Abstract
This paper proposes a method that maps the coupling strength of an arbitrary number of signals D, D ≥ 2, into a single time series. It is motivated by the inability of multiscale entropy to jointly analyze more than two signals. The coupling strength is determined using the copula density defined over a [0 1]D copula domain. The copula domain is decomposed into the Voronoi regions, with volumes inversely proportional to the dependency level (coupling strength) of the observed joint signals. A stream of dependency levels, ordered in time, creates a new time series that shows the fluctuation of the signals’ coupling strength along the time axis. The composite multiscale entropy (CMSE) is then applied to three signals, systolic blood pressure (SBP), pulse interval (PI), and body temperature (tB), simultaneously recorded from rats exposed to different ambient temperatures (tA). The obtained results are consistent with the results from the classical studies, and the method itself offers more levels of freedom than the classical analysis.
Highlights
Approximate [1,2] and sample entropies [3], ApEn and SampEn, have been intensively implemented in a range of scientific fields to quantify the unpredictability of time series fluctuations
Mapping the signals into the dependency time series takes into account the delay between entropy analysis
Results are presented as a mean ± SE
Summary
Approximate [1,2] and sample entropies [3], ApEn and SampEn, have been intensively implemented in a range of scientific fields to quantify the unpredictability of time series fluctuations. Contributions that apply ApEn and SampEn are measured by thousands [4], confirming their significance. Descriptions of (cross) entropy concepts can be found in numerous articles, but a recent comprehensive review [7] provides an excellent tutorial with the guidelines aimed to help the research society to understand ApEn and SampEn and to apply them correctly [7]. Multiscale entropy (MSE) [8,9], based on SampEn, investigates the changes in complexity caused by a change of the time scale. A comprehensive study of fixed and variable thresholds at different scales presents an excellent review of the MSE improvements [12]
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