{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T06:16:49Z","timestamp":1775197009722,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T00:00:00Z","timestamp":1724716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Functional of China","award":["62376184"],"award-info":[{"award-number":["62376184"]}]},{"name":"National Natural Science Functional of China","award":["62303445"],"award-info":[{"award-number":["62303445"]}]},{"name":"National Natural Science Functional of China","award":["62206196"],"award-info":[{"award-number":["62206196"]}]},{"name":"National Natural Science Functional of China","award":["62176177"],"award-info":[{"award-number":["62176177"]}]},{"name":"National Natural Science Functional of China","award":["YDZJSX20231A017"],"award-info":[{"award-number":["YDZJSX20231A017"]}]},{"name":"National Natural Science Functional of China","award":["2023M733669"],"award-info":[{"award-number":["2023M733669"]}]},{"name":"National Natural Science Functional of China","award":["JCYJ20230807140719040"],"award-info":[{"award-number":["JCYJ20230807140719040"]}]},{"name":"National Natural Science Functional of China","award":["202303021221034"],"award-info":[{"award-number":["202303021221034"]}]},{"name":"National Natural Science Functional of China","award":["20210302124550"],"award-info":[{"award-number":["20210302124550"]}]},{"name":"National Natural Science Functional of China","award":["202103021223035"],"award-info":[{"award-number":["202103021223035"]}]},{"name":"National Natural Science Functional of China","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["62376184"],"award-info":[{"award-number":["62376184"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["62303445"],"award-info":[{"award-number":["62303445"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["62206196"],"award-info":[{"award-number":["62206196"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["62176177"],"award-info":[{"award-number":["62176177"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["YDZJSX20231A017"],"award-info":[{"award-number":["YDZJSX20231A017"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["2023M733669"],"award-info":[{"award-number":["2023M733669"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["JCYJ20230807140719040"],"award-info":[{"award-number":["JCYJ20230807140719040"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["202303021221034"],"award-info":[{"award-number":["202303021221034"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["20210302124550"],"award-info":[{"award-number":["20210302124550"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["202103021223035"],"award-info":[{"award-number":["202103021223035"]}]},{"name":"Shanxi Province Free Exploration Basic Research Project","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]},{"name":"China Postdoctoral Science Foundation","award":["62376184"],"award-info":[{"award-number":["62376184"]}]},{"name":"China Postdoctoral Science Foundation","award":["62303445"],"award-info":[{"award-number":["62303445"]}]},{"name":"China Postdoctoral Science Foundation","award":["62206196"],"award-info":[{"award-number":["62206196"]}]},{"name":"China Postdoctoral Science Foundation","award":["62176177"],"award-info":[{"award-number":["62176177"]}]},{"name":"China Postdoctoral Science Foundation","award":["YDZJSX20231A017"],"award-info":[{"award-number":["YDZJSX20231A017"]}]},{"name":"China Postdoctoral Science Foundation","award":["2023M733669"],"award-info":[{"award-number":["2023M733669"]}]},{"name":"China Postdoctoral Science Foundation","award":["JCYJ20230807140719040"],"award-info":[{"award-number":["JCYJ20230807140719040"]}]},{"name":"China Postdoctoral Science Foundation","award":["202303021221034"],"award-info":[{"award-number":["202303021221034"]}]},{"name":"China Postdoctoral Science Foundation","award":["20210302124550"],"award-info":[{"award-number":["20210302124550"]}]},{"name":"China Postdoctoral Science Foundation","award":["202103021223035"],"award-info":[{"award-number":["202103021223035"]}]},{"name":"China Postdoctoral Science Foundation","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]},{"name":"Shenzhen Science and Technology Program","award":["62376184"],"award-info":[{"award-number":["62376184"]}]},{"name":"Shenzhen Science and Technology Program","award":["62303445"],"award-info":[{"award-number":["62303445"]}]},{"name":"Shenzhen Science and Technology Program","award":["62206196"],"award-info":[{"award-number":["62206196"]}]},{"name":"Shenzhen Science and Technology Program","award":["62176177"],"award-info":[{"award-number":["62176177"]}]},{"name":"Shenzhen Science and Technology