Training during the COVID-19 lockdown : knowledge, beliefs, and practices of 12,526 athletes from 142 countries and six continents

OBJECTIVE Our objective was to explore the training-related knowledge, beliefs, and practices of athletes and the influence of lockdowns in response to the coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). METHODS Athletes (n = 12,526, comprising 13% world class, 21% international, 36% national, 24% state, and 6% recreational) completed an online survey that was available from 17 May to 5 July 2020 and explored their training behaviors (training knowledge, beliefs/attitudes, and practices), including specific questions on their training intensity, frequency, and session duration before and during lockdown (March–June 2020). RESULTS Overall, 85% of athletes wanted to “maintain training,” and 79% disagreed with the statement that it is “okay to not train during lockdown,” with a greater prevalence for both in higher-level athletes. In total, 60% of athletes considered “coaching by correspondence (remote coaching)” to be sufficient (highest amongst world-class athletes). During lockdown, < 40% were able to maintain sport-specific training (e.g., long endurance [39%], interval training [35%], weightlifting [33%], most (83%) training for “general fitness and health maintenance” during lockdown. Athletes trained alone (80%) and focused on bodyweight (65%) and cardiovascular (59%) exercise/training during lockdown. Compared with before lockdown, most athletes reported reduced training frequency (from between five and seven sessions per week to four or fewer), shorter training sessions (from ≥ 60 to < 60 min), and lower sport-specific intensity (~ 38% reduction), irrespective of athlete classification. CONCLUSIONS COVID-19-related lockdowns saw marked reductions in athletic training specificity, intensity, frequency, and duration, with notable within-sample differences (by athlete classification). Higher classification athletes had the strongest desire to “maintain” training and the greatest opposition to “not training” during lockdowns. These higher classification athletes retained training specificity to a greater degree than others, probably because of preferential access to limited training resources. More higher classification athletes considered “coaching by correspondence” as sufficient than did lower classification athletes. These lockdown-mediated changes in training were not conducive to maintenance or progression of athletes’ physical capacities and were also likely detrimental to athletes’ mental health. These data can be used by policy makers, athletes, and their multidisciplinary teams to modulate their practice, with a degree of individualization, in the current and continued pandemic-related scenario. Furthermore, the data may drive training-related educational resources for athletes and their multidisciplinary teams. Such upskilling would provide athletes with evidence to inform their training modifications in response to germane situations (e.g., COVID related, injury, and illness).A specific funding was provided by the National Sports Institute of Malaysia for this study.The National Sports Institute of Malaysia.https://www.springer.com/journal/40279am2023Sports Medicin

COVID-19 lockdown : a global study investigating athletes’ sport classification and sex on training practices

PURPOSE : To investigate differences in athletes’ knowledge, beliefs, and training practices during COVID-19 lockdowns with reference to sport classification and sex. This work extends an initial descriptive evaluation focusing on athlete classification. METHODS : Athletes (12,526; 66% male; 142 countries) completed an online survey (May–July 2020) assessing knowledge, beliefs, and practices toward training. Sports were classified as team sports (45%), endurance (20%), power/technical (10%), combat (9%), aquatic (6%), recreational (4%), racquet (3%), precision (2%), parasports (1%), and others (1%). Further analysis by sex was performed. RESULTS : During lockdown, athletes practiced body-weight-based exercises routinely (67% females and 64% males), ranging from 50% (precision) to 78% (parasports). More sport-specific technical skills were performed in combat, parasports, and precision (∼50%) than other sports (∼35%). Most athletes (range: 50% [parasports] to 75% [endurance]) performed cardiorespiratory training (trivial sex differences). Compared to prelockdown, perceived training intensity was reduced by 29% to 41%, depending on sport (largest decline: ∼38% in team sports, unaffected by sex). Some athletes (range: 7%–49%) maintained their training intensity for strength, endurance, speed, plyometric, change-of-direction, and technical training. Athletes who previously trained ≥5 sessions per week reduced their volume (range: 18%–28%) during lockdown. The proportion of athletes (81%) training ≥60 min/session reduced by 31% to 43% during lockdown. Males and females had comparable moderate levels of training knowledge (56% vs 58%) and beliefs/attitudes (54% vs 56%). CONCLUSIONS : Changes in athletes’ training practices were sport-specific, with few or no sex differences. Team-based sports were generally more susceptible to changes than individual sports. Policy makers should provide athletes with specific training arrangements and educational resources to facilitate remote and/or home-based training during lockdown-type events.https://journals.humankinetics.com/view/journals/ijspp/ijspp-overview.xmlhj2023Sports Medicin

THE SPACE OF LINEAR MAPS INTO A GRASSMANN MANIFOLD

Abstract. We show that the space of all holomorphic maps of degree one from the Riemann sphere into a Grassmann manifold is a sphere bundle over a flag manifold. Using the notions of “kernel ” and “span ” of a map, we completely identify the space of unparameterized maps as well. The illustrative case of maps into the quadric Grassmann manifold is discussed in details and the homology of the corresponding spaces computed. 1

Polynomial Expansions for Solutions of Higher-order q-Bessel Heat Equation

[[abstract]]In this paper we give the q-analogue of the higher-order Bessel opera- tors studied by M. I. Klyuchantsev [12] and A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [3]. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs similar to the classical case. Second our goal is to construct the associated q-Fourier transform and the q-analogue of the theory of the heat polynomials introduced by P. C. Rosenbloom and D. V. Widder [13]. Our operator for some value of the vector index generalize the q-j Bessel operator of the second order in [4] and a q-Third operator in [6]

Automated importance sampling via optimal control for stochastic reaction networks: A Markovian projection–based approach

We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of Ben Hammouda et al. (2023), an efficient path-dependent measure change is derived based on a connection between determining optimal importance sampling (IS) parameters within a class of probability measures and a stochastic optimal control formulation, corresponding to solving a variance minimization problem. In this work, we propose a novel approach to address the encountered curse of dimensionality by mapping the problem to a significantly lower-dimensional space via a Markovian projection (MP) idea. The output of this model reduction technique is a low-dimensional SRN (potentially even one dimensional) that preserves the marginal distribution of the original high-dimensional SRN system. The dynamics of the projected process are obtained by solving a related optimization problem via a discrete regression. By solving the resulting projected Hamilton–Jacobi–Bellman (HJB) equations for the reduced-dimensional SRN, we obtain projected IS parameters, which are then mapped back to the original full-dimensional SRN system, resulting in an efficient IS-MC estimator for rare events probabilities of the full-dimensional SRN. Our analysis and numerical experiments reveal that the proposed MP-HJB-IS approach substantially reduces the MC estimator variance, resulting in a lower computational complexity in the rare event regime than standard MC estimators