{"id":"https://openalex.org/W1495850155","doi":"https://doi.org/10.3390/e17064413","title":"Detecting Chronotaxic Systems from Single-Variable Time Series with Separable Amplitude and Phase","display_name":"Detecting Chronotaxic Systems from Single-Variable Time Series with Separable Amplitude and Phase","publication_year":2015,"publication_date":"2015-06-23","ids":{"openalex":"https://openalex.org/W1495850155","doi":"https://doi.org/10.3390/e17064413","mag":"1495850155"},"language":"en","primary_location":{"id":"doi:10.3390/e17064413","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17064413","pdf_url":"https://www.mdpi.com/1099-4300/17/6/4413/pdf?version=1435048796","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,"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"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/17/6/4413/pdf?version=1435048796","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042498583","display_name":"Gemma Lancaster","orcid":null},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Gemma Lancaster","raw_affiliation_strings":["Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK","institution_ids":["https://openalex.org/I67415387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036395430","display_name":"Philip T. Clemson","orcid":"https://orcid.org/0000-0003-4935-6035"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Philip Clemson","raw_affiliation_strings":["Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK","institution_ids":["https://openalex.org/I67415387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034374556","display_name":"Yevhen F. Suprunenko","orcid":"https://orcid.org/0000-0001-5927-7571"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]},{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yevhen Suprunenko","raw_affiliation_strings":["Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK","Institute of Integrative Biology, University of Liverpool, L69 7ZB, Liverpool, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK","institution_ids":["https://openalex.org/I67415387"]},{"raw_affiliation_string":"Institute of Integrative Biology, University of Liverpool, L69 7ZB, Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065665623","display_name":"Tomislav Stankovski","orcid":"https://orcid.org/0000-0003-2974-2836"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tomislav Stankovski","raw_affiliation_strings":["Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK","institution_ids":["https://openalex.org/I67415387"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022001835","display_name":"Aneta Stefanovska","orcid":"https://orcid.org/0000-0001-6952-8370"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Aneta Stefanovska","raw_affiliation_strings":["Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK","institution_ids":["https://openalex.org/I67415387"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5022001835"],"corresponding_institution_ids":["https://openalex.org/I67415387"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6661,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67805657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"6","first_page":"4413","last_page":"4438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9937000274658203,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6549285650253296},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5565664768218994},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5458176732063293},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.5045329332351685},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.46082767844200134},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.45155322551727295},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4343600869178772},{"id":"https://openalex.org/keywords/system-dynamics","display_name":"System dynamics","score":0.43399107456207275},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.414695143699646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39394843578338623},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33912599086761475},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30919235944747925},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.24306347966194153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22291332483291626},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12379175424575806}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6549285650253296},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5565664768218994},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5458176732063293},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.5045329332351685},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.46082767844200134},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.45155322551727295},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4343600869178772},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.43399107456207275},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.414695143699646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39394843578338623},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33912599086761475},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30919235944747925},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.24306347966194153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22291332483291626},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12379175424575806},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e17064413","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17064413","pdf_url":"https://www.mdpi.com/1099-4300/17/6/4413/pdf?version=1435048796","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,"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":"pmh:oai:eprints.lancs.ac.uk:129763","is_oa":true,"landing_page_url":null,"pdf_url":"https://eprints.lancs.ac.uk/id/eprint/129763/1/entropy2.pdf","source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:doaj.org/article:7760bcc1aac1476dbdd9e09894b4ad61","is_oa":true,"landing_page_url":"https://doaj.org/article/7760bcc1aac1476dbdd9e09894b4ad61","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,"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 