Program","award":["YDZJSX20231A017"],"award-info":[{"award-number":["YDZJSX20231A017"]}]},{"name":"Shenzhen Science and Technology Program","award":["2023M733669"],"award-info":[{"award-number":["2023M733669"]}]},{"name":"Shenzhen Science and Technology Program","award":["JCYJ20230807140719040"],"award-info":[{"award-number":["JCYJ20230807140719040"]}]},{"name":"Shenzhen Science and Technology Program","award":["202303021221034"],"award-info":[{"award-number":["202303021221034"]}]},{"name":"Shenzhen Science and Technology Program","award":["20210302124550"],"award-info":[{"award-number":["20210302124550"]}]},{"name":"Shenzhen Science and Technology Program","award":["202103021223035"],"award-info":[{"award-number":["202103021223035"]}]},{"name":"Shenzhen Science and Technology Program","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["62376184"],"award-info":[{"award-number":["62376184"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["62303445"],"award-info":[{"award-number":["62303445"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["62206196"],"award-info":[{"award-number":["62206196"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["62176177"],"award-info":[{"award-number":["62176177"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["YDZJSX20231A017"],"award-info":[{"award-number":["YDZJSX20231A017"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["2023M733669"],"award-info":[{"award-number":["2023M733669"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["JCYJ20230807140719040"],"award-info":[{"award-number":["JCYJ20230807140719040"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["202303021221034"],"award-info":[{"award-number":["202303021221034"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["20210302124550"],"award-info":[{"award-number":["20210302124550"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["202103021223035"],"award-info":[{"award-number":["202103021223035"]}]},{"name":"Fundamental Research Program of Shanxi Province","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["62376184"],"award-info":[{"award-number":["62376184"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["62303445"],"award-info":[{"award-number":["62303445"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["62206196"],"award-info":[{"award-number":["62206196"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["62176177"],"award-info":[{"award-number":["62176177"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["YDZJSX20231A017"],"award-info":[{"award-number":["YDZJSX20231A017"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["2023M733669"],"award-info":[{"award-number":["2023M733669"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["JCYJ20230807140719040"],"award-info":[{"award-number":["JCYJ20230807140719040"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["202303021221034"],"award-info":[{"award-number":["202303021221034"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["20210302124550"],"award-info":[{"award-number":["20210302124550"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["202103021223035"],"award-info":[{"award-number":["202103021223035"]}]},{"name":"Scientific and Technological Achievement Transformation Program of Shanxi Province","award":["202304021301035"],"award-info":[{"award-number":["202304021301035"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multivariate entropy algorithms have proven effective in the complexity dynamic analysis of electroencephalography (EEG) signals, with researchers commonly configuring the variables as multi-channel time series. However, the complex quantification of brain dynamics from a multi-frequency perspective has not been extensively explored, despite existing evidence suggesting interactions among brain rhythms at different frequencies. In this study, we proposed a novel algorithm, termed multi-frequency entropy (mFreEn), enhancing the capabilities of existing multivariate entropy algorithms and facilitating the complexity study of interactions among brain rhythms of different frequency bands. Firstly, utilizing simulated data, we evaluated the mFreEn\u2019s sensitivity to various noise signals, frequencies, and amplitudes, investigated the effects of parameters such as the embedding dimension and data length, and analyzed its anti-noise performance. The results indicated that mFreEn demonstrated enhanced sensitivity and reduced parameter dependence compared to traditional multivariate entropy algorithms. Subsequently, the mFreEn algorithm was applied to the analysis of real EEG data. We found that mFreEn exhibited a good diagnostic performance in analyzing resting-state EEG data from various brain disorders. Furthermore, mFreEn showed a good classification performance for EEG activity induced by diverse task stimuli. Consequently, mFreEn provides another important perspective to quantify complex dynamics.