{"id":"https://openalex.org/W2023849895","doi":"https://doi.org/10.1137/12088183x","title":"Time-Scale Separation from Diffusion-Mapped Delay Coordinates","display_name":"Time-Scale Separation from Diffusion-Mapped Delay Coordinates","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2023849895","doi":"https://doi.org/10.1137/12088183x","mag":"2023849895"},"language":"en","primary_location":{"id":"doi:10.1137/12088183x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12088183x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008051410","display_name":"T. Berry","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Berry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024364678","display_name":"John R. Cressman","orcid":"https://orcid.org/0000-0003-3621-2075"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. R. Cressman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5097719324","display_name":"Z. Greguri\u0107-Feren\u010dek","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Z. Greguri\u0107-Feren\u010dek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029217710","display_name":"Timothy Sauer","orcid":"https://orcid.org/0000-0002-8501-8722"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Sauer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.0725,"has_fulltext":false,"cited_by_count":83,"citation_normalized_percentile":{"value":0.98727483,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"12","issue":"2","first_page":"618","last_page":"649"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9902999997138977,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9902999997138977,"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"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9804999828338623,"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":0.9771999716758728,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7079596519470215},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5969747304916382},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5948652625083923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5663715600967407},{"id":"https://openalex.org/keywords/spiral","display_name":"Spiral (railway)","score":0.5334762334823608},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5129794478416443},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5007398128509521},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.49995875358581543},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.48461756110191345},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46103954315185547},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42292121052742004},{"id":"https://openalex.org/keywords/diffusion-map","display_name":"Diffusion map","score":0.4131217300891876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2849483788013458},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.28411686420440674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22829961776733398},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21320515871047974},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15430903434753418},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.12863510847091675},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07995474338531494}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7079596519470215},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5969747304916382},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5948652625083923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5663715600967407},{"id":"https://openalex.org/C174128100","wikidata":"https://www.wikidata.org/wiki/Q846907","display_name":"Spiral (railway)","level":2,"score":0.5334762334823608},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5129794478416443},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5007398128509521},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.49995875358581543},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.48461756110191345},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46103954315185547},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42292121052742004},{"id":"https://openalex.org/C55128770","wikidata":"https://www.wikidata.org/wiki/Q5275440","display_name":"Diffusion map","level":4,"score":0.4131217300891876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2849483788013458},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.28411686420440674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22829961776733398},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21320515871047974},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15430903434753418},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.12863510847091675},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07995474338531494},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/12088183x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12088183x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1601723819","https://openalex.org/W1967771793","https://openalex.org/W1975964493","https://openalex.org/W1984032850","https://openalex.org/W1984391316","https://openalex.org/W1987236926","https://openalex.org/W1998727969","https://openalex.org/W2001141328","https://openalex.org/W2004741305","https://openalex.org/W2012825614","https://openalex.org/W2017147656","https://openalex.org/W2032227660","https://openalex.org/W2038419284","https://openalex.org/W2044359900","https://openalex.org/W2051057090","https://openalex.org/W2053509043","https://openalex.org/W2080991705","https://openalex.org/W2117684310","https://openalex.org/W2154882140","https://openalex.org/W2167364100","https://openalex.org/W2962936676","https://openalex.org/W4210770595","https://openalex.org/W4213367101","https://openalex.org/W4239340087"],"related_works":["https://openalex.org/W2362377451","https://openalex.org/W2081900870","https://openalex.org/W2071676784","https://openalex.org/W4292513318","https://openalex.org/W2287611352","https://openalex.org/W2013985456","https://openalex.org/W2951564084","https://openalex.org/W4302984940","https://openalex.org/W2776807270","https://openalex.org/W2392685819"],"abstract_inverted_index":{"It":[0],"has":[1],"long":[2],"been":[3],"known":[4],"that":[5,26],"the":[6,27,35,38,51,71],"method":[7],"of":[8,30,77,85,92],"time-delay":[9,31],"embedding":[10],"can":[11,47],"be":[12,48],"used":[13],"to":[14,55,58],"reconstruct":[15],"nonlinear":[16],"dynamics":[17,60],"from":[18,65],"time":[19,63],"series":[20],"data.":[21,68],"A":[22],"less-appreciated":[23],"fact":[24],"is":[25],"induced":[28],"geometry":[29],"coordinates":[32],"increasingly":[33],"biases":[34],"reconstruction":[36],"toward":[37],"stable":[39],"directions":[40],"as":[41],"delays":[42],"are":[43],"added.":[44],"This":[45],"bias":[46],"exploited,":[49],"using":[50],"diffusion":[52],"maps":[53],"approach":[54],"dimension":[56],"reduction,":[57],"extract":[59],"on":[61,73],"desired":[62],"scales":[64],"high-dimensional":[66],"observed":[67],"We":[69],"demonstrate":[70],"technique":[72],"a":[74,83,93],"wide":[75],"range":[76],"examples,":[78],"including":[79],"data":[80],"generated":[81],"by":[82],"model":[84],"meandering":[86],"spiral":[87],"waves":[88],"and":[89],"video":[90],"recordings":[91],"liquid-crystal":[94],"experiment.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
