We prove a law of large numbers for the range of rotor walks with random initial configuration on regular trees and on Galton-Watson trees. We also show the existence of the speed for such rotor walks. More precisely, we show that on the classes of trees under consideration, even in the case when the rotor walk is recurrent, the range grows at linear speed.The lockdown caused by the COVID-19 pandemic represents a great unknown regarding the physiological changes induced in elite football players. Although it will differ from country to country, the return to sport for professional football players will follow a forced lockdown never experienced and longer than the normal annual season break. Moreover, in addition to an obvious decrease in performance, the lockdown will possibly lead to an increase of the injury risk. find more In fact, preseason is always a period with a specific football injury epidemiology, with an increase in the incidence and prevalence of overuse injuries. Therefore, it seems appropriate to recommend that specific training and injury prevention programmes be developed, with careful load monitoring. Training sessions should include specific aerobic, resistance, speed and flexibility training programmes. The aerobic, resistance and speed training should respect some specific phases based on the progressiveness of the training load and the consequent physiological adaptation response. These different phases, based on the current evidence found in the literature, are described in their practical details. Moreover, injury prevention exercises should be incorporated, especially focusing on overuse injuries such as tendon and muscle lesions. The aim of this paper is to provide practical recommendations for the preparation of training sessions for professional footballers returning to sport after the lockdown.Recently, there has been increasing attention to research related to the effect of skill-based or game-based training on soccer players' physical performance. Therefore, this study aimed to compare the effectiveness of skill-based training (SBT) at maximum intensity versus the small-sided game (SSG) on the physical performance characteristics of young soccer players during the pre-season period. Twenty-two male soccer players (mean age 15.3 ± 3 years) were randomly assigned to either an SBT or SSG fully controlled intervention programme, running parallel for eight weeks and held twice a week. On three non-consecutive days before and after training players completed a test battery consisting of the 20 m sprint, T-run, countermovement jump, running anaerobic sprint test (RAST) and 20 m shuttle run. Data were analysed with a two-way ANOVA test for repeated measures. SBT and SSG interventions induced a significant improvement in the anaerobic power (10.9% vs 6.2%), explosive power (8.5% vs 5.6%), VO2max (6.7% vs 6.5%) and vertical jump (5.3% vs 2.9%), respectively. When the improvements in the physical performance variables of both groups are compared, the SBT group achieved greater improvement than the SSG group in anaerobic power (by 4.7%), in explosive power (by 2.8%), in vertical jumping (by 2.3%), in the 20 m sprint (by 2.2%) and T-test scores (by 1.7%). However, improvements in the VO2max were similar in both groups. The results of the present study suggest that SBT at maximum intensity may be more effective than SSG in improving the physical performance characteristics of young soccer players in the pre-competitive season.Whole genome sequencing (WGS) has great potential to explore all possible DNA variants associated with physical performance, psychological traits and health conditions of athletes. Here we present, for the first time, annotation of genomic variants of elite athletes, based on the WGS of 20 Tatar male wrestlers. The maximum number of high-quality variants per sample was over 3.8 M for single nucleotide polymorphisms (SNPs) and about 0.64 M for indels. The maximum number of nonsense mutations was 148 single nucleotide variants (SNVs) per individual. Athletes' genomes on average contained 18.9 nonsense SNPs in a homozygous state per sample, while non-athletes' exomes (Tatar controls, n = 19) contained 18 nonsense SNPs. Finally, we applied genomic data for the association analysis and used reaction time (RT) as an example. Out of 1884 known genome-wide significant SNPs related to RT, we identified four SNPs (KIF27 rs10125715, APC rs518013, TMEM229A rs7783359, LRRN3 rs80054135) associated with RT in wrestlers. The cumulative number of favourable alleles (KIF27 A, APC A, TMEM229A T, LRRN3 T) was significantly correlated with RT both in wrestlers (P = 0.0003) and an independent cohort (n = 43) of physically active subjects (P = 0.029). Furthermore, we found that the frequencies of the APC A (53.3 vs 44.0%, P = 0.033) and LRRN3 T (7.5 vs 2.8%, P = 0.009) alleles were significantly higher in elite athletes (n = 107) involved in sports with RT as an essential component of performance (combat sports, table tennis and volleyball) compared to less successful (n = 176) athletes. The LRRN3 T allele was also over-represented in elite athletes (7.5%) in comparison with 189 controls (2.9%, P = 0.009). In conclusion, we present the first WGS study of athletes showing that WGS can be applied in sport and exercise science.The aim of this study was to determine the frequency of upper respiratory tract symptoms (URS) in elite female gymnasts during a training season. In addition, we aimed to observe the extent to which salivary immunoglobulin A (sIgA) is associated with URS in these athletes, including potential effects of the season and timing of sample collection. Over one year, 18 elite female gymnasts completed URS and fatigue questionnaires weekly and provided 1 mL of saliva after a minimum 36 h of rest (morning or afternoon) to measure relative sIgA concentration (= mean absolute sIgA value of the week divided by the mean absolute sIgA value of the weeks without URS). Mean weekly URS and mean relative sIgA values per gymnast correlated negatively (r = -0.606, P = 0.022). Most URS were noted in the most fatigued gymnasts (7.4 ± 10.1 vs. 2.5 ± 5.6 (P less then 0.001) for 'normal' and 2.1 ± 3.7 (P = 0.001) for 'better than normal' rested). In spring, relative sIgA was higher compared to autumn (112 ± 55 vs. 89 ± 41%, P less then 0.