Splitting methods for constrained diffusion-reaction systems

We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure seems promising as we can treat the nonlinearity separately. This has some computational advantages, since we only have to solve a linear constrained system and a nonlinear ODE. However, Strang splitting suffers from order reduction which limits its efficiency. This is caused by the fact that the nonlinear subsystem produces inconsistent initial values for the constrained subsystem. The incorporation of an additional correction term resolves this problem without increasing the computational cost. Numerical examples including a coupled mechanical system illustrate the proven convergence results

XenDB: Full length cDNA prediction and cross species mapping in Xenopus laevis

BACKGROUND: Research using the model system Xenopus laevis has provided critical insights into the mechanisms of early vertebrate development and cell biology. Large scale sequencing efforts have provided an increasingly important resource for researchers. To provide full advantage of the available sequence, we have analyzed 350,468 Xenopus laevis Expressed Sequence Tags (ESTs) both to identify full length protein encoding sequences and to develop a unique database system to support comparative approaches between X. laevis and other model systems. DESCRIPTION: Using a suffix array based clustering approach, we have identified 25,971 clusters and 40,877 singleton sequences. Generation of a consensus sequence for each cluster resulted in 31,353 tentative contig and 4,801 singleton sequences. Using both BLASTX and FASTY comparison to five model organisms and the NR protein database, more than 15,000 sequences are predicted to encode full length proteins and these have been matched to publicly available IMAGE clones when available. Each sequence has been compared to the KOG database and ~67% of the sequences have been assigned a putative functional category. Based on sequence homology to mouse and human, putative GO annotations have been determined. CONCLUSION: The results of the analysis have been stored in a publicly available database XenDB . A unique capability of the database is the ability to batch upload cross species queries to identify potential Xenopus homologues and their associated full length clones. Examples are provided including mapping of microarray results and application of 'in silico' analysis. The ability to quickly translate the results of various species into 'Xenopus-centric' information should greatly enhance comparative embryological approaches. Supplementary material can be found at

Endurance Capacities in Professional Soccer Players: Are Performance Profiles Position Specific?

The aim of this study was to investigate position-specific endurance performance of soccer players. 136 professional players competing in the 1st and 2nd division in Germany were divided into the positional groups goalkeepers (GK), central defenders (CD), wingers (WI), central midfielders (CM), and forwards (FW). All players performed an incremental treadmill test with blood lactate sampling until exhaustion with the following endurance parameters being obtained: Fixed aerobic threshold (v2mmol/l), fixed anaerobic threshold (v4mmol/l), individual aerobic threshold (vLT), individual anaerobic threshold (vIAT), and maximum velocity (vmax). Results revealed significant differences between GK and all outfield playing positions for all endurance parameters (p ≤ 0.03; ES 0.87–2.19). No significant differences among outfield playing positions were evident for any of the parameters. However, trends were found in favor of the CM compared to the WI (p = 0.11; ES = 0.68) and the FW (p = 0.06; ES = 0.47) relating to vLT as well as in favor of the CM compared to the WI (p = 0.10; ES = 0.56) relating to vIAT. Findings suggest that goalkeepers possess the lowest endurance capacity compared to other playing positions. While outfield players in general showed similar endurance performance, CM seem to possess the highest aerobic capacity of all positions as indicated by all lactate-based thresholds, however, with only small to moderate ES. These findings could lead one to question the appropriateness of current endurance training regimes to prepare all players adequately for their positional match-running demands. Indeed, endurance training of players should be specific to their match-running demands. However, it remains unknown to what extent these demands are position or player specific

The “hockey” assist makes the difference:validation of a defensive disruptiveness model to evaluate passing sequences in elite soccer

