Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises
The complexity and the disorder of a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noise time series are quantified by entropy of entropy (EoE...
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/10/1127 |
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| author | Chang Francis Hsu Long Hsu Sien Chi |
| author_facet | Chang Francis Hsu Long Hsu Sien Chi |
| author_sort | Chang Francis Hsu |
| collection | DOAJ |
| description | The complexity and the disorder of a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> 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/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises of various values of <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> exhibits a distinct inverted U curve. For the 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises, we have shown that <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> decreases monotonically as AE increases, which indicates that <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is also a measure of disorder. Furthermore, a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises for <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 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 <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, while it is 0.73 when using spectral-analysis-based <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. |
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| institution | Directory Open Access Journal |
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| spelling | doaj.art-e5ae38188729456684b48604ff2f82062023-11-20T16:03:49ZengMDPI AGEntropy1099-43002020-10-012210112710.3390/e22101127Complexity and Disorder of 1/<i>f</i><sup>α</sup> NoisesChang Francis Hsu0Long Hsu1Sien Chi2Department of Electrophyics, National Chiao Tung University, Hsinchu 30010, TaiwanDepartment of Electrophyics, National Chiao Tung University, Hsinchu 30010, TaiwanDepartment of Photonics, National Chiao Tung University, Hsinchu 30010, TaiwanThe complexity and the disorder of a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> 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/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises of various values of <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> exhibits a distinct inverted U curve. For the 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises, we have shown that <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> decreases monotonically as AE increases, which indicates that <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is also a measure of disorder. Furthermore, a 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/<inline-formula><math display="inline"><semantics><msup><mi>f</mi><mi>α</mi></msup></semantics></math></inline-formula> noises for <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> = 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 <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, while it is 0.73 when using spectral-analysis-based <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>.https://www.mdpi.com/1099-4300/22/10/11271/<i>f<sup>α</sup></i> noisespower lawcomplexitydisorderinverted U curveheart rate variability |
| spellingShingle | Chang Francis Hsu Long Hsu Sien Chi Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises Entropy 1/<i>f<sup>α</sup></i> noises power law complexity disorder inverted U curve heart rate variability |
| title | Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises |
| title_full | Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises |
| title_fullStr | Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises |
| title_full_unstemmed | Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises |
| title_short | Complexity and Disorder of 1/<i>f</i><sup>α</sup> Noises |
| title_sort | complexity and disorder of 1 i f i sup α sup noises |
| topic | 1/<i>f<sup>α</sup></i> noises power law complexity disorder inverted U curve heart rate variability |
| url | https://www.mdpi.com/1099-4300/22/10/1127 |
| work_keys_str_mv | AT changfrancishsu complexityanddisorderof1ifisupasupnoises AT longhsu complexityanddisorderof1ifisupasupnoises AT sienchi complexityanddisorderof1ifisupasupnoises |