<\/jats:p>","DOI":"10.3390\/e26090728","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T06:19:01Z","timestamp":1724739541000},"page":"728","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multi-Frequency Entropy for Quantifying Complex Dynamics and Its Application on EEG Data"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8136-6631","authenticated-orcid":false,"given":"Yan","family":"Niu","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9758-6954","authenticated-orcid":false,"given":"Jie","family":"Xiang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinglong","family":"Wu","sequence":"additional","affiliation":[{"name":"Research Center for Medical Artificial Intelligence, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6470-9452","authenticated-orcid":false,"given":"Jie","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7771-5360","authenticated-orcid":false,"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9538-6302","authenticated-orcid":false,"given":"Runan","family":"Ding","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingliang","family":"Dou","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Software, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohong","family":"Cui","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology (College of Data Science), Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengni","family":"Zhou","sequence":"additional","affiliation":[{"name":"Research Center for Medical Artificial Intelligence, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ahamed, S.I., Rabbani, M., and Povinelli, R.J. (2023, January 2\u20138). A Comprehensive Survey on Detection of Non-linear Analysis Techniques for EEG Signal. Proceedings of the IEEE International Conference on Digital Health (IEEE ICDH) at the IEEE World Congress on Services (SERVICES), Chicago, IL, USA.","DOI":"10.1109\/ICDH60066.2023.00034"},{"key":"ref_2","first-page":"2309","article-title":"Analysis of EEG signals using nonlinear dynamics and chaos: A review","volume":"9","year":"2015","journal-title":"Appl. Math. Infom. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"125008","DOI":"10.1103\/PhysRevD.100.125008","article-title":"Entropy bounds and nonlinear electrodynamics","volume":"100","author":"Falciano","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"W\u0105torek, M., Tomczyk, W., Gaw\u0142owska, M., Golonka-Afek, N., \u017byrkowska, A., Marona, M., Wnuk, M., S\u0142owik, A., Ochab, J.K., and Fafrowicz, M. (2024). Multifractal organization of EEG signals in multiple sclerosis. Biomed. Signal Process., 91.","DOI":"10.1016\/j.bspc.2023.105916"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ji, G. (2023). Feature extraction method of ship-radiated noise based on dispersion entropy: A review. Front. Phys., 11.","DOI":"10.3389\/fphy.2023.1146493"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"71905","DOI":"10.1109\/ACCESS.2023.3294473","article-title":"Application of Entropy for Automated Detection of Neurological Disorders With Electroencephalogram Signals: A Review of the Last Decade (2012\u20132022)","volume":"11","author":"Jui","year":"2023","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.chaos.2015.09.002","article-title":"Complexity testing techniques for time series data: A comprehensive literature review","volume":"81","author":"Tang","year":"2015","journal-title":"Chaos Solitons Fractals"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"051001","DOI":"10.1088\/1741-2552\/acf8fa","article-title":"Entropy and fractal analysis of brain-related neurophysiological signals in Alzheimer\u2019s and Parkinson\u2019s disease","volume":"20","author":"Averna","year":"2023","journal-title":"J. Neural Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Keshmiri, S. (2020). Entropy and the Brain: An Overview. Entropy, 22.","DOI":"10.3390\/e22090917"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Rocha, P.L., Barros, A.K., Silva, W.S., Sousa, G.C., Sousa, P., and da Silva, A.M. (2020). Classification of the interictal state with hypsarrhythmia from Zika Virus Congenital Syndrome and of the ictal state from epilepsy in childhood without hypsarrhythmia in EEGs using entropy measures. Comput. Biol. Med., 126.","DOI":"10.1016\/j.compbiomed.2020.104014"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"102601","DOI":"10.1088\/1361-6633\/ace6bc","article-title":"Statistical models of complex brain networks: A maximum entropy approach","volume":"86","author":"Dichio","year":"2023","journal-title":"Rep. Prog. