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Taken together, those results suggest that more fatigable Type II motor units are involved in men, resulting in greater lactic acid and ions accumulations during fatigue. This difference in muscle's metabolic and ionic state could be responsible for a greater reflex-induced decrease of motor units firing rates in men compared with boys. This firing rate decrease could be explained using the "muscular wisdom" hypothesis and would express a nervous command adaptation to sustain a maximal contraction.

A group of 24 subjects performed on a cycle ergometer a fatigue test consisting of four successive all-out sprints against the same braking torque. The subjects were not allowed time to recover between sprints and consequently the test duration was shorter than 30 s. The pedal velocity was recorded every 10 ms from a disc fixed to the flywheel with 360 slots passing in front of a photo-electric cell linked to a microcomputer which processed the data. Taking into account the variation of kinetic energy of the ergometer flywheel, it was possible to determine the linear torque velocity relationship from data obtained during the all-out cycling exercise by computing torque and velocity from zero velocity to peak velocity according to a method proposed previously. The maximal theoretical velocity (v(0)) and the maximal theoretical torque (T(0)) were estimated by extrapolation of each torque-velocity relationship. Maximal power (P(max)) was calculated from the values of T(0) and v(0) (P(max) = 0.25v(0)T(0). The kinetics of v(0), T(0) and P(max) was assumed to express the effects of fatigue on the muscle contractile properties (maximal shortening velocity, maximal muscle strength and maximal power). Fatigue induced a parallel shift to the left of the torque-velocity relationships. The v( 0), T(0) and P(max) decreases were equal to 16.3 percent, 17.3 percent and 31 percent, respectively. The magnitude of the decrease was similar for v(0) and T(0) which suggested that P max decreased because of a slowing of maximal shortening velocity as well as a loss in maximal muscle strength. However, the interpretation of a decrease in cycling v(0) which has the dimension of a maximal cycling frequency is made difficult by the possible interactions between the agonistic and the antagonistic muscles and could also be explained by a slowing of the muscle relaxation rate.

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Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.