{"id":"https://openalex.org/W2897035928","doi":"https://doi.org/10.3390/e20090665","title":"Assessing Time Series Reversibility through Permutation Patterns","display_name":"Assessing Time Series Reversibility through Permutation Patterns","publication_year":2018,"publication_date":"2018-09-03","ids":{"openalex":"https://openalex.org/W2897035928","doi":"https://doi.org/10.3390/e20090665","mag":"2897035928","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265754","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/7513188"},"language":"en","primary_location":{"id":"doi:10.3390/e20090665","doi":"https://doi.org/10.3390/e20090665","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090665","pdf_url":"https://www.mdpi.com/1099-4300/20/9/665/pdf?version=1536230091","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/9/665/pdf?version=1536230091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031146559","display_name":"Massimiliano Zanin","orcid":"https://orcid.org/0000-0002-5839-0393","observed_orcids":["https://orcid.org/0000-0002-5839-0393"]},"institutions":[{"id":"https://openalex.org/I83558840","display_name":"Universidade Nova de Lisboa","ror":"https://ror.org/02xankh89","country_code":"PT","type":"education","lineage":["https://openalex.org/I83558840"]},{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES","PT"],"is_corresponding":true,"raw_author_name":"Massimiliano Zanin","raw_affiliation_strings":["Center for Biomedical Technology , Universidad Polit\u00e9cnica de Madrid , 28223 Pozuelo de Alarc\u00f3n , Madrid , Spain","Department of Computer Science, Faculty of Science and Technology, Universidade Nova de Lisboa, 2829-516 Lisboa, Portugal"],"raw_orcid":"https://orcid.org/0000-0002-5839-0393","affiliations":[{"raw_affiliation_string":"Center for Biomedical Technology , Universidad Polit\u00e9cnica de Madrid , 28223 Pozuelo de Alarc\u00f3n , Madrid , Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Department of Computer Science, Faculty of Science and Technology, Universidade Nova de Lisboa, 2829-516 Lisboa, Portugal","institution_ids":["https://openalex.org/I83558840"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013323586","display_name":"Alejandro Rodr\u00edguez\u2010Gonz\u00e1lez","orcid":"https://orcid.org/0000-0001-8801-4762","observed_orcids":["https://orcid.org/0000-0001-8801-4762"]},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alejandro Rodr\u00edguez Gonz\u00e1lez","raw_affiliation_strings":["Center for Biomedical Technology , Universidad Polit\u00e9cnica de Madrid , 28223 Pozuelo de Alarc\u00f3n , Madrid , Spain","Center for Biomedical Technology, Universidad Polit\u00e9cnica de Madrid, 28223 Pozuelo de Alarc\u00f3n, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8801-4762","affiliations":[{"raw_affiliation_string":"Center for Biomedical Technology , Universidad Polit\u00e9cnica de Madrid , 28223 Pozuelo de Alarc\u00f3n , Madrid , Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Center for Biomedical Technology, Universidad Polit\u00e9cnica de Madrid, 28223 Pozuelo de Alarc\u00f3n, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078567927","display_name":"Ernestina Menasalvas","orcid":"https://orcid.org/0000-0002-5615-6798","observed_orcids":["https://orcid.org/0000-0002-5615-6798"]},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ernestina Menasalvas Ruiz","raw_affiliation_strings":["Center for Biomedical Technology , Universidad Polit\u00e9cnica de Madrid , 28223 Pozuelo de Alarc\u00f3n , Madrid , Spain","Center for Biomedical Technology, Universidad Polit\u00e9cnica de Madrid, 28223 Pozuelo de Alarc\u00f3n, 28040 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Biomedical Technology , Universidad Polit\u00e9cnica de Madrid , 28223 Pozuelo de Alarc\u00f3n , Madrid , Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Center for Biomedical Technology, Universidad Polit\u00e9cnica de Madrid, 28223 Pozuelo de Alarc\u00f3n, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072967282","display_name":"David Papo","orcid":"https://orcid.org/0000-0003-1889-2791","observed_orcids":["https://orcid.org/0000-0003-1889-2791"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2279609970","display_name":"Universit\u00e9 de Lille","ror":"https://ror.org/02kzqn938","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970"]},{"id":"https://openalex.org/I4210166223","display_name":"Sciences Cognitives et Sciences Affectives","ror":"https://ror.org/05rqwc876","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210150854","https://openalex.org/I4210166223"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"David Papo","raw_affiliation_strings":["University of Lille , 59800 Villeneuve d'Ascq , France","SCALab