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol. Heart C"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.cmpb.2016.02.008","article-title":"Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation","volume":"128","author":"Azami","year":"2016","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.physa.2016.01.044","article-title":"Applications, Refined scale-dependent permutation entropy to analyze systems complexity","volume":"450","author":"Wu","year":"2016","journal-title":"Phys. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s11071-022-07847-z","article-title":"Composite multi-scale phase reverse permutation entropy and its application to fault diagnosis of rolling bearing","volume":"111","author":"Zheng","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"127506","DOI":"10.1016\/j.physa.2022.127506","article-title":"Fractional multiscale phase permutation entropy for quantifying the complexity of nonlinear time series","volume":"600","author":"Wan","year":"2022","journal-title":"Phys. A"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Bajic, D., and Japundzic-Zigon, N. (2022). On Quantization Errors in Approximate and Sample Entropy. Entropy, 24.","DOI":"10.3390\/e24010073"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Lizama, L.E.C., He, X., Kalincik, T., Galea, M.P., and Panisset, M.G. (2024). Sample Entropy Improves Assessment of Postural Control in Early-Stage Multiple Sclerosis. Sensors, 24.","DOI":"10.3390\/s24030872"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1186\/s12984-018-0465-9","article-title":"On the use of approximate entropy and sample entropy with centre of pressure time-series","volume":"15","author":"Montesinos","year":"2018","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1750054","DOI":"10.1142\/S012906571750054X","article-title":"Neural Correlates of Phrase Quadrature Perception in Harmonic Rhythm: An EEG Study Using a Brain-Computer Interface","volume":"28","author":"Latorre","year":"2018","journal-title":"Int. J. Neural Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.3390\/e14071186","article-title":"Multivariate Multi-Scale Permutation Entropy for Complexity Analysis of Alzheimer\u2019s Disease EEG","volume":"14","author":"Morabito","year":"2012","journal-title":"Entropy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"061918","DOI":"10.1103\/PhysRevE.84.061918","article-title":"Multivariate multiscale entropy: A tool for complexity analysis of multichannel data","volume":"84","author":"Ahmed","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.ymssp.2017.08.010","article-title":"An integrated method based on CEEMD-SampEn and the correlation analysis algorithm for the fault diagnosis of a gearbox under different working conditions","volume":"113","author":"Chen","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108271","DOI":"10.1016\/j.apacoust.2021.108271","article-title":"Multivariate hierarchical multiscale fluctuation dispersion entropy: Applications to fault diagnosis of rotating machinery","volume":"182","author":"Zhou","year":"2021","journal-title":"Appl. Acoust."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Xi, C., Yang, G., Liu, L., Jiang, H., and Chen, X. (2021). A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery. Entropy, 23.","DOI":"10.3390\/e23010128"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ma, D., He, S., and Sun, K. (2021). A modified multivariable complexity measure algorithm and its application for identifying mental arithmetic task. Entropy, 23.","DOI":"10.3390\/e23080931"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"046056","DOI":"10.1088\/1741-2552\/abd685","article-title":"Multiscale multivariate transfer entropy and application to functional corticocortical coupling","volume":"18","author":"Zhang","year":"2021","journal-title":"J. Neural Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.tics.2010.09.001","article-title":"The functional role of cross-frequency coupling","volume":"14","author":"Canolty","year":"2010","journal-title":"Trends Cogn. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.tics.2007.05.003","article-title":"Cross-frequency coupling between neuronal oscillations","volume":"11","author":"Jensen","year":"2007","journal-title":"Trends Cogn. