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In line with the previous work of their laboratory, Tucker et al 
recently proposed a new point of view on the dynamic control mechanisms of
the athlete during self-paced exercise. The authors should be thanked for
their innovative contribution to exercise physiology, and we think that
the tools they used need some complements.
Firstly, some methodological caution should be taken into accou...
Firstly, some methodological caution should be taken into account for
forthcoming studies. Indeed, the number of analyzed data points (100 for
the entire trial and only 20 for each interval) seems insufficient for non-linear analyses. A recent study showed a dramatical decrease in
performance of spectral analysis with short series.  So we suggest that
a minimum of 512 points should be considered to improve the validity of
the method. Furthermore, the authors also used the Higuchi method for the
determination of a fractal dimension on the number of available points.
However Higuchi's algorithm primarily assesses geometric fractal
properties, and much more relevant methods for the assessment of
statistical fractal properties have widely been developed. So we suggest
that a temporal method as Detrended Fluctuation Analysis (DFA) should be
associated to spectral analysis, and completed by a method like
ARFIMA/ARMA modeling, which provides a statistical probability for series
to be fractal.
Secondly, data showed the presence of an endspurt leading the non-stationary of the signal. The authors concluded themselves that "the
dominant low frequency cycle is probably caused by, or related to, the
decrease in power output evident in most athletes during the middle period
of the event, and the endspurt which occurs at the end of the event". That
is precisely the reason why fractal analysis have to be applied on
stationary signals. So we suggest that the drift of the data across the
events should be corrected. The absence of steady-state is confirmed by
the facts that "the dominant frequency spikes found when analyzing shorter
time epochs at the beginning, middle and end of the time trial were
different to those found when analyzing the frequency spectrum of the
entire time trial". This result seems in contradiction with the self-similarity properties of fractal series. [4-5] In the same line, data
reporting multiple peaks frequency peaks seems fundamentally opposed to
1/f-like scaling properties. [4-5] From a general point of view, non
random fluctuations are not automatically fractal , and even if series
in this study were indeed fractal, fractal properties are conceived to be
generated by the interaction of several subsystems [4-5] and do not allow
to conclude to the presence of one central governor.
1 Tucker R, Bester A, Lambert EV, et al. Non-random fluctuations in
power output during self-paced exercise. Br J Sports Med. 2006, 40: 912-917.
2 Delignieres D, Ramdani S, Lemoine L, et al. Fractal analyses for
‘short’ time series: A re-assessment of classical methods. J Math Psychol.
3 Torre K, Delignières D, Lemoine L. Detection of long-range
dependence and estimation of fractal exponents through ARFIMA modeling.
Brit J Math Stat Psy. In press
4 Beltz BC, Kello CT. On the intrinsic fluctuations of human
behavior. In: Sohob SP, ed. Trends in Cognitive Psychology. New York: Nova
5 Goldberger AL. Nonlinear dynamics, fractals and chaos theory:
Implications for neuroautonomic heart control in health and disease. In:
Bolis CL, Licinio J, eds. The Autonomic Nervous System. Genova: World
Health Organization 1999.