UMR CNRS 9193, University of Lille, 59800 Villeneuve d'Ascq, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Lille , 59800 Villeneuve d'Ascq , France","institution_ids":["https://openalex.org/I2279609970"]},{"raw_affiliation_string":"SCALab UMR CNRS 9193, University of Lille, 59800 Villeneuve d'Ascq, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2279609970","https://openalex.org/I4210166223"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5031146559"],"corresponding_institution_ids":["https://openalex.org/I83558840","https://openalex.org/I88060688"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":8.2153,"has_fulltext":true,"cited_by_count":59,"citation_normalized_percentile":{"value":0.97330103,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"9","first_page":"665","last_page":"665"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/time-irreversibility","display_name":"time irreversibility","score":0.9959999918937683},{"id":"https://openalex.org/keywords/time-reversal-symmetry","display_name":"time-reversal symmetry","score":0.8109999895095825},{"id":"https://openalex.org/keywords/permutation-entropy","display_name":"permutation entropy","score":0.9829999804496765},{"id":"https://openalex.org/keywords/permutation-patterns","display_name":"permutation patterns","score":0.9589999914169312},{"id":"https://openalex.org/keywords/financial-time-series","display_name":"financial time series","score":0.9129999876022339},{"id":"https://openalex.org/keywords/stock-market","display_name":"stock market","score":0.6029999852180481},{"id":"https://openalex.org/keywords/stock-market-indices","display_name":"stock market indices","score":0.9049999713897705},{"id":"https://openalex.org/keywords/visibility-graph","display_name":"visibility graph","score":0.7369999885559082},{"id":"https://openalex.org/keywords/non-equilibrium-systems","display_name":"nonequilibrium systems","score":0.7390000224113464},{"id":"https://openalex.org/keywords/predictability","display_name":"predictability","score":0.753000020980835}],"concepts":[{"id":"https://openalex.org/C197640229","wikidata":"https://www.wikidata.org/wiki/Q2534066","display_name":"Predictability","level":2,"score":0.7746321558952332},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6497014760971069},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5409494638442993},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5103961825370789},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.5023903846740723},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4499000310897827},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4417419135570526},{"id":"https://openalex.org/C173362246","wikidata":"https://www.wikidata.org/wiki/Q8216024","display_name":"Visibility graph","level":3,"score":0.41059979796409607},{"id":"https://openalex.org/C123403432","wikidata":"https://www.wikidata.org/wiki/Q654068","display_name":"Visibility","level":2,"score":0.4100014567375183},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4025292694568634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39613091945648193},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3923186659812927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36738288402557373},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3226497769355774},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20980516076087952},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.11568158864974976},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.09954506158828735},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e20090665","doi":"https://doi.org/10.3390/e20090665","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090665","pdf_url":"https://www.mdpi.com/1099-4300/20/9/665/pdf?version=1536230091","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"doi:10.20944/preprints201808.0083.v1","doi":"https://doi.org/10.20944/preprints201808.0083.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints201808.0083.v1","pdf_url":"https://www.preprints.org/manuscript/201808.0083/v1/download","source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:pubmedcentral.nih.gov:7513188","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7513188","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmid:33265754","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265754","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:381a47e230124507a68f2aa7bde414cb","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/381a47e230124507a68f2aa7bde414cb","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 20, Iss 9, p 665 (2018)","raw_type":"article"},{"id":"pmh:oai:sfera.unife.it:11392/2483592","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11392/2483592","pdf_url":null,"source":{"id":"https://openalex.org/S4306400369","display_name":"Institutional