1P075 COMPLEX MULTI-SCALE NETWORKS AND INFORMATION FLOWS FOR PROTEIN DYNAMICS FROM SINGLE-MOLECULE TIME SERIES(Proteins-functions, methodology, and protein enigineering,Oral Presentations)

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

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Scale-dependent intrinsic entropies of complex time series

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2015.0204 ◽

2016 ◽

Vol 374 (2065) ◽

pp. 20150204 ◽

Cited By ~ 2

Author(s):

Jia-Rong Yeh ◽

Chung-Kang Peng ◽

Norden E. Huang

Keyword(s):

Time Series ◽

Time Scales ◽

Spatial Scales ◽

Multiple Time Scales ◽

Multiple Time ◽

Complex Time ◽

Multi Scale ◽

Mode Decomposition ◽

Simulated Time ◽

Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

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