\log n)$, where $M(n)$ is the time for $n$-bit multiplication. We outline some of the results and algorithms given in Pi and the AGM, and present some related (but new) results. In particular, we improve the published error bounds for some quadratically and quartically convergent algorithms for $\pi$, such as the Gauss-Legendre algorithm. We show that an iteration of the Borwein-Borwein quartic algorithm for $\pi$ is equivalent to two iterations of the Gauss-Legendre quadratic algorithm for $\pi$, in the sense that they produce exactly the same sequence of approximations to $\pi$ if performed using exact arithmetic.Comment: 24 pages, 6 tables. Changed style file and reformatted algorithms in v

Time-trial performance is not impaired in either competitive athletes or untrained individuals following a prolonged cognitive task

This is the final version. Available from Springer via the DOI in this record.It has been reported that mental fatigue decreases exercise performance during high-intensity constant-work-rate exercise (CWR) and self-paced time trials (TT) in recreationally-trained individuals. The purpose of this study was to determine whether performance is impaired following a prolonged cognitive task in individuals trained for competitive sport. Ten trained competitive athletes (ATH) and ten untrained healthy men (UNT) completed a 6-min severe-intensity CWR followed by a 6-min cycling TT immediately following cognitive tasks designed to either perturb (Stroop colour-word task and N-back task; PCT) or maintain a neutral (documentary watching; CON) mental state. UNT had a higher heart rate (75 ± 9 v. 69 ± 7 bpm; P = 0.002) and a lower positive affect PANAS score (19.9 ± 7.5 v. 24.3 ± 4.6; P = 0.036) for PCT compared to CON. ATH showed no difference in heart rate, but had a higher negative affect score for PCT compared to CON (15.1 ± 3.7 v. 12.2 ± 2.7; P = 0.029). Pulmonary O 2 uptake during CWR was not different between PCT and CON for ATH or UNT. Work completed during TT was not different between PCT and CON for ATH (PCT 103 ± 12 kJ; CON 102 ± 12 kJ; P > 0.05) or UNT (PCT 75 ± 11 kJ; CON 74 ± 12 kJ; P > 0.05). Compared to CON, during PCT, UNT showed unchanged psychological stress responses, whereas ATH demonstrated increased psychological stress responses. However, regardless of this distinction, exercise performance was not affected by PCT in either competitive athletes or untrained individuals

Impact of Public Charging Infrastructure on the Adoption of Electric Vehicles in London

The discussion on the importance of public charging infrastructure is usually framed around the ‘chicken-egg’ challenge of consumers feeling reluctant to purchase without the necessary infrastructure and policy makers reluctant to invest in the infrastructure without the demand. However, public charging infrastructure may be more crucial to EV adoption than previously thought. Historically, access to residential charging was thought to be a major factor in potential for growth in the EV market as it offered a guaranteed place for a vehicle to be charged. However, these conclusions were reached through studies conducted in regions with a high percentage of homes that have access to residential parking. The purpose of this study is to understand how the built environment may encourage uptake of EVs by seeking a correlation between EV ownership and public charging points in an urban and densely populated city such as London. Using a statistical approach with data from the Department for Transport and Zap Map, a statistically significant correlation was found between the total (slow, fast and rapid) number of public charging points and number of EV registrations per borough—with the strongest correlation found between EV registrations and rapid chargers. This research does not explicitly prove that there is a cause-and-effect relationship between public charging points EVs but challenges some of the previous literature which indicates that public charging infrastructure is not as important as home charging. The study also supports the notion that the built environment can influence human behaviour

Should physical activity recommendations be ethnicity-specific? Evidence from a cross-sectional study of south Asian and European men

Background Expert bodies and health organisations recommend that adults undertake at least 150 min.week−1 of moderate-intensity physical activity (MPA). However, the underpinning data largely emanate from studies of populations of European descent. It is unclear whether this level of activity is appropriate for other ethnic groups, particularly South Asians, who have increased cardio-metabolic disease risk compared to Europeans. The aim of this study was to explore the level of MPA required in South Asians to confer a similar cardio-metabolic risk profile to that observed in Europeans undertaking the currently recommended MPA level of 150 min.week−1.<p></p> Methods Seventy-five South Asian and 83 European men, aged 40–70, without cardiovascular disease or diabetes had fasted blood taken, blood pressure measured, physical activity assessed objectively (using accelerometry), and anthropometric measures made. Factor analysis was used to summarise measured risk biomarkers into underlying latent ‘factors’ for glycaemia, insulin resistance, lipid metabolism, blood pressure, and overall cardio-metabolic risk. Age-adjusted regression models were used to determine the equivalent level of MPA (in bouts of ≥10 minutes) in South Asians needed to elicit the same value in each factor as Europeans undertaking 150 min.week−1 MPA.<p></p> Findings For all factors, except blood pressure, equivalent MPA values in South Asians were significantly higher than 150 min.week−1; the equivalent MPA value for the overall cardio-metabolic risk factor was 266 (95% CI 185-347) min.week−1.<p></p> Conclusions South Asian men may need to undertake greater levels of MPA than Europeans to exhibit a similar cardio-metabolic risk profile, suggesting that a conceptual case can be made for ethnicity-specific physical activity guidance. Further study is needed to extend these findings to women and to replicate them prospectively in a larger cohort.<p></p&gt

Male Circumcision at Different Ages in Rwanda: A Cost-Effectiveness Study

Agnes Binagwaho and colleagues predict that circumcision of newborn boys would be effective and cost-saving as a long-term strategy to prevent HIV in Rwanda

Challenges of Loss to Follow-up in Tuberculosis Research.