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lin, A.J., Liu, K.K.L., Bartsch, R.P., and Ivanov, P.C. (2020). Dynamic network interactions among distinct brain rhythms as a hallmark of physiologic state and function. Commun. Biol., 3.","DOI":"10.1038\/s42003-020-0878-4"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"046064","DOI":"10.1088\/1741-2552\/abf773","article-title":"An automatic sleep disorder detection based on EEG cross-frequency coupling and random forest model","volume":"18","author":"Dimitriadis","year":"2021","journal-title":"J. Neural Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"186","DOI":"10.3389\/fnhum.2010.00186","article-title":"Shaping functional architecture by oscillatory alpha activity: Gating by inhibition","volume":"4","author":"Jensen","year":"2010","journal-title":"Front. Hum. Neurosci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Chen, B., Ciria, L.F., Hu, C., and Ivanov, P.C. (2022). Ensemble of coupling forms and networks among brain rhythms as function of states and cognition. Commun. Biol., 5.","DOI":"10.1038\/s42003-022-03017-4"},{"key":"ref_35","first-page":"320","article-title":"Neural Cross-Frequency Coupling Functions in Sleep","volume":"52","author":"Manasova","year":"2023","journal-title":"Neuroscience"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s11571-016-9418-9","article-title":"Multivariate multi-scale weighted permutation entropy analysis of EEG complexity for Alzheimer\u2019s disease","volume":"11","author":"Deng","year":"2017","journal-title":"Cogn. Neurodynamics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1177\/14759217231195275","article-title":"Multivariate variational mode decomposition and generalized composite multiscale permutation entropy for multichannel fault diagnosis of hoisting machinery system","volume":"23","author":"Li","year":"2024","journal-title":"Struct. Health Monit."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2449","DOI":"10.1007\/s11071-019-04933-7","article-title":"Multivariate multiscale complexity-entropy causality plane analysis for complex time series","volume":"96","author":"Mao","year":"2019","journal-title":"Nonlinear Dynam."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Azami, H., Smith, K., Fernandez, A., and Escudero, J. (2015, January 25\u201329). Evaluation of resting-state magnetoencephalogram complexity in Alzheimer\u2019s disease with multivariate multiscale permutation and sample entropies. Proceedings of the 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Milan, Italy.","DOI":"10.1109\/EMBC.2015.7320107"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Xiao, H., Chanwimalueang, T., and Mandic, D.P. (2022). Multivariate multiscale cosine similarity entropy and its application to examine circularity properties in division algebras. Entropy, 24.","DOI":"10.3390\/e24091287"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zheng, J., Tu, D., Pan, H., Hu, X., Liu, T., and Liu, Q. (2017). A refined composite multivariate multiscale fuzzy entropy and Laplacian score-based fault diagnosis method for rolling bearings. Entropy, 19.","DOI":"10.3390\/e19110585"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.physa.2018.09.165","article-title":"Multivariate multiscale fractional order weighted permutation entropy of nonlinear time series","volume":"515","author":"Chen","year":"2019","journal-title":"Phys. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"124485","DOI":"10.1016\/j.physa.2020.124485","article-title":"Multiscale complexity analysis on airport air traffic flow volume time series","volume":"548","author":"Liu","year":"2020","journal-title":"Phys. A"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Liu, J., Lu, H.B., Zhang, X.R., Li, X.L., Wang, L., Yin, S.M., and Cui, D. (2023). Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?. Entropy, 25.","DOI":"10.3390\/e25030396"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.parkreldis.2020.08.001","article-title":"Linear predictive coding distinguishes spectral EEG features of Parkinson\u2019s disease","volume":"79","author":"Anjum","year":"2020","journal-title":"Parkinsonism Relat. Disord."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3785","DOI":"10.1109\/TFUZZ.2021.3128957","article-title":"Fuzzy dispersion entropy: A nonlinear measure for signal analysis","volume":"30","author":"Rostaghi","year":"2021","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"114436","DOI":"10.1016\/j.chaos.2023.114436","article-title":"Optimized multivariate multiscale slope entropy for nonlinear dynamic analysis of mechanical signals","volume":"179","author":"Li","year":"2024","journal-title":"Chaos Soliton Fract."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"111190","DOI":"10.1016\/j.measurement.2022.111190","article-title":"Rolling mill bearings fault diagnosis based on improved multivariate variational mode decomposition and multivariate composite multiscale weighted permutation entropy","volume":"195","author":"Zhao","year":"2022","journal-title":"Measurement"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"e744","DOI":"10.7717\/peerj-cs.744","article-title":"Prediction of epileptic seizures based on multivariate multiscale modified-distribution entropy","volume":"7","author":"Aung","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1016\/j.bspc.2018.08.004","article-title":"Multivariate improved weighted multiscale permutation entropy and its application on EEG data","volume":"52","author":"Jomaa","year":"2019","journal-title":"Biomed. Signal Proces."