With the growing availability of position data in sports, spatiotemporal analysis in soccer is a topic of rising interest. The aim of this study is to validate a performance indicator, namely D-Def, measuring passing effectiveness. D-Def calculates the change of the teams’ centroid, centroids of formation lines (e.g., defensive line), teams’ surface area, and teams’ spread in the following three seconds after a pass and therefore results in a measure of disruption of the opponents’ defense following a pass. While this measure was introduced earlier, in this study we aim to prove the usefulness to evaluate attacking sequences. In this study, 258 games of Dutch Eredivisie season 2018/19 were included, resulting in 13,094 attacks. D-Def, pass length, pass velocity, and pass angle of the last four passes of each attack were calculated and compared between successful and unsuccessful attacks. D-Def showed higher values for passes of successful compared to unsuccessful attacks (0.001 28) needs to be present. In addition, the penultimate pass (“hockey assist”) of an attack seems crucial in characterizing successful attacks

The “hockey” assist makes the difference—validation of a defensive disruptiveness model to evaluate passing sequences in elite soccer

With the growing availability of position data in sports, spatiotemporal analysis in soccer is a topic of rising interest. The aim of this study is to validate a performance indicator, namely D-Def, measuring passing effectiveness. D-Def calculates the change of the teams’ centroid, centroids of formation lines (e.g., defensive line), teams’ surface area, and teams’ spread in the following three seconds after a pass and therefore results in a measure of disruption of the opponents’ defense following a pass. While this measure was introduced earlier, in this study we aim to prove the usefulness to evaluate attacking sequences. In this study, 258 games of Dutch Eredivisie season 2018/19 were included, resulting in 13,094 attacks. D-Def, pass length, pass velocity, and pass angle of the last four passes of each attack were calculated and compared between successful and unsuccessful attacks. D-Def showed higher values for passes of successful compared to unsuccessful attacks (0.001 28) needs to be present. In addition, the penultimate pass (“hockey assist”) of an attack seems crucial in characterizing successful attacks

Differences in physical match performance and injury occurence before and after the COVID-19 break in professional European soccer leagues: a systematic review

Purpose. Due of the Covid-19 pandemic, matches and soccer-specific training were suspended for several weeks, matches after resumption were congested, and substitutions per team and game increased from three to five. Therefore, the aim of this review was to examine possible differences in physical match performance and injuries between before and after the Covid-19 induced break of matches and training in professional male European soccer leagues during the 2019/2020 season. Methods. A systematic search identified all scientifically peer-reviewed publications involving elite male soccer players competing in the European leagues which reported physical match performance variables such as total running distance and running distance at different speed zones and/or injury parameters pre and post Covid-19 induced break. Results. In total, 11 articles were included, which were coming from German Bundesliga, Polish Ekstraklasa, Croatian HNL, Spanish La Liga, and Italian Serie A. In all studies investigating the German Bundesliga, most parameters of physical match performance remained unaffected (0.08 ≤ p ≤ 0.82; -0.15 ≤ ES 0.15), while studies investigating the Polish Ekstraklasa (p ≤ 0.03; -0.27 ≤ ES -0.18), Croatian HNL (p ≤ 0.04; -1.42 ≤ ES ≤ 1.44), Spanish La Liga (p ≤ 0.017; -0.32 ≤ ES ≤ 5.5), and Italian Serie A (p ≤ 0.014; -1.01 ≤ ES 0.24) showed a decrease in most parameters of physical match performance after the Covid-19 break. Injury rates where only investigated by studies targeting the German Bundesliga and Italian Serie A. In the majority of studies (3 out of 4 studies), there occurred no difference in injuries between pre and post Covid-19 break (p > 0.05; ES = N/A). Conclusion. Results indicate that Bundesliga teams maintained physical match performance during the 9-weeks break in matches and 3-weeks break in group training, whereas a longer match and group training interruption up to 15 weeks and 8 weeks, respectively, in the other leagues appeared to lead to a decreased physical match performance. Regarding injuries, we speculate that the increase of substitutions from 3 to 5 substitutions per game might prevent an increase in injury occurrence during matches. The underlying studies’ results provide hints for possible upcoming unexpected interruptions with respect to optimal physical preparations for the resumption of matches and a congested schedule to maintain physical match performance, or for possible rule changes such as 5 instead of 3 substitutions to avoid physical overload during congested match schedules

