  By means of the concept of balanced estimation of diffusion entropy we
evaluate reliable scale-invariance embedded in different sleep stages and
stride records. Segments corresponding to Wake, light sleep, REM, and deep
sleep stages are extracted from long-term EEG signals. For each stage the
scaling value distributes in a considerable wide range, which tell us that the
scaling behavior is subject- and sleep cycle- dependent. The average of the
scaling exponent values for wake segments is almost the same with that for REM
segments ($\sim 0.8$). Wake and REM stages have significant high value of
average scaling exponent, compared with that for light sleep stages ($\sim
0.7$). For the stride series, the original diffusion entropy (DE) and balanced
estimation of diffusion entropy (BEDE) give almost the same results for
de-trended series. Evolutions of local scaling invariance show that the
physiological states change abruptly, though in the experiments great efforts
have been done to keep conditions unchanged. Global behaviors of a single
physiological signal may lose rich information on physiological states.
Methodologically, BEDE can evaluate with considerable precision
scale-invariance in very short time series ($\sim 10^2$), while the original DE
method sometimes may underestimate scale-invariance exponents or even fail in
detecting scale-invariant behavior. The BEDE method is sensitive to trends in
time series. Existence of trend may leads to a unreasonable high value of
scaling exponent, and consequent mistake conclusions.