In studies evaluating methods for diagnosing tuberculosis (TB), follow-up to verify the presence or absence of active TB is crucial and high dropout rates may significantly affect the validity of the results. In a study assessing the diagnostic performance of the QuantiFERON®-TB Gold In-Tube test in TB suspect children in Tanzania, factors influencing patient adherence to attend follow-up examinations and reasons for not attending were examined. In 160 children who attended and 102 children who did not attend scheduled 2-month follow-up baseline health characteristics, demographic data and risk factors for not attending follow-up were determined. Qualitative interviews were used to understand patient and caretakers reasons for not returning for scheduled follow-up. Being treated for active tb in the dots program (OR: 4.14; 95% CI:1.99-8.62;p-value<0.001) and receiving money for the bus fare (OR:129; 95% CI 16->100;P-value<0.001) were positive predictors for attending follow-up at 2 months, and 21/85(25%) of children not attending scheduled follow-up had died. Interviews revealed that limited financial resources, i.e. lack of money for transportation and poor communication, were related to non-adherence. Patients lost to follow-up is a potential problem for TB research. Receiving money for transportation to the hospital and communication is crucial for adherence to follow-up conducted at a study facility. Strategies to ensure follow-up should be part of any study protocol

Rings in the Solar System: a short review

Rings are ubiquitous around giant planets in our Solar System. They evolve jointly with the nearby satellite system. They could form either during the giant planet formation process or much later, as a result of large scale dynamical instabilities either in the local satellite system, or at the planetary scale. We review here the main characteristics of rings in our solar system, and discuss their main evolution processes and possible origin. We also discuss the recent discovery of rings around small bodies.Comment: Accepted for the Handbook of Exoplanet

Prioritising surveillance for alien organisms transported as stowaways on ships travelling to South Africa

The global shipping network facilitates the transportation and introduction of marine and terrestrial organisms to regions where they are not native, and some of these organisms become invasive. South Africa was used as a case study to evaluate the potential for shipping to contribute to the introduction and establishment of marine and terrestrial alien species (i.e. establishment debt) and to assess how this varies across shipping routes and seasons. As a proxy for the number of species introduced (i.e. 'colonisation pressure') shipping movement data were used to determine, for each season, the number of ships that visited South African ports from foreign ports and the number of days travelled between ports. Seasonal marine and terrestrial environmental similarity between South African and foreign ports was then used to estimate the likelihood that introduced species would establish. These data were used to determine the seasonal relative contribution of shipping routes to South Africa's marine and terrestrial establishment debt. Additionally, distribution data were used to identify marine and terrestrial species that are known to be invasive elsewhere and which might be introduced to each South African port through shipping routes that have a high relative contribution to establishment debt. Shipping routes from Asian ports, especially Singapore, have a particularly high relative contribution to South Africa's establishment debt, while among South African ports, Durban has the highest risk of being invaded. There was seasonal variation in the shipping routes that have a high relative contribution to the establishment debt of the South African ports. The presented method provides a simple way to prioritise surveillance effort and our results indicate that, for South Africa, port-specific prevention strategies should be developed, a large portion of the available resources should be allocated to Durban, and seasonal variations and their consequences for prevention strategies should be explored further. (Résumé d'auteur

The frequency of osteogenic activities and the pattern of intermittence between periods of physical activity and sedentary behaviour affects bone mineral content: the cross-sectional NHANES study

BACKGROUND: Sedentary behaviours, defined as non exercising seated activities, have been shown to have deleterious effects on health. It has been hypothesised that too much sitting time can have a detrimental effect on bone health in youth. The aim of this study is to test this hypothesis by exploring the association between objectively measured volume and patterns of time spent in sedentary behaviours, time spent in specific screen-based sedentary pursuits and bone mineral content (BMC) accrual in youth. METHODS: NHANES 2005–2006 cycle data includes BMC of the femoral and spinal region via dual-energy X-ray absorptiometry (DEXA), assessment of physical activity and sedentary behaviour patterns through accelerometry, self reported time spent in screen based pursuits (watching TV and using a computer), and frequency of vigorous playtime and strengthening activities. Multiple regression analysis, stratified by gender was performed on N = 671 males and N = 677 females aged from 8 to 22 years. RESULTS: Time spent in screen-based sedentary behaviours is negatively associated with femoral BMC (males and females) and spinal BMC (females only) after correction for time spent in moderate and vigorous activity. Regression coefficients indicate that an additional hour per day of screen-based sitting corresponds to a difference of −0.77 g femoral BMC in females [95% CI: -1.31 to −0.22] and of −0.45 g femoral BMC in males [95% CI: -0.83 to −0.06]. This association is attenuated when self-reported engagement in regular (average 5 times per week) strengthening exercise (for males) and vigorous playing (for both males and females) is taken into account. Total sitting time and non screen-based sitting do not appear to have a negative association with BMC, whereas screen based sedentary time does. Patterns of intermittence between periods of sitting and moderate to vigorous activity appears to be positively associated with bone health when activity is clustered in time and inter-spaced with long continuous bouts of sitting. CONCLUSIONS: Some specific sedentary pursuits (screen-based) are negatively associated with bone health in youth. This association is specific to gender and anatomical area. This relationship between screen-based time and bone health is independent of the total amount of physical activity measured objectively, but not independent of self-reported frequency of strengthening and vigorous play activities. The data clearly suggests that the frequency, rather than the volume, of osteogenic activities is important in counteracting the effect of sedentary behaviour on bone health. The pattern of intermittence between sedentary periods and activity also plays a role in bone accrual, with clustered short bouts of activity interspaced with long periods of sedentary behaviours appearing to be more beneficial than activities more evenly spread in time