17, Iss 6, Pp 4413-4438 (2015)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/17/6/4413/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e17064413","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e17064413","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17064413","pdf_url":"https://www.mdpi.com/1099-4300/17/6/4413/pdf?version=1435048796","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,"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":[],"awards":[{"id":"https://openalex.org/G3953951772","display_name":null,"funder_award_id":"EP/I00999X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1495850155.pdf","grobid_xml":"https://content.openalex.org/works/W1495850155.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W123426918","https://openalex.org/W1203142710","https://openalex.org/W1222544342","https://openalex.org/W1499683578","https://openalex.org/W1766888123","https://openalex.org/W1969187341","https://openalex.org/W1970126268","https://openalex.org/W1970847522","https://openalex.org/W1973520061","https://openalex.org/W1973676211","https://openalex.org/W1976804176","https://openalex.org/W1978389345","https://openalex.org/W1985088274","https://openalex.org/W1990509398","https://openalex.org/W1992709191","https://openalex.org/W1993005167","https://openalex.org/W2001849957","https://openalex.org/W2002996884","https://openalex.org/W2003411364","https://openalex.org/W2006371574","https://openalex.org/W2007218348","https://openalex.org/W2007919714","https://openalex.org/W2017821362","https://openalex.org/W2021722152","https://openalex.org/W2029365653","https://openalex.org/W2032859229","https://openalex.org/W2040603148","https://openalex.org/W2041531026","https://openalex.org/W2045823870","https://openalex.org/W2059561254","https://openalex.org/W2061564920","https://openalex.org/W2065096279","https://openalex.org/W2066188397","https://openalex.org/W2073893638","https://openalex.org/W2085409886","https://openalex.org/W2086946336","https://openalex.org/W2090218979","https://openalex.org/W2098330912","https://openalex.org/W2111259476","https://openalex.org/W2112575160","https://openalex.org/W2115810652","https://openalex.org/W2116966666","https://openalex.org/W2122057898","https://openalex.org/W2127535256","https://openalex.org/W2134164118","https://openalex.org/W2137958317","https://openalex.org/W2140552266","https://openalex.org/W2143351549","https://openalex.org/W2150177284","https://openalex.org/W2154123408","https://openalex.org/W2156944202","https://openalex.org/W2166328099","https://openalex.org/W2243427678","https://openalex.org/W2315544299","https://openalex.org/W2321552821","https://openalex.org/W2324462497","https://openalex.org/W2973818247","https://openalex.org/W4212886848","https://openalex.org/W4248877910","https://openalex.org/W6682747227"],"related_works":["https://openalex.org/W4321064619","https://openalex.org/W2009525028","https://openalex.org/W2053599029","https://openalex.org/W3011179836","https://openalex.org/W2962925412","https://openalex.org/W2023672523","https://openalex.org/W4246719751","https://openalex.org/W2483165346","https://openalex.org/W2055243143","https://openalex.org/W4297752497"],"abstract_inverted_index":{"The":[0,49],"recent":[1],"introduction":[2],"of":[3,30,40,51,57,61,66],"chronotaxic":[4,73],"systems":[5,12],"provides":[6],"the":[7,31,38,55,64,67,113],"means":[8],"to":[9,21,101],"describe":[10],"nonautonomous":[11],"with":[13],"stable":[14],"yet":[15],"time-varying":[16],"frequencies":[17],"which":[18,44],"are":[19,99],"resistant":[20],"continuous":[22],"external":[23],"perturbations.":[24],"This":[25],"approach":[26,53],"facilitates":[27],"realistic":[28],"characterization":[29],"oscillations":[32],"observed":[33],"in":[34,42,72,88],"living":[35],"systems,":[36],"including":[37,116],"observation":[39],"transitions":[41],"dynamics":[43,68,90],"were":[45],"not":[46],"considered":[47],"previously.":[48],"novelty":[50],"this":[52],"necessitated":[54],"development":[56],"a":[58,93],"new":[59],"set":[60],"methods":[62],"for":[63],"inference":[65,80],"and":[69,81,104,119,125],"interactions":[70],"present":[71],"systems.":[74],"These":[75],"methods,":[76,115],"based":[77],"on":[78,122],"Bayesian":[79],"detrended":[82],"fluctuation":[83],"analysis,":[84],"can":[85],"identify":[86],"chronotaxicity":[87],"phase":[89],"extracted":[91],"from":[92],"single":[94],"time":[95],"series.":[96],"Here,":[97],"they":[98],"applied":[100],"numerical":[102],"examples":[103],"real":[105],"experimental":[106],"electroencephalogram":[107],"(EEG)":[108],"data.":[109],"We":[110],"also":[111],"review":[112],"current":[114],"their":[117,123],"assumptions":[118],"limitations,":[120],"elaborate":[121],"implementation,":[124],"discuss":[126],"future":[127],"perspectives.":[128]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}