{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:16Z","timestamp":1760143636353,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We propose a new tool for estimating the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to describe the signal as efficiently as prior proposed parameters, such as permutation entropy (PE) or modified permutation entropy (mPE). Firstly, this method reduces the size of the sample that is necessary to estimate the parameter value, and secondly it enables the use of the Kullback\u2013Leibler divergence to estimate the \u201cdistance\u201d between the time series data and random signals.<\/jats:p>","DOI":"10.3390\/axioms13020130","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T03:18:38Z","timestamp":1708312718000},"page":"130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Entropy of Difference: A New Tool for Measuring Complexity"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3712-191X","authenticated-orcid":false,"given":"Pasquale","family":"Nardone","sequence":"first","affiliation":[{"name":"Physics Department, Universit\u00e9 Libre de Bruxelles, 50 av F. D. Roosevelt, 1050 Bruxelles, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giorgio","family":"Sonnino","sequence":"additional","affiliation":[{"name":"Physics Department, Universit\u00e9 Libre de Bruxelles, 50 av F. D. Roosevelt, 1050 Bruxelles, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,19]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"021906","DOI":"10.1103\/PhysRevE.85.021906","article-title":"Modified permutation-entropy analysis of heartbeat dynamics","volume":"85","author":"Bian","year":"2012","journal-title":"Phys. Rev. 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Permutation entropy improves fetal behavioural state classification based on heart rate analysis from biomagnetic recordings in near term fetuses. Med. Biol. Eng. Comput., 44.","DOI":"10.1007\/s11517-005-0015-z"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1093\/bja\/aen290","article-title":"Permutation entropy of the electroencephalogram: A measure of anaesthetic drug effect","volume":"101","author":"Olofsen","year":"2008","journal-title":"Br. J. Anaesth."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"061114","DOI":"10.1103\/PhysRevE.76.061114","article-title":"Extracting features of Gaussian self-similar stochastic processes via the Bandt\u2013Pompe approach","volume":"76","author":"Rosso","year":"2007","journal-title":"Phys. Rev. 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Available online: http:\/\/www.wessa.net\/."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/2\/130\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:02:02Z","timestamp":1760104922000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/2\/130"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,19]]},"references-count":14,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["axioms13020130"],"URL":"https:\/\/doi.org\/10.3390\/axioms13020130","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,2,19]]}}}