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Olaf Hoos, Tobias Boeselt, Martin Steiner, Kuno Hottenrott and Ralph Beneke

Purpose:

To analyze time-domain, spectral, and fractal properties of speed regulation during half-marathon racing.

Methods:

In 21 male experienced runners, high-resolution data on speed (V), stride frequency (SF), and stride length (SL) were assessed during half-marathon competition (21,098 m). Performance times, timeand frequency-domain variability, spectral-scaling exponent (beta), and fractal dimension (FD) of V, SF, and SL were analyzed.

Results:

V of 3.65 ± 0.41 m/s, SF of 1.41 ± 0.05 Hz, and SL of 2.58 ± 0.25 m occurred with higher (P < .05) individual variability in V and SL than in SF. Beta and FD were always 1.04–1.88 and 1.56–1.99, respectively. Beta and FD differed (P < .05) in SF and SL compared with V and were correlated in V and SL (r = .91, P < .05). Spectral peaks of V, SF, and SL occurred at wavelengths of 3–35 min, and those of V and SL were interrelated (r = .56, P < .05). Mean SF and mean SL were significantly correlated with performance (r = .59 and r = .95, P < .05). SL accounted for 84% ± 6% and SF for 16% ± 6% of speed variability.

Conclusions:

The observed nonrandom fluctuations in V, SF, and SL correspond to nonstationary fractional Brownian motion with inherent long-range correlations. This indicates a similar complex regulation process in experienced runners that is primarily mediated via SL.

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Ana Diniz, João Barreiros and Nuno Crato

Repetitive movements lead to isochronous serial interval production which exhibit inherent variability. The Wing-Kristofferson model offers a decomposition of the interresponse intervals in tapping tasks based on a cognitive component and on a motor component. We suggest a new theoretical and fully parametric approach to this model in which the cognitive component is modeled as a long-memory process and the motor component is treated as a white noise process, mutually independent. Under these assumptions, we obtained the autocorrelation function and the spectral density function. Furthermore, we propose an estimator based on the maximization of the frequency-domain representation of the likelihood function. Finally, we conducted a simulation study to assess the properties of this estimator and performed an experimental study involving tapping tasks with two target frequencies (1.250 Hz and 0.625 Hz).

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Joel T. Fuller, Clint R. Bellenger, Dominic Thewlis, John Arnold, Rebecca L. Thomson, Margarita D. Tsiros, Eileen Y. Robertson and Jonathan D. Buckley

Purpose:

Stride-to-stride fluctuations in running-stride interval display long-range correlations that break down in the presence of fatigue accumulated during an exhaustive run. The purpose of the study was to investigate whether long-range correlations in running-stride interval were reduced by fatigue accumulated during prolonged exposure to a high training load (functional overreaching) and were associated with decrements in performance caused by functional overreaching.

Methods:

Ten trained male runners completed 7 d of light training (LT7), 14 d of heavy training (HT14) designed to induce a state of functional overreaching, and 10 d of light training (LT10) in a fixed order. Running-stride intervals and 5-km time-trial (5TT) performance were assessed after each training phase. The strength of long-range correlations in running-stride interval was assessed at 3 speeds (8, 10.5, and 13 km/h) using detrended fluctuation analysis.

Results:

Relative to performance post-LT7, time to complete the 5TT was increased after HT14 (+18 s; P < .05) and decreased after LT10 (–20 s; P = .03), but stride-interval long-range correlations remained unchanged at HT14 and LT10 (P > .50). Changes in stride-interval long-range correlations measured at a 10.5-km/h running speed were negatively associated with changes in 5TT performance (r –.46; P = .03).

Conclusions:

Runners who were most affected by the prolonged exposure to high training load (as evidenced by greater reductions in 5TT performance) experienced the greatest reductions in stride-interval long-range correlations. Measurement of stride-interval long-range correlations may be useful for monitoring the effect of high training loads on athlete performance.

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Scott W. Ducharme and Richard E.A. van Emmerik

system that exhibits long-range correlations can be quantified via simple integration ( Hausdorff, Peng, Wei, & Goldberger, 2000 ). DFA evaluates the magnitude of variability in a signal at different temporal scales, or window sizes. To accomplish this, the biophysical signal is first integrated, then

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Stephen M. Glass, Brian L. Cone, Christopher K. Rhea, Donna M. Duffy and Scott E. Ross

each channel. The nonlinear outcomes used in this study were (1) detrended fluctuation analysis (DFA) and (2) multivariate multiscale sample entropy (MMSE). These 2 outcomes were selected as indicators of long-range correlation and multiscale complexity, respectively. 22 Both nonlinear outcomes were

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Owen Jeffries, Mark Waldron, Stephen D. Patterson and Brook Galna

 = .05 resulting from the detrended fluctuation analysis as random noise. By contrast, values of 0 <  α  < .5 and .5 <  α  < 1.0 indicate persistent long-range correlations in the fluctuation of power output. 17 Statistical Analysis A paired Student t test was used to examine paired data for

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Philip W. Fink, Sarah P. Shultz, Eva D’Hondt, Matthieu Lenoir and Andrew P. Hills

more traditional methods of analysis (e.g., COP displacement) might miss ( Ihlen, Skjæret, & Vereijken, 2013 ; Norris, Marsh, Smith, Kohut, & Miller, 2005 ). Fractal processes contain long range correlations in the time series and can show either persistence (i.e., a positive correlation in time or a

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Curtis Kindel and John Challis

white noise, a random process; a value greater than 0.5 and less than (or equal to) 1.0 indicates persistent long range correlations, while a value less than 0.5 indicates long range anti-correlations. Finally a value of 1.5 indicates Brown noise. For all variables measured, peak moments, CV, ApEn, and