{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T07:57:36Z","timestamp":1768723056316,"version":"3.49.0"},"reference-count":50,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61971374"],"award-info":[{"award-number":["61971374"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61603327"],"award-info":[{"award-number":["61603327"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Cross-frequency phase\u2013amplitude coupling (PAC) plays an important role in neuronal oscillations network, reflecting the interaction between the phase of low-frequency oscillation (LFO) and amplitude of the high-frequency oscillations (HFO). Thus, we applied four methods based on permutation analysis to measure PAC, including multiscale permutation mutual information (MPMI), permutation conditional mutual information (PCMI), symbolic joint entropy (SJE), and weighted-permutation mutual information (WPMI). To verify the ability of these four algorithms, a performance test including the effects of coupling strength, signal-to-noise ratios (SNRs), and data length was evaluated by using simulation data. It was shown that the performance of SJE was similar to that of other approaches when measuring PAC strength, but the computational efficiency of SJE was the highest among all these four methods. Moreover, SJE can also accurately identify the PAC frequency range under the interference of spike noise. All in all, the results demonstrate that SJE is better for evaluating PAC between neural oscillations.<\/jats:p>","DOI":"10.3390\/e23081070","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T10:54:35Z","timestamp":1629284075000},"page":"1070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Estimating Phase Amplitude Coupling between Neural Oscillations Based on Permutation and Entropy"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3928-1965","authenticated-orcid":false,"given":"Liyong","family":"Yin","sequence":"first","affiliation":[{"name":"Department of Internal Medicine, Hebei Medical University, Shijiazhuang 050011, China"}]},{"given":"Fan","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering (School of Software), Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Rui","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering (School of Software), Yanshan University, Qinhuangdao 066004, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4009-4374","authenticated-orcid":false,"given":"Zhaohui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering (School of Software), Yanshan University, Qinhuangdao 066004, China"},{"name":"Hebei Key Laboratory of Information Transmission and Signal Processing, Yanshan University, Qinhuangdao 066004, China"}]},{"given":"Fuzai","family":"Yin","sequence":"additional","affiliation":[{"name":"Department of Internal Medicine, Hebei Medical University, Shijiazhuang 050011, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1038\/nature08573","article-title":"Frequency of gamma oscillations routes flow of information in the hippocampus","volume":"462","author":"Colgin","year":"2009","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1016\/j.neuroimage.2013.06.022","article-title":"Theta rhythm and the encoding and retrieval of space and time","volume":"85","author":"Hasselmo","year":"2014","journal-title":"NeuroImage"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"573","DOI":"10.3389\/fnins.2019.00573","article-title":"Quantification of Phase-Amplitude Coupling in Neuronal Oscillations: Comparison of Phase-Locking Value, Mean Vector Length, Modulation Index, and Generalized-Linear-Modeling-Cross-Frequency-Coupling","volume":"13","author":"Naumann","year":"2019","journal-title":"Front Neurosci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1109\/TKDE.2019.2931687","article-title":"Incremental Factorization of Big Time Series Data with Blind Factor Approximation","volume":"33","author":"Chen","year":"2021","journal-title":"IEEE Trans. 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