ExSEnt: Extrema-Segmented Entropy Analysis of Time Series

ExSEnt: Extrema-Segmented Entropy Analysis of Time Series | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article ExSEnt: Extrema-Segmented Entropy Analysis of Time Series Sara Kamali, Fabiano Baroni, Pablo Varona This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7906274/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 15 You are reading this latest preprint version Abstract We introduce Extrema-Segmented Entrop y (ExSEnt), a feature-decomposed framework for quantifying time-series complexity that separates temporal from amplitude contributions. The method partitions a signal into monotonic segments by detecting sign changes in the first-order increments. For each segment, it extracts the interval duration and the net amplitude change, generating two sequences that reflect timing and magnitude variability, respectively. Complexity is then quantified by computing sample entropy on durations and amplitudes, together with their joint entropy. This decomposition reveals whether overall irregularity is driven by duration, amplitude, or their coupling, providing a richer and more interpretable characterization than unidimensional metrics. We validate ExSEnt on canonical nonlinear dynamical systems (Logistic map, Rössler system, Rulkov map), demonstrating its ability to track complexity changes across control parameter sweeps and detect transitions between regular to chaotic regimes. Then, we illustrate the empirical utility of ExSEnt metrics to isolate feature-specific sources of complexity in real data (electromyography and ankle acceleration in Parkinson’s disease). Thus, ExSEnt complements existing entropy measures by attributing complexity to distinct signal features, improving interpretability and supporting applications in a broad range of domains, including physiology, finance, and geoscience. Time-Series Complexity Sample Entropy Extrema-Based Segmentation Event-Based Segmentation Information Theory Bifurcation Analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 06 Feb, 2026 Reviews received at journal 05 Dec, 2025 Reviews received at journal 29 Nov, 2025 Reviews received at journal 25 Nov, 2025 Reviews received at journal 15 Nov, 2025 Reviews received at journal 05 Nov, 2025 Reviewers agreed at journal 30 Oct, 2025 Reviewers agreed at journal 29 Oct, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers agreed at journal 27 Oct, 2025 Reviewers invited by journal 27 Oct, 2025 Editor assigned by journal 25 Oct, 2025 Submission checks completed at journal 25 Oct, 2025 First submitted to journal 20 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7906274","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":537233589,"identity":"775448a2-18f7-49d8-a573-e7ee0aa897ea","order_by":0,"name":"Sara Kamali","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYNCCA0DMztj4gEQtzIzNBqRqYWCTIEqxfPvZhx8YzthF8zczt1Xz1Gxj4Oc/gF+LwZl0YwmGG8m5Mw4ztt3mOXabQXJGAgEtDGkMEgwfmHMbwFrYbjMY3CDksP5nzD8YPtTnzgdqKeb5d5vB/jwBhzHcSAP6+sbh3A1ALcy8bUBbGAg57MYzNouEM8dzNx5mbJac23ebR+IGAS3y/WnMNz4cq86dd7z94Yc3327L8fcTchgIIBvLQ4T6UTAKRsEoGAWEAAAFW0Udl2l8VwAAAABJRU5ErkJggg==","orcid":"","institution":"Autonomous University of Madrid","correspondingAuthor":true,"prefix":"","firstName":"Sara","middleName":"","lastName":"Kamali","suffix":""},{"id":537233590,"identity":"5ecb8b62-001f-46b4-a1c8-7bd1880063c5","order_by":1,"name":"Fabiano Baroni","email":"","orcid":"","institution":"Autonomous University of Madrid","correspondingAuthor":false,"prefix":"","firstName":"Fabiano","middleName":"","lastName":"Baroni","suffix":""},{"id":537233591,"identity":"415170a5-35ea-4d8e-92c3-a752ff256a3b","order_by":2,"name":"Pablo Varona","email":"","orcid":"","institution":"Autonomous University of Madrid","correspondingAuthor":false,"prefix":"","firstName":"Pablo","middleName":"","lastName":"Varona","suffix":""}],"badges":[],"createdAt":"2025-10-20 13:38:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7906274/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7906274/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95178401,"identity":"51149e08-adbb-43a6-b3cc-a262061eae34","added_by":"auto","created_at":"2025-11-05 07:55:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":17908570,"visible":true,"origin":"","legend":"","description":"","filename":"KamalietalExSEnt.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7906274/v1/f6dfb596edd67a2f0712a267.pdf"},{"id":95178400,"identity":"0b818456-204b-412c-a6b3-96c07fe11421","added_by":"auto","created_at":"2025-11-05 07:55:06","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5821,"visible":true,"origin":"","legend":"","description":"","filename":"19d3bd53b915405d9cc15c7bd6ff301a.json","url":"https://assets-eu.researchsquare.com/files/rs-7906274/v1/2afff9e3bc1688b29466bf19.json"},{"id":95228608,"identity":"c3107d32-4754-4d87-b841-d9051c120848","added_by":"auto","created_at":"2025-11-05 16:34:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5377015,"visible":true,"origin":"","legend":"","description":"","filename":"KamalietalExSEnt.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7906274/v1_covered_a18ed766-8be0-4e6a-bfed-463eddc0fc2d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"ExSEnt: Extrema-Segmented Entropy Analysis of Time Series","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Time-Series Complexity, Sample Entropy, Extrema-Based Segmentation, Event-Based Segmentation, Information Theory, Bifurcation Analysis","lastPublishedDoi":"10.21203/rs.3.rs-7906274/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7906274/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe introduce \u003cem\u003eExtrema-Segmented Entrop\u003c/em\u003ey (ExSEnt),\u0026nbsp; 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Then, we illustrate the empirical utility of ExSEnt metrics to isolate feature-specific sources of complexity in real data (electromyography and ankle acceleration in Parkinson’s disease). 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