Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Actigraph Accelerometer-Defined Boundaries for Sedentary Behaviour and Physical Activity Intensities in 7 Year Old Children

Background: Accurate objective assessment of sedentary and physical activity behaviours during childhood is integral to the understanding of their relation to later health outcomes, as well as to documenting the frequency and distribution of physical activity within a population.Purpose: To calibrate the Actigraph GT1M accelerometer, using energy expenditure (EE) as the criterion measure, to define thresholds for sedentary behaviour and physical activity categories suitable for use in a large scale epidemiological study in young children.Methods: Accelerometer-based assessments of physical activity (counts per minute) were calibrated against EE measures (kcal.kg(-1).hr(-1)) obtained over a range of exercise intensities using a COSMED K4b(2) portable metabolic unit in 53 seven-year-old children. Children performed seven activities: lying down viewing television, sitting upright playing a computer game, slow walking, brisk walking, jogging, hopscotch and basketball. Threshold count values were established to identify sedentary behaviour and light, moderate and vigorous physical activity using linear discriminant analysis (LDA) and evaluated using receiver operating characteristic (ROC) curve analysis.Results: EE was significantly associated with counts for all non-sedentary activities with the exception of jogging. Threshold values for accelerometer counts (counts. minute(-1)) were = 3841 for light, moderate and vigorous physical activity respectively. The area under the ROC curves for discrimination of sedentary behaviour and vigorous activity were 0.98. Boundaries for light and moderate physical activity were less well defined (0.61 and 0.60 respectively). Sensitivity and specificity were higher for sedentary (99% and 97%) and vigorous (95% and 91%) than for light (60% and 83%) and moderate (61% and 76%) thresholds.Conclusion: The accelerometer cut points established in this study can be used to classify sedentary behaviour and to distinguish between light, moderate and vigorous physical activity in children of this age

ISSN exercise & sport nutrition review: research & recommendations

Sports nutrition is a constantly evolving field with hundreds of research papers published annually. For this reason, keeping up to date with the literature is often difficult. This paper is a five year update of the sports nutrition review article published as the lead paper to launch the JISSN in 2004 and presents a well-referenced overview of the current state of the science related to how to optimize training and athletic performance through nutrition. More specifically, this paper provides an overview of: 1.) The definitional category of ergogenic aids and dietary supplements; 2.) How dietary supplements are legally regulated; 3.) How to evaluate the scientific merit of nutritional supplements; 4.) General nutritional strategies to optimize performance and enhance recovery; and, 5.) An overview of our current understanding of the ergogenic value of nutrition and dietary supplementation in regards to weight gain, weight loss, and performance enhancement. Our hope is that ISSN members and individuals interested in sports nutrition find this review useful in their daily practice and consultation with their clients

The effect of high-altitude on human skeletal muscle energetics: 31P-MRS results from the caudwell xtreme everest expedition

Many disease states are associated with regional or systemic hypoxia. The study of healthy individuals exposed to high-altitude hypoxia offers a way to explore hypoxic adaptation without the confounding effects of disease and therapeutic interventions. Using 31P magnetic resonance spectroscopy and imaging, we investigated skeletal muscle energetics and morphology after exposure to hypobaric hypoxia in seven altitude-naïve subjects (trekkers) and seven experienced climbers. The trekkers ascended to 5300 m while the climbers ascended above 7950 m. Before the study, climbers had better mitochondrial function (evidenced by shorter phosphocreatine recovery halftime) than trekkers: 16±1 vs. 22±2 s (mean ± SE, p<0.01). Climbers had higher resting [Pi] than trekkers before the expedition and resting [Pi] was raised across both groups on their return (PRE: 2.6±0.2 vs. POST: 3.0±0.2 mM, p<0.05). There was significant muscle atrophy post-CXE (PRE: 4.7±0.2 vs. POST: 4.5±0.2 cm2, p<0.05), yet exercising metabolites were unchanged. These results suggest that, in response to high altitude hypoxia, skeletal muscle function is maintained in humans, despite significant atrophy

The FTO A/T polymorphism and elite athletic performance: A study involving three groups of European athletes

Objective: The FTO A/T polymorphism (rs9939609) is a strong candidate to influence obesity-related traits. Elite athletes from many different sporting disciplines are characterized by low body fat. Therefore, the aim of this study was to assess whether athletic status is associated with the FTO A/T polymorphism. Subjects and Methods: A large cohort of European Caucasians from Poland, Russia and Spain were tested to examine the association between FTO A/T polymorphism (rs9939609) and athletic status. A total of 551 athletes were divided by type of sport (endurance athletes, n = 266 vs. sprint/power athletes, n = 285) as well as by level of competition (elite-level vs. national-level). The control group consisted of 1,416 ethnically-matched, non-athletic participants, all Europeans. Multinomial logistic regression analyses were conducted to assess the association between FTO A/T genotypes and athletic status/competition level. Results: There were no significantly greater/lesser odds of harbouring any type of genotype when comparing across athletic status (endurance athletes, sprint/power athletes or control participants). These effects were observed after controlling for sex and nationality. Furthermore, no significantly greater/lesser odds ratios were observed for any of the genotypes in respect to the level of competition (elite-level vs. national-level). Conclusion: The FTO A/T polymorphism is not associated with elite athletic status in the largest group of elite athletes studied to date. Large collaborations and data sharing between researchers, as presented here, are strongly recommended to enhance the research in the field of exercise genomics. E-pub: e6057