Research Information System University of Ferrara (University of Ferrara)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I201324441","host_organization_name":"University of Ferrara","host_organization_lineage":["https://openalex.org/I201324441"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/e20090665","doi":"https://doi.org/10.3390/e20090665","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090665","pdf_url":"https://www.mdpi.com/1099-4300/20/9/665/pdf?version=1536230091","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2897035928.pdf","grobid_xml":"https://content.openalex.org/works/W2897035928.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W45781964","https://openalex.org/W615883550","https://openalex.org/W755194005","https://openalex.org/W1539024229","https://openalex.org/W1590967632","https://openalex.org/W1965555277","https://openalex.org/W1967210573","https://openalex.org/W1967851828","https://openalex.org/W1978983095","https://openalex.org/W1984433477","https://openalex.org/W1987027200","https://openalex.org/W1999996900","https://openalex.org/W2000839378","https://openalex.org/W2003168004","https://openalex.org/W2012471970","https://openalex.org/W2014683958","https://openalex.org/W2029173860","https://openalex.org/W2034543182","https://openalex.org/W2034628756","https://openalex.org/W2041804068","https://openalex.org/W2051981079","https://openalex.org/W2055538060","https://openalex.org/W2069523214","https://openalex.org/W2074713002","https://openalex.org/W2077230322","https://openalex.org/W2080303295","https://openalex.org/W2080744992","https://openalex.org/W2086909453","https://openalex.org/W2093433505","https://openalex.org/W2104198280","https://openalex.org/W2105767494","https://openalex.org/W2114199009","https://openalex.org/W2131773668","https://openalex.org/W2147884875","https://openalex.org/W2152229836","https://openalex.org/W2152254020","https://openalex.org/W2156402547","https://openalex.org/W2157881370","https://openalex.org/W2157895285","https://openalex.org/W2162704317","https://openalex.org/W2164727176","https://openalex.org/W2213481886","https://openalex.org/W2280024434","https://openalex.org/W2318640187","https://openalex.org/W2471663382","https://openalex.org/W2560504456","https://openalex.org/W2620176693","https://openalex.org/W2963225319","https://openalex.org/W3124635921","https://openalex.org/W4232856026","https://openalex.org/W4300567850"],"related_works":["https://openalex.org/W3194192827","https://openalex.org/W3211966607","https://openalex.org/W4416550162","https://openalex.org/W3213653849","https://openalex.org/W2963225319","https://openalex.org/W4416128683","https://openalex.org/W2791424562","https://openalex.org/W6959945422","https://openalex.org/W2950215618","https://openalex.org/W2883133840"],"abstract_inverted_index":{"Time":[0,28],"irreversibility,":[1],"i.e.,":[2],"the":[3,8,43,46,49,53,105,123,143],"lack":[4],"of":[5,7,11,21,26,45,107,127,145],"invariance":[6],"statistical":[9,35,93],"properties":[10,38],"a":[12,18,78,117,133],"system":[13,47],"under":[14],"time":[15,50,61,64,109],"reversal,":[16],"is":[17,31,40,86],"fundamental":[19],"property":[20],"all":[22],"systems":[23],"operating":[24],"out":[25],"equilibrium.":[27],"reversal":[29],"symmetry":[30],"associated":[32],"with":[33,130],"important":[34],"and":[36,39,95,114,141,152],"physical":[37],"related":[41],"to":[42,59,104,132],"predictability":[44],"generating":[48],"series.":[51],"Over":[52],"past":[54],"fifteen":[55],"years,":[56],"various":[57],"methods":[58],"quantify":[60],"irreversibility":[62,119],"in":[63],"series":[65],"have":[66],"been":[67],"proposed,":[68],"but":[69],"these":[70],"can":[71],"be":[72],"computationally":[73],"expensive.":[74],"Here,":[75],"we":[76],"propose":[77],"new":[79],"method,":[80],"based":[81,137],"on":[82,138],"permutation":[83],"entropy,":[84],"which":[85],"essentially":[87],"parameter-free,":[88],"temporally":[89],"local,":[90],"yields":[91],"straightforward":[92],"tests,":[94],"has":[96],"fast":[97],"convergence":[98],"properties.":[99],"We":[100,121],"apply":[101],"this":[102],"method":[103,129,136],"study":[106],"financial":[108,149],"series,":[110],"showing":[111],"that":[112],"stocks":[113],"indices":[115],"present":[116],"rich":[118],"dynamics.":[120],"illustrate":[122],"comparative":[124],"methodological":[125],"advantages":[126],"our":[128,146],"respect":[131],"recently":[134],"proposed":[135],"visibility":[139],"graphs,":[140],"discuss":[142],"implications":[144],"results":[147],"for":[148],"data":[150],"analysis":[151],"interpretation.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2018-10-26T00:00:00"}