{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T08:05:40Z","timestamp":1772784340243,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,4]],"date-time":"2020-10-04T00:00:00Z","timestamp":1601769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Ministry of Science and Technology of the Republic of China","award":["108-2221-E-009-055"],"award-info":[{"award-number":["108-2221-E-009-055"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The complexity and the disorder of a 1\/f\u03b1 noise time series are quantified by entropy of entropy (EoE) and average entropy (AE), respectively. The resulting EoE vs. AE plot of a series of 1\/f\u03b1 noises of various values of \u03b1 exhibits a distinct inverted U curve. For the 1\/f\u03b1 noises, we have shown that \u03b1 decreases monotonically as AE increases, which indicates that \u03b1 is also a measure of disorder. Furthermore, a 1\/f\u03b1 noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1\/f\u03b1 noises for \u03b1 around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at \u03b1 = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at \u03b1 = 0 is more disordered than AF RR interval series. These results, based on AE, are different from the previous ones based on spectral analysis. The testing macro-average F-score is 0.93 when classifying the RR interval series of three groups using AE-based \u03b1, while it is 0.73 when using spectral-analysis-based \u03b1.<\/jats:p>","DOI":"10.3390\/e22101127","type":"journal-article","created":{"date-parts":[[2020,10,5]],"date-time":"2020-10-05T08:35:57Z","timestamp":1601886957000},"page":"1127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Complexity and Disorder of 1\/f\u03b1 Noises"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9254-9364","authenticated-orcid":false,"given":"Chang Francis","family":"Hsu","sequence":"first","affiliation":[{"name":"Department of Electrophyics, National Chiao Tung University, Hsinchu 30010, Taiwan"}]},{"given":"Long","family":"Hsu","sequence":"additional","affiliation":[{"name":"Department of Electrophyics, National Chiao Tung University, Hsinchu 30010, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8674-1963","authenticated-orcid":false,"given":"Sien","family":"Chi","sequence":"additional","affiliation":[{"name":"Department of Photonics, National Chiao Tung University, Hsinchu 30010, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mitchell, M. 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