Reachability for Updatable Timed Automata Made Faster and More Effective

Updatable timed automata (UTA) are extensions of classical timed automata that allow special updates to clock variables, like x: = x - 1, x : = y + 2, etc., on transitions. Reachability for UTA is undecidable in general. Various subclasses with decidable reachability have been studied. A generic approach to UTA reachability consists of two phases: first, a static analysis of the automaton is performed to compute a set of clock constraints at each state; in the second phase, reachable sets of configurations, called zones, are enumerated. In this work, we improve the algorithm for the static analysis. Compared to the existing algorithm, our method computes smaller sets of constraints and guarantees termination for more UTA, making reachability faster and more effective. As the main application, we get an alternate proof of decidability and a more efficient algorithm for timed automata with bounded subtraction, a class of UTA widely used for modelling scheduling problems. We have implemented our procedure in the tool TChecker and conducted experiments that validate the benefits of our approach

Reachability in Timed Automata with Diagonal Constraints

We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test Z <= Z\u27 which ascertains that zone Z does not reach more states than zone Z\u27, and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. We propose a simulation relation <=_{LU}^d for timed automata with diagonal constraints. On the negative side, we show that deciding Z not <=_{LU}^d Z\u27 is NP-complete. On the positive side, we identify a witness for Z not <=_{LU}^d Z\u27 and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice

Simulations for Event-Clock Automata

Event-clock automata are a well-known subclass of timed automata which enjoy admirable theoretical properties, e.g., determinizability, and are practically useful to capture timed specifications. However, unlike for timed automata, there exist no implementations for event-clock automata. A main reason for this is the difficulty in adapting zone-based algorithms, critical in the timed automata setting, to the event-clock automata setting. This difficulty was studied in [Gilles Geeraerts et al., 2011; Gilles Geeraerts et al., 2014], where the authors also proposed a solution using zone extrapolations. In this paper, we propose an alternative zone-based algorithm, using simulations for finiteness, to solve the reachability problem for event-clock automata. Our algorithm exploits the ?-simulation framework, which is the coarsest known simulation relation for reachability, and has been recently used for advances in other extensions of timed automata

The role of a self-report measure in athlete preparation

Athlete self-report measures (ASRM) are a common and cost-effective method of athlete monitoring. It is purported that ASRM be used to detect athletes at risk of overtraining, injury or illness, allowing intervention through training modification. However it is not known whether ASRM are actually being used for or are achieving these objectives in the applied sport setting. Therefore the aim of this study was to better understand how ASRM are being used in elite sports and their role in athletic preparation. Semi-structured interviews were conducted one-on-one with athletes, coaches and sports science and medicine staff (n=30) at a national sporting institute. Interview recordings were transcribed and analysed for emergent themes. Twelve day-to-day and seven longer-term practices were identified which contributed to a four-step process of ASRM use (record data, review data, contextualize, act). In addition to the purported uses, ASRM facilitated information disclosure and communication amongst athletes and staff and between staff, and improved the understanding and management of athlete preparation. These roles of ASRM are best achieved through engagement of athletes, coaches and support staff in the systematic, cyclic process

Monitoring athletes through self-report: factors influencing implementation

Monitoring athletic preparation facilitates the evaluation and adjustment of practices to optimize performance outcomes. Self-report measures such as questionnaires and diaries are suggested to be a simple and cost-effective approach to monitoring an athlete&rsquo;s response to training, however their efficacy is dependent on how they are implemented and used. This study sought to identify the perceived factors influencing the implementation of athlete self-report measures (ASRM) in elite sport settings. Semi-structured interviews were conducted with athletes, coaches and sports science and medicine staff at a national sporting institute (n = 30). Interviewees represented 20 different sports programs and had varying experience with ASRM. Purported factors influencing the implementation of ASRM related to the measure itself (e.g., accessibility, timing of completion), and the social environment (e.g., buy-in, reinforcement). Social environmental factors included individual, inter-personal and organizational levels which is consistent with a social ecological framework. An adaptation of this framework was combined with the factors associated with the measure to illustrate the inter-relations and influence upon compliance, data accuracy and athletic outcomes. To improve implementation of ASRM and ultimately athletic outcomes, a multi-factorial and multi-level approach is needed

Metabolic Power Method: Underestimation of Energy Expenditure in Field-Sport Movements Using a Global Positioning System Tracking System

