Computing circadian rhythmic patterns and beyond: introduction to a new non-Fourier analysis

We introduce a new computational approach for recognizing and analyzing rhythmic dynamics hidden in lengthy recording of animal’s locomotive activity. This recoding is presented in a form of event-time series, and termed actogram in biological rhythm literature. Upon an actogram, we lay out the construction of our computational approach, called hierarchical segmentation (HS) approach, on a platform based on 3-level-coding algorithm with detailed heuristic ideas and statistical explanation. Our HS approach is then demonstrated to objectively compute and identify a series of phase-markers, which in turn partition the whole actogram into a series of circadian rhythmic cycles of varying lengths. Among these rhythmic cycles, common waveform pattern is also extracted as the chief characteristic of recognizing individual circadian dynamics, and period is calculated as the averaged length of the series of rhythmic cycles. Also we demonstrate how to measure the essential ingredients of rhythmic dynamics: phase-shifts due to Zeitgeber and their information contents, through simple linear regression analysis on subseries of phase-markers before and after Zeitgeber. Along our development explicit contrasts are made to explain the shortcomings of periodogram or Fourier transform based spectrum analysis which rigidly determines rhythmic cycles with equal length, and in general ignores the waveform identification completely. We then show a new construction for the phase response curve (PRC) with confidence band. This construction is proved to be critical for biologists who endeavor to make unbiased inferences on circadian rhythm. Examples of real data analysis on actogram of German cockroach are realistically illustrated. Beyond as being an alternative, we conclude that our computational approach can deliver viable non-Fourier rhythmic pattern recognition on circadian rhythms.