Though coherence, a classical method to describe the linear correlation between two time series, has wideranging applications, from economics to neuroscience, it fails to illustrate the inherently multi-time scalesbas...Though coherence, a classical method to describe the linear correlation between two time series, has wideranging applications, from economics to neuroscience, it fails to illustrate the inherently multi-time scalesbased correlations. In this paper, we proposed a multiscale-like coherence model, defined as composite multiscalecoherence (CMSC) by combining the kth coarse-grain processing with the coherence. We made a comparison withthe multiscale coherence (MSC) with coarse-grain process in numerical data to compare the sensitivity profiles tothe coupling strength, data length and white Gaussian noise. After that, we applied the proposed model to explorethe functional corticomuscular coupling (FCMC) by analyzing the correlation between the EEG and EMG signals.Simulation results reflected that the CMSC method were sensitive to the coupling strength, data length and thewhite Gaussian noise, and presented more stability along the time scale compared to the MSC method. Ourapplication of CMSC methods on the EEG and EMG signals indicated that the FCMC was of multi-time scalecharacteristics and higher coherence mainly consisted in the alpha and beta bands at about scale 10, thoughsignificant area showed a gradual decline with the scale increasing. Further comparison indicated that bothmodels are equally effective to describe the multiscale characteristics of the FCMC at lower time scales, whilesome differences emerge at the high time scales. Both simulation and experimental data demonstrate the effectiveness of the proposed multiscale-like model to describe the multiscale correlation between two time series. Thisstudy extends the relative researches on the FCMC to the multi-time scale.展开更多
基金funded by National Natural Science Foundation of China grant(U20A20192 and 62076216)Hebei Natural Science Foundation(F2022203002,F2021203033 and G2020203012)+2 种基金Cultivation Project for Basic Research and Innovation of Yanshan University(2021LGZD010)the Funding Program for Innovative Ability Training of graduate students of Hebei Provincial Department of Education under Grant CXZZSS2022123Hebei Innovation Capability Improvement Plan Project(22567619H).
文摘Though coherence, a classical method to describe the linear correlation between two time series, has wideranging applications, from economics to neuroscience, it fails to illustrate the inherently multi-time scalesbased correlations. In this paper, we proposed a multiscale-like coherence model, defined as composite multiscalecoherence (CMSC) by combining the kth coarse-grain processing with the coherence. We made a comparison withthe multiscale coherence (MSC) with coarse-grain process in numerical data to compare the sensitivity profiles tothe coupling strength, data length and white Gaussian noise. After that, we applied the proposed model to explorethe functional corticomuscular coupling (FCMC) by analyzing the correlation between the EEG and EMG signals.Simulation results reflected that the CMSC method were sensitive to the coupling strength, data length and thewhite Gaussian noise, and presented more stability along the time scale compared to the MSC method. Ourapplication of CMSC methods on the EEG and EMG signals indicated that the FCMC was of multi-time scalecharacteristics and higher coherence mainly consisted in the alpha and beta bands at about scale 10, thoughsignificant area showed a gradual decline with the scale increasing. Further comparison indicated that bothmodels are equally effective to describe the multiscale characteristics of the FCMC at lower time scales, whilesome differences emerge at the high time scales. Both simulation and experimental data demonstrate the effectiveness of the proposed multiscale-like model to describe the multiscale correlation between two time series. Thisstudy extends the relative researches on the FCMC to the multi-time scale.