Validity and reliability of speed tests used in soccer: A systematic review

Introduction Speed is an important prerequisite in soccer. Therefore, a large number of tests have been developed aiming to investigate several speed skills relevant to soccer. This systematic review aimed to examine the validity and reliability of speed tests used in adult soccer players. Methods A systematic search was performed according to the PRISMA guidelines. Studies were included if they investigated speed tests in adult soccer players and reported validity (construct and criterion) or reliability (intraday and interday) data. The tests were categorized into linear-sprint, repeated-sprint, change-of-direction sprint, agility, and tests incorporating combinations of these skills. Results In total, 90 studies covering 167 tests were included. Linear-sprint (n = 67) and change-of-direction sprint (n = 60) were studied most often, followed by combinations of the aforementioned (n = 21) and repeated-sprint tests (n = 15). Agility tests were examined fewest (n = 4). Mainly based on construct validity studies, acceptable validity was reported for the majority of the tests in all categories, except for agility tests, where no validity study was identified. Regarding intraday and interday reliability, ICCs>0.75 and CVs<3.0% were evident for most of the tests in all categories. These results applied for total and average times. In contrast, measures representing fatigue such as percent decrement scores indicated inconsistent validity findings. Regarding reliability, ICCs were 0.11–0.49 and CVs were 16.8–51.0%. Conclusion Except for agility tests, several tests for all categories with acceptable levels of validity and high levels of reliability for adult soccer players are available. Caution should be given when interpreting fatigue measures, e.g., percent decrement scores. Given the lack of accepted gold-standard tests for each category, researchers and practitioners may base their test selection on the broad database provided in this systematic review. Future research should pay attention to the criterion validity examining the relationship between test results and match parameters as well as to the development and evaluation of soccer-specific agility tests

Center backs work hardest when playing in a back three: The influence of tactical formation on physical and technical match performance in professional soccer

The purpose of this study was to investigate whether tactical formation affects the physical and technical match performance of professional soccer players in the first German Bundesliga. From official match data of the Bundesliga season 2018/19, physical (total distance, high-intensity distance, sprinting distance, accelerations, maximum velocity) and technical performance (short/middle/long passes, dribblings, ball-possessions) of players were analyzed. Players were categorized into five playing positions (center back, full back, central midfielder, wide midfielder, forward) and teams into eight different tactical formations (4-4-2, 4-4-2 diamond, 4-2-2-2, 4-3-3, 4-5-1, 4-2-3-1, 3-4-3, 3-5-2). Results revealed that the degree to which tactical formation affects match performance is position dependent. In terms of physical performance, center backs and full backs showed highest sprinting distances when playing in a formation with only three defenders in the back row (3-4-3, 3-5-2) compared to all other formations (ES range: 0.13≤ES≤1.27). Regarding technical performance, all positions except forwards displayed fewer short passes, middle passes and ball-possessions in the formations 4-3-3 and 4-2-3-1 compared to all other formations (0.02≤ES≤1.19). In conclusion, physical and technical performance of center backs, full backs and wide midfielders differed markedly between the tactical formations. Conversely, the physical and technical performance of central midfielders and forwards only showed small differences between the different tactical formations. These findings can help coaches scheduling their practice. For example, if a coach wants to change the playing formation, he can anticipate the physical and technical match performance changes depending on the respective playing position

A macrocyclic ‛Co0’ complex: the relevance of ligand non-innocence to reactivity

We present a formally zero-valent compound, [Co(Mabiq)Na(OEt2)]2 (1). The complex was characterized by crystallographic, spectroscopic and DFT computational methods. The electronic structure is described as a CoII–(ligand-biradical). Compound 1 is reactive toward proton sources; CoI or CoII products result, depending on the source of protons used. The redox non-innocence of the Mabiq ligand, which accepts both protons and electrons, has important ramifications for reactivity