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David R. Collins, Hyeongsaeng Park and Michael T. Turvey

Von Holst (1939/1973) parsed intersegmental coordination into relative and absolute to distinguish moderate and extreme forms. Kelso and DeGuzman (1992) discussed an interpretation of relative coordination in terms of the chaotic phenomenon of intermittency. The data of concern (DeGuzman & Kelso, 1991) do not, however, exclude a stochastic interpretation, which is detailed here following earlier suggestions. The key difference is modeling relative coordination by stochastic variability about weak attractors rather than by deterministic variability about remnants of attractors (”ghost attractors”). The intermittency interpretation is not robust in the presence of noise and, therefore, is not well disposed to account for uncertainty in detailing a model of behavioral data or its parameters. In contrast, the stochastic interpretation is based upon an approximation of unknown underlying processes in the form of Gaussian white noise. A stochastic method for estimating model parameters from a stationary probability distribution and a mean first passage time is illustrated using experimental and simulated data.

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Joseph P. Stitt and Karl M. Newell

This paper presents the stochastic modeling of isometric force variability in the steady-state time series recorded from the index finger of young adults in the act of attempting to hold different levels of constant force. The isometric force time series were examined by assuming that the stochastic (random) models were linear. System identification techniques were employed to estimate the parameters of each linear model. Once the models were parameterized, the values of the estimated parameters were compared to determine if a single linear time-invariant model was applicable across the entire isometric force range. Although the overall random models were found to be nonlinear functions of the target force level, within a fixed target level, linear modeling provided adequate estimates of the underlying processes thus enabling the use of well-known linear system identification algorithms.

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Chris R. Abbiss, Paolo Menaspà, Vincent Villerius and David T. Martin

A number of laboratory-based performance tests have been designed to mimic the dynamic and stochastic nature of road cycling. However, the distribution of power output and thus physical demands of high-intensity surges performed to establish a breakaway during actual competitive road cycling are unclear. Review of data from professional road-cycling events has indicated that numerous short-duration (5–15 s), high-intensity (~9.5–14 W/kg) surges are typically observed in the 5–10 min before athletes’ establishing a breakaway (ie, riding away from a group of cyclists). After this initial high-intensity effort, power output declined but remained high (~450–500 W) for a further 30 s to 5 min, depending on race dynamics (ie, the response of the chase group). Due to the significant influence competitors have on pacing strategies, it is difficult for laboratory-based performance tests to precisely replicate this aspect of mass-start competitive road cycling. Further research examining the distribution of power output during competitive road racing is needed to refine laboratory-based simulated stochastic performance trials and better understand the factors important to the success of a breakaway.

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Gregory T. Levin, Paul B. Laursen and Chris R. Abbiss


To assess the reliability of a 5-min-stage graded exercise test (GXT) and determine the association between physiological attributes and performance over stochastic cycling trials of varying distance.


Twenty-eight well-trained male cyclists performed 2 GXTs and either a 30-km (n = 17) or a 100-km stochastic cycling time trial (n = 9). Stochastic cycling trials included periods of high-intensity efforts for durations of 250 m, 1 km, or 4 km depending on the test being performing.


Maximal physiological attributes were found to be extremely reliable (maximal oxygen uptake [VO2max]: coefficient of variation [CV] 3.0%, intraclass correlation coefficient [ICC] .911; peak power output [PPO]: CV 3.0%, ICC .913), but a greater variability was found in ventilatory thresholds and economy. All physiological variables measured during the GXT, except economy at 200 W, were correlated with 30-km cycling performance. Power output during the 250-m and 1-km efforts of the 30-km trial were correlated with VO2max, PPO, and the power output at the second ventilatory threshold (r = .58–.82). PPO was the only physiological attributed measured during the GXT to be correlated with performance during the 100-km cycling trial (r = .64).


Many physiological variables from a reliable GXT were associated with performance over shorter (30-km) but not longer (100-km) stochastic cycling trials.

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Jess S. Boronico and Scott L. Newbert

This manuscript presents a model to assist in the determination of optimal American football play selection for first down and goal situations. A game theoretic approach is embedded within a stochastic dynamic programming formulation, resulting in a mixed strategy satisfying the ex-ante declared objective of maximizing the probability of scoring a touchdown. The methodology provides a quantitative framework to a problem that impacts on team performance and addresses a gap in the literature concerning the application of quantitative methods to sports.

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James W. Roberts

.13% = 1 SD ). For this inference to be so, the error that is incurred prior to “homing-in” should be somewhat random or stochastic in nature and reflect a normal distribution. However, it is also possible that the changes reported in spatial variability across kinematic landmarks may reflect a systematic

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Amber Collins, Troy Blackburn, Chris Olcott, Joanne M. Jordan, Bing Yu and Paul Weinhold

Extended use of knee sleeves in populations at risk for knee osteoarthritis progression has shown functional and quality of life benefits; however, additional comprehensive kinematic and kinetic analyses are needed to determine possible physical mechanisms of these benefits which may be due to the sleeve’s ability to enhance knee proprioception. A novel means of extending these enhancements may be through stochastic resonance stimulation. Our goal was to determine whether the use of a knee sleeve alone or combined with stochastic resonance electrical stimulation improves knee mechanics in knee osteoarthritis. Gait kinetics and kinematics were assessed in subjects with medial knee osteoarthritis when presented with four conditions: control1, no electrical stimulation/sleeve, 75% threshold stimulation/sleeve, and control2. An increase in knee flexion angle throughout stance and a decrease in flexion moment occurring immediately after initial contact were seen in the stimulation/sleeve and sleeve alone conditions; however, these treatment conditions did not affect the knee adduction angle and internal knee abduction moment during weight acceptance. No differences were found between the sleeve alone and the stochastic resonance with sleeve conditions. A knee sleeve can improve sagittal-plane knee kinematics and kinetics, although adding the current configuration of stochastic resonance did not enhance these effects.

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Ying Hwa Kee, Iti Chaturvedi, Chee Keng John Wang and Lung Hung Chen

The capacity for random movement production is known to be limited in humans (e.g., Newell, Deutsch, & Morrison, 2000). We examined the effects of a brief mindfulness induction on random movement production because there are useful implications for variability in solving movement-related problems. The main task involved randomly clicking the 9 boxes in a 3 × 3 grid presented on a computer screen for five minutes. We characterized the sequence of clicking in terms of degrees of randomness, or periodicity, based on the fit, or probability, of the experimental data with its best fitting Bayesian network (4-click memory nodes) using the Markov chain Monte Carlo (MCMC) approach. Sixty-three participants were randomly assigned to either the experimental or the control condition. Mixed design repeated-measures ANOVA results show that the short mindfulness induction had a positive effect on the randomness of the sequence subsequently produced. This finding suggests that mindfulness may be a suitable strategy for increasing random movement behavior.

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Yi-Ching Chen, I-Chen Lin, Yen-Ting Lin, Wei-Min Huang, Chien-Chun Huang and Ing-Shiou Hwang

priori standard of internally paced movement. Hence, force output during rhythmic force production is never smooth; it is composed of a deterministic (predictable) component and a stochastic component (or force fluctuations). One hallmark of aging is reduction of the ratio of the deterministic component

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Cruz Hogan, Martyn J. Binnie, Matthew Doyle, Leanne Lester and Peter Peeling

combination of PO, SR, and HR measures when monitoring training intensities could therefore better inform coaches when evaluating the training responses for their individual athletes. In road cycling research, a limitation identified in the use of PO was the stochastic nature of power during field