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Effects of sampling rate on multiscale entropy of electroencephalogram time series

Zheng Jinlin, Li Yan, Zhai Yawen, Zhang Nan, Yu Haoyang, Tang Chi, Yan Zheng, Luo Erping, Xie Kangning

Biocybernetics and Biomedical Engineering

2023

Vol. 43, no. 1

233--245

A physiological system encompasses numerous components that function at various time scales. To characterize the scale-dependent feature, the multiscale entropy (MSE) analysis has been proposed to describe the complex processes on multiple time scales. However, MSE analysis uses the relative scale factors to reveal the time-related dynamics, which may cause in-comparability of results from diverse studies with inconsistent sampling rates. In this study, in addition to the conventional MSE with relative scale factors, we also expressed MSE with absolute time scales (MaSE). We compared the effects of sampling rates on MSE and MaSE of simulated and real EEG time series. The results show that the previously found phenomenon (down-sampling can increase sample entropy) is just the projection of the compressing effect of down-sampling on MSE. And we have also shown the compressing effect of down-sampling on MSE does not change MaSE’s profile, despite some minor right-sliding. In addition, by analyzing a public EEG dataset of emotional states, we have demonstrated improved classification rate after choosing appropriate sampling rate. We have finally proposed a working strategy to choose an appropriate sampling rate, and suggested using MaSE to avoid confusion caused by sampling rate inconsistency. This novel study may apply to a broad range of studies that would traditionally utilize sample entropy and MSE to analyze the complexity of an underlying dynamic process.

Complexity analyses of Godavari and Krishna river streamflow using the concept of entropy

Singh Rahul Kumar, Jain Manoj Kumar

Acta Geophysica

2021

Vol. 69, no. 6

2325--2338

The hydrological regime in both the Godavari and Krishna River has been altered due to both human-induced and environmental changes. The present study utilizes the sample entropy and its more generalized approach known as multiscale entropy to investigate the temporal and spatial distribution of complexity and quantify them using SampEn values. Daily streamflow for five stations, three from Godavari River (Dhalegaon, Nowrangpur, and Polavaram), and two from Krishna River (Yadgir and K. Agraharam), was analysed for the complexity analyses. Trends in the streamflow for the selected gauging stations and their annual entropy values have also been evaluated using the Mann–Kendall test. The trend results revealed that three (Dhalegaon and Nowrangpur in Godavari basin and Yadgir in Krishna basin) out of five stations showed significant decreasing trends for both monthly and annual streamflow series. The declining trend in streamflow could be attributed to both anthropogenic (reservoir operation, increased water abstraction, etc.) and climatic (change in monsoon rainfall, temperature, etc.) factors. The most significant reduction in annual streamflow during the post-impact period was observed at Dhalegaon station in Godavari Basin (from 53,573 to 19,555 m3/s) signifying maximum alteration in annual flow regime. The entropy analysis results of streamflow showed that there was obvious spatial and temporal variation in the complexity, as indicated by the annual SampEn values. Although not profound, a negative correlation exists between the annual runoff and SampEn values (highest −0.42 at K. Agraharam) and hence a reverse correspondence exists between them. In MSE analysis, the original streamflow series increased with time scale (up to 30 days was chosen for this study), whereas entropy decreased with an increased time scale. Due to the fully operational state of the dams upstream of the gauging stations, the entropy values during the post-impact period were less the pre-impact period. The present study can be used as a scientific reference to use information science to detect hydrologic alterations in the river basins. Future studies should focus on considering both climatic and land-use changes in conjunction with the human-induced changes for more comprehensive river system disorder analysis.

Bootstrapping the empirical bounds on the variability of Sample Entropy in 24-hour ECG recordings for 1 hour segments

Zurek S., Grabowski W., Kosmider M., Jurga S., Guzik P., Piskorski J.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 2

105--113

We investigate the variability of one of the most often used complexity measures in the analysis of the time series of RR intervals, i.e. Sample Entropy. The analysis is carried out for a dense matrix of possible r thresholds in 79 24h recordings, for segments consisting of 5000 consecutive beats, randomly selected from the whole recording. It is repeated for the same recordings in random order. This study is made possible by the novel NCM algorithm which is many orders of magnitude faster than the alternative approaches. We find that the bootstrapped standard errors for Sample entropy are large for RR intervals in physiological order compared to the standard errors for shuffled data which correspond to the maximum available entropy. This result indicates that Sample Entropy varies widely over the circadian period. This paper is purely methodological and no physiological interpretations are attempted.