The purpose of this study was to assess the validity of a global positioning system (GPS) tracking system to estimate energy expenditure (EE) during exercise and field-sport locomotor movements. Twenty-seven participants each completed a 90-min exercise session on an outdoor synthetic futsal pitch. During the exercise session, they wore a 5-Hz GPS unit interpolated to 15 Hz and a portable gas analyzer that acted as the criterion measure of EE. The exercise session was composed of alternating 5-minute exercise bouts of randomized walking, jogging, running, or a field-sport circuit (×3) followed by 10 min of recovery. One-way analysis of variance showed significant (P &lt; .01) and very large underestimations between GPS metabolic power– derived EE and oxygen-consumption (VO2) -derived EE for all field-sport circuits (% difference ≈ –44%). No differences in EE were observed for the jog (7.8%) and run (4.8%), whereas very large overestimations were found for the walk (43.0%). The GPS metabolic power EE over the entire 90-min session was significantly lower (P &lt; .01) than the VO2 EE, resulting in a moderate underestimation overall (–19%). The results of this study suggest that a GPS tracking system using the metabolic power model of EE does not accurately estimate EE in field-sport movements or over an exercise session consisting of mixed locomotor activities interspersed with recovery periods; however, is it able to provide a reasonably accurate estimation of EE during continuous jogging and running.</jats:p

Zone-based verification of timed automata: extrapolations, simulations and what next?

Timed automata have been introduced by Rajeev Alur and David Dill in the early 90's. In the last decades, timed automata have become the de facto model for the verification of real-time systems. Algorithms for timed automata are based on the traversal of their state-space using zones as a symbolic representation. Since the state-space is infinite, termination relies on finite abstractions that yield a finite representation of the reachable states. The first solution to get finite abstractions was based on extrapolations of zones, and has been implemented in the industry-strength tool Uppaal. A different approach based on simulations between zones has emerged in the last ten years, and has been implemented in the fully open source tool TChecker. The simulation-based approach has led to new efficient algorithms for reachability and liveness in timed automata, and has also been extended to richer models like weighted timed automata, and timed automata with diagonal constraints and updates. In this article, we survey the extrapolation and simulation techniques, and discuss some open challenges for the future.Comment: Invited contribution at FORMATS'2

Game and training load differences in elite junior Australian football

Game demands and training practices within team sports such as Australian football (AF) have changed considerably over recent decades, including the requirement of coaching staff to effectively control, manipulate and monitor training and competition loads. The purpose of this investigation was to assess the differences in external and internal physical load measures between game and training in elite junior AF. Twenty five male, adolescent players (mean &plusmn;SD: age 17.6 &plusmn; 0.5 y) recruited from three elite under 18 AF clubs participated. Global positioning system (GPS), heart rate (HR) and rating of perceived exertion (RPE) data were obtained from 32 game files during four games, and 84 training files during 19 training sessions. Matched-pairs statistics along with Cohen\u27s d effect size and percent difference were used to compare game and training events. Players were exposed to a higher physical load in the game environment, for both external (GPS) and internal (HR, Session-RPE) load parameters, compared to in-season training. Session time (d = 1.23; percent difference = 31.4% (95% confidence intervals = 17.4 - 45.4)), total distance (3.5; 63.5% (17.4 - 45.4)), distance per minute (1.93; 33.0% (25.8 - 40.1)), high speed distance (2.24; 77.3% (60.3 - 94.2)), number of sprints (0.94; 43.6% (18.9 - 68.6)), mean HR (1.83; 14.3% (10.5 - 18.1)), minutes spent above 80% of predicted HRmax (2.65; 103.7% (89.9 - 117.6)) and Session-RPE (1.22; 48.1% (22.1 - 74.1)) were all higher in competition compared to training. While training should not be expected to fully replicate competition, the observed differences suggest that monitoring of physical load in both environments is warranted to allow comparisons and evaluate whether training objectives are being met. Key pointsPhysical loads, including intensity, are typically lower in training compared to competition in junior elite Australian football.Monitoring of player loads in team sports should include both internal and external measures.Selected training drills should look to replicate game intensities, however training is unlikely to match the overall physical demands of competition

Validity of an upper-body-mounted accelerometer to measure peak vertical and resultant force during running and change-of-direction tasks

This study assessed the validity of a tri-axial accelerometer worn on the upper body to estimate peak forces during running and change-of-direction tasks. Seventeen participants completed four different running and change-of-direction tasks (0&deg;, 45&deg;, 90&deg;, and 180&deg;; five trials per condition). Peak crania-caudal and resultant acceleration was converted to force and compared against peak force plate ground reaction force (GRF) in two formats (raw and smoothed). The resultant smoothed (10 Hz) and crania-caudal raw (except 180&deg;) accelerometer values were not significantly different to resultant and vertical GRF for all running and change-of-direction tasks, respectively. Resultant accelerometer measures showed no to strong significant correlations (r = 0.00&ndash;0.76) and moderate to large measurement errors (coefficient of variation [CV] = 11.7&ndash;23.9%). Crania-caudal accelerometer measures showed small to moderate correlations (r = &minus; 0.26 to 0.39) and moderate to large measurement errors (CV = 15.0&ndash;20.6%). Accelerometers, within integrated micro-technology tracking devices and worn on the upper body, can provide a relative measure of peak impact force experienced during running and two change-of-direction tasks (45&deg; and 90&deg;) provided that resultant smoothed values are used