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Azami, H., Fern\u00e1ndez, A., and Escudero, J. (2019). Multivariate multiscale dispersion entropy of biomedical times series. Entropy, 21.","DOI":"10.3390\/e21090913"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"051112","DOI":"10.1103\/PhysRevE.83.051112","article-title":"Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique","volume":"83","author":"Faes","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.neucom.2013.01.059","article-title":"Non uniform Embedding based on Relevance Analysis with reduced computational complexity: Application to the detection of pathologies from biosignal recordings","volume":"132","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.compbiomed.2011.02.007","article-title":"Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series","volume":"42","author":"Faes","year":"2012","journal-title":"Comput. Biol. Med."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3109","DOI":"10.1109\/TIE.2021.3063979","article-title":"Variational embedding multiscale diversity entropy for fault diagnosis of large-scale machinery","volume":"69","author":"Wang","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Porta, A., Faes, L., Nollo, G., Bari, V., Marchi, A., De Maria, B., Takahashi, A.C., and Catai, A.M. (2015). Conditional self-entropy and conditional joint transfer entropy in heart period variability during graded postural challenge. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0132851"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Xiao, H., and Mandic, D.P. (2021). Variational embedding multiscale sample entropy: A tool for complexity analysis of multichannel systems. Entropy, 24.","DOI":"10.3390\/e24010026"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"063125","DOI":"10.1063\/5.0150205","article-title":"Improved multivariate multiscale sample entropy and its application in multi-channel data","volume":"331","author":"Li","year":"2023","journal-title":"Chaos"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Porta, A., Faes, L., Bari, V., Marchi, A., Bassani, T., Nollo, G., Perseguini, N.M., Milan, J., Minatel, V., and Borghi-Silva, A. (2014). Effect of age on complexity and causality of the cardiovascular control: Comparison between model-based and model-free approaches. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0089463"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1038\/s41593-022-01081-x","article-title":"Individual variability in brain representations of pain","volume":"25","author":"Kohoutova","year":"2022","journal-title":"Nat. Neurosci."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"3468","DOI":"10.1002\/hbm.25013","article-title":"Towards a brain-based predictome of mental illness","volume":"41","author":"Rashid","year":"2020","journal-title":"Hum. Brain Mapp."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1109\/TCSS.2022.3154442","article-title":"Ensemble Hybrid Learning Methods for Automated Depression Detection","volume":"10","author":"Ansari","year":"2023","journal-title":"IEEE Trans. Comput. Soc. Syst."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"5537","DOI":"10.1523\/JNEUROSCI.0135-23.2023","article-title":"Visual Information Is Predictively Encoded in Occipital Alpha\/Low-Beta Oscillations","volume":"43","author":"Turner","year":"2023","journal-title":"J. Neurosci."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/j.neuroimage.2016.12.074","article-title":"Semantic attributes are encoded in human electrocorticographic signals during visual object recognition","volume":"148","author":"Rupp","year":"2017","journal-title":"Neuroimage"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1016\/j.physa.2016.06.012","article-title":"Multivariate permutation entropy and its application for complexity analysis of chaotic systems","volume":"461","author":"He","year":"2016","journal-title":"Phys. A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/9\/728\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:43:27Z","timestamp":1760111007000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/9\/728"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,27]]},"references-count":65,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["e26090728"],"URL":"https:\/\/doi.org\/10.3390\/e26090728","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,27]]}}}