BioSimulator.jl: Stochastic simulation in Julia

Biological systems with intertwined feedback loops pose a challenge to mathematical modeling efforts. Moreover, rare events, such as mutation and extinction, complicate system dynamics. Stochastic simulation algorithms are useful in generating time-evolution trajectories for these systems because they can adequately capture the influence of random fluctuations and quantify rare events. We present a simple and flexible package, BioSimulator.jl, for implementing the Gillespie algorithm, $\tau$-leaping, and related stochastic simulation algorithms. The objective of this work is to provide scientists across domains with fast, user-friendly simulation tools. We used the high-performance programming language Julia because of its emphasis on scientific computing. Our software package implements a suite of stochastic simulation algorithms based on Markov chain theory. We provide the ability to (a) diagram Petri Nets describing interactions, (b) plot average trajectories and attached standard deviations of each participating species over time, and (c) generate frequency distributions of each species at a specified time. BioSimulator.jl's interface allows users to build models programmatically within Julia. A model is then passed to the simulate routine to generate simulation data. The built-in tools allow one to visualize results and compute summary statistics. Our examples highlight the broad applicability of our software to systems of varying complexity from ecology, systems biology, chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages the use of stochastic simulation, minimizes tedious programming efforts, and reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table

Accurate Stochastic Simulation via the Step Anticipation τ-Leaping (SAL) Algorithm

Stochastic simulation methods are important in modeling chemical reactions, and biological and physical stochastic processes describable as continuous-time discrete-state Markov chains with a finite number of reactant species and reactions. The current algorithm of choice, τ-leaping, achieves fast and accurate stochastic simulation by taking large time steps that leap over individual reactions. During a leap interval (t, t + τ) in τ-leaping, each reaction channel operates as a Poisson process with a constant intensity. We modify τ-leaping to allow linear and quadratic changes in reaction intensities. Because our version of τ-leaping accurately anticipates how intensities change over time, we propose calling it the step anticipation τ-leaping (SAL) algorithm. We apply SAL to four examples: Kendall's process, a two-type branching process, Ehrenfest's model of diffusion, and Michaelis-Menten enzyme kinetics. In each case, SAL is more accurate than ordinary τ-leaping. The degree of improvement varies with the situation. Near stochastic equilibrium, reaction intensities are roughly constant, and SAL and ordinary τ-leaping perform about equally well

Epidemiology of Injury in English Women's Super league Football: A Cohort Study

INTRODUCTION: The epidemiology of injury in male professional football has been well documented (Ekstrand, Hägglund, & Waldén, 2011) and used as a basis to understand injury trends for a number of years. The prevalence and incidence of injuries occurring in womens super league football is unknown. The aim of this study is to estimate the prevalence and incidence of injury in an English Super League Women’s Football squad. METHODS: Following ethical approval from Leeds Beckett University, players (n = 25) signed to a Women’s Super League Football club provided written informed consent to complete a self-administered injury survey. Measures of exposure, injury and performance over a 12-month period was gathered. Participants were classified as injured if they reported a football injury that required medical attention or withdrawal from participation for one day or more. Injuries were categorised as either traumatic or overuse and whether the injury was a new injury and/or re-injury of the same anatomical site RESULTS: 43 injuries, including re-injury were reported by the 25 participants providing a clinical incidence of 1.72 injuries per player. Total incidence of injury was 10.8/1000 h (95% CI: 7.5 to 14.03). Participants were at higher risk of injury during a match compared with training (32.4 (95% CI: 15.6 to 48.4) vs 8.0 (95% CI: 5.0 to 10.85)/1000 hours, p 28 days) of which there were three non-contact anterior cruciate ligament (ACL) injuries. The epidemiological incidence proportion was 0.80 (95% CI: 0.64 to 0.95) and the average probability that any player on this team will sustain at least one injury was 80.0% (95% CI: 64.3% to 95.6%) CONCLUSION: This is the first report capturing exposure and injury incidence by anatomical site from a cohort of English players and is comparable to that found in Europe (6.3/1000 h (95% CI 5.4 to 7.36) Larruskain et al 2017). The number of ACL injuries highlights a potential injury burden for a squad of this size. Multi-site prospective investigations into the incidence and prevalence of injury in women’s football are require