Figure 1. Quantitative description of human locomotor activity tracks. (A) Individuals with the same daily average level of activity can yet differ by their chronological age, health status and activity distribution during the day. Representative 2-day long locomotor activity tracks of two NHANES 2003−2006 cohort participants aged 43 (upper) and 65 (lower) illustrate how movement patterns can be visually different while having the same level of daily average activity. We quantify individual sample by dividing activity levels into 8 bins (left panel, histograms) and then counting the probabilities Wij of random jumps from each discrete activity state j to every other state i per unit time (right panel, color corresponds to intensity of transitions with respect to the population average). (B) The eigenfrequencies of the Markov chain transition matrices are calculated for same two middle-aged and old individuals and represented by vertical bars (note the difference in the positions of the bars). The distribution of the eigenfrequencies in the relevant age-cohorts of 35-45 y.o. 65-75 y.o. are illustrated by overlaid transparent histograms (the light green and dark blue, respectively). Power Spectral Densities (PSD) reconstructed for Markov chain transition matrices (see Appendix A for details) reproduces the approximately a scale-invariant segment of the true PSD of the signal on time-scales up to tens of minutes. This characteristic shift of the cross-over frequency with age has been reported in numerous studies of human and animal locomotor activity (see text).