{"id":"https://openalex.org/W4221142935","doi":"https://doi.org/10.3390/e24070855","title":"Causal Inference in Time Series in Terms of R\u00e9nyi Transfer Entropy","display_name":"Causal Inference in Time Series in Terms of R\u00e9nyi Transfer Entropy","publication_year":2022,"publication_date":"2022-06-22","ids":{"openalex":"https://openalex.org/W4221142935","doi":"https://doi.org/10.3390/e24070855","pmid":"https://pubmed.ncbi.nlm.nih.gov/35885081"},"language":"en","primary_location":{"id":"doi:10.3390/e24070855","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24070855","pdf_url":"https://www.mdpi.com/1099-4300/24/7/855/pdf?version=1655899863","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":["arxiv","crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/7/855/pdf?version=1655899863","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055596286","display_name":"Petr Jizba","orcid":"https://orcid.org/0000-0002-7940-204X"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Petr Jizba","raw_affiliation_strings":["Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-7940-204X","affiliations":[{"raw_affiliation_string":"Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001521152","display_name":"Hynek Lavi\u010dka","orcid":"https://orcid.org/0000-0001-7868-106X"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Hynek Lavi\u010dka","raw_affiliation_strings":["Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0001-7868-106X","affiliations":[{"raw_affiliation_string":"Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057793728","display_name":"Zlata Tabachov\u00e1","orcid":"https://orcid.org/0000-0001-8423-8574"},"institutions":[{"id":"https://openalex.org/I4210112164","display_name":"Complexity Science Hub","ror":"https://ror.org/023dz9m50","country_code":"AT","type":"nonprofit","lineage":["https://openalex.org/I4210112164"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Zlata Tabachov\u00e1","raw_affiliation_strings":["Complexity Science Hub Vienna, Josefst\u00e4dter Stra\u00dfe 39, 1080 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0001-8423-8574","affiliations":[{"raw_affiliation_string":"Complexity Science Hub Vienna, Josefst\u00e4dter Stra\u00dfe 39, 1080 Vienna, Austria","institution_ids":["https://openalex.org/I4210112164"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055596286"],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02663319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"7","first_page":"855","last_page":"855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10241","display_name":"Functional Brain Connectivity Studies","score":0.2890999913215637,"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/T10241","display_name":"Functional Brain Connectivity Studies","score":0.2890999913215637,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.17810000479221344,"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"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.08540000021457672,"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/transfer-entropy","display_name":"Transfer entropy","score":0.8470357656478882},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5735501050949097},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5111847519874573},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4752207398414612},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.45661893486976624},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.45028549432754517},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.4314412474632263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42355093359947205},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4222796559333801},{"id":"https://openalex.org/keywords/causal-inference","display_name":"Causal inference","score":0.41534411907196045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.373239129781723},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.26481300592422485},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2587711811065674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21322527527809143},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12216410040855408}],"concepts":[{"id":"https://openalex.org/C182049051","wikidata":"https://www.wikidata.org/wiki/Q17147155","display_name":"Transfer entropy","level":3,"score":0.8470357656478882},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5735501050949097},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5111847519874573},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4752207398414612},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.45661893486976624},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.45028549432754517},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.4314412474632263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42355093359947205},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4222796559333801},{"id":"https://openalex.org/C158600405","wikidata":"https://www.wikidata.org/wiki/Q5054566","display_name":"Causal inference","level":2,"score":0.41534411907196045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.373239129781723},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.26481300592422485},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2587711811065674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21322527527809143},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12216410040855408},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e24070855","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24070855","pdf_url":"https://www.mdpi.com/1099-4300/24/7/855/pdf?version=1655899863","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":"pmid:35885081","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35885081","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,"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":null},{"id":"pmh:oai:arXiv.org:2203.11407","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2203.11407","pdf_url":"https://arxiv.org/pdf/2203.11407","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:doaj.org/article:23d69224993a4935969436e8a9c4a426","is_oa":true,"landing_page_url":"https://doaj.org/article/23d69224993a4935969436e8a9c4a426","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 24, Iss 7, p 855 (2022)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9321760","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9321760","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,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2203.11407","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2203.11407","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.3390/e24070855","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24070855","pdf_url":"https://www.mdpi.com/1099-4300/24/7/855/pdf?version=1655899863","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/G161741471","display_name":null,"funder_award_id":"18696","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G1970708878","display_name":null,"funder_award_id":"19-16066S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G5078538160","display_name":null,"funder_award_id":"W911NF-17-1-0108","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G5100297708","display_name":null,"funder_award_id":"W911NF-17-1-0108","funder_id":"https://openalex.org/F4320337655","funder_display_name":"Research, Development and Engineering Command"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320337655","display_name":"Research, Development and Engineering Command","ror":"https://ror.org/02rdkx920"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4221142935.pdf","grobid_xml":"https://content.openalex.org/works/W4221142935.grobid-xml"},"referenced_works_count":70,"referenced_works":["https://openalex.org/W186513846","https://openalex.org/W360650912","https://openalex.org/W1840880509","https://openalex.org/W1924249641","https://openalex.org/W1966523973","https://openalex.org/W1967008192","https://openalex.org/W1970442252","https://openalex.org/W1981050900","https://openalex.org/W1983874169","https://openalex.org/W1995875735","https://openalex.org/W2001885186","https://openalex.org/W2001935257","https://openalex.org/W2010821195","https://openalex.org/W2011301426","https://openalex.org/W2015042120","https://openalex.org/W2024383241","https://openalex.org/W2025371899","https://openalex.org/W2027607571","https://openalex.org/W2030308994","https://openalex.org/W2035245840","https://openalex.org/W2041782669","https://openalex.org/W2050552960","https://openalex.org/W2055309977","https://openalex.org/W2055963033","https://openalex.org/W2059889790","https://openalex.org/W2067348345","https://openalex.org/W2072718918","https://openalex.org/W2079656335","https://openalex.org/W2083278075","https://openalex.org/W2085009317","https://openalex.org/W2095595785","https://openalex.org/W2098746383","https://openalex.org/W2108771950","https://openalex.org/W2117554772","https://openalex.org/W2120253913","https://openalex.org/W2122158731","https://openalex.org/W2130535167","https://openalex.org/W2131729872","https://openalex.org/W2139364442","https://openalex.org/W2140120387","https://openalex.org/W2148516180","https://openalex.org/W2159402338","https://openalex.org/W2167038453","https://openalex.org/W2174534725","https://openalex.org/W2178225550","https://openalex.org/W2317895244","https://openalex.org/W2323767983","https://openalex.org/W2326655560","https://openalex.org/W2409978206","https://openalex.org/W2731426526","https://openalex.org/W2755154271","https://openalex.org/W2759333314","https://openalex.org/W2884343086","https://openalex.org/W2887427821","https://openalex.org/W2901930902","https://openalex.org/W2913075478","https://openalex.org/W3003257820","https://openalex.org/W3035965352","https://openalex.org/W3142744896","https://openalex.org/W3148918439","https://openalex.org/W6652048447","https://openalex.org/W6652138857","https://openalex.org/W6656063028","https://openalex.org/W6659838882","https://openalex.org/W6673222303","https://openalex.org/W6673765422","https://openalex.org/W6673770565","https://openalex.org/W6677514541","https://openalex.org/W6736836267","https://openalex.org/W6768503551"],"related_works":["https://openalex.org/W5114467","https://openalex.org/W1852553","https://openalex.org/W7527563","https://openalex.org/W6771511","https://openalex.org/W14682586","https://openalex.org/W9920088","https://openalex.org/W10228111","https://openalex.org/W14007254","https://openalex.org/W14771028","https://openalex.org/W916550"],"abstract_inverted_index":{"Uncovering":[0],"causal":[1,89,156],"interdependencies":[2,90],"from":[3,180,229],"observational":[4],"data":[5],"is":[6,69,82],"one":[7],"of":[8,12,28,51,75,97,108,201,212,221,239,253],"the":[9,26,41,76,95,164,210,219,237,250,254],"great":[10],"challenges":[11],"a":[13,83,145,199,213],"nonlinear":[14],"time":[15,47,92,177],"series":[16,48,178],"analysis.":[17],"In":[18,37,111,227],"this":[19,23,112],"paper,":[20],"we":[21,39,63,114,131,162,187,233],"discuss":[22],"topic":[24],"with":[25],"help":[27],"an":[29],"information-theoretic":[30,152],"concept":[31],"known":[32],"as":[33,102],"R\u00e9nyi's":[34,52,60,172,190,230],"information":[35,43,67,173],"measure.":[36],"particular,":[38],"tackle":[40],"directional":[42],"flow":[44,174],"between":[45,72,147,175,218],"bivariate":[46,176],"in":[49,80,91],"terms":[50],"transfer":[53,125,191,231],"entropy.":[54],"We":[55],"show":[56],"that":[57,68,117,189,216],"by":[58],"choosing":[59],"parameter":[61],"\u03b1,":[62],"can":[64],"appropriately":[65],"control":[66],"transferred":[70],"only":[71,194,244],"selected":[73],"parts":[74],"underlying":[77],"distributions.":[78],"This,":[79],"turn,":[81],"particularly":[84],"potent":[85],"tool":[86],"for":[87,118,245],"quantifying":[88],"series,":[93],"where":[94],"knowledge":[96],"\"black":[98],"swan\"":[99],"events,":[100],"such":[101],"spikes":[103],"or":[104],"sudden":[105],"jumps,":[106],"are":[107,127,262],"key":[109],"importance.":[110],"connection,":[113],"first":[115],"prove":[116],"Gaussian":[119],"variables,":[120],"Granger":[121],"causality":[122],"and":[123,149,170,224],"R\u00e9nyi":[124,150],"entropy":[126,168,192],"entirely":[128],"equivalent.":[129],"Moreover,":[130],"also":[132,205],"partially":[133],"extend":[134],"these":[135],"results":[136,142],"to":[137,154,197],"heavy-tailed":[138],"\u03b1-Gaussian":[139],"variables.":[140],"These":[141],"allow":[143],"establishing":[144],"connection":[146],"autoregressive":[148],"entropy-based":[151],"approaches":[153],"data-driven":[155],"inference.":[157],"To":[158],"aid":[159],"our":[160],"intuition,":[161],"employed":[163],"Leonenko":[165],"et":[166],"al.":[167],"estimator":[169],"analyzed":[171],"generated":[179],"two":[181,259],"unidirectionally":[182],"coupled":[183,263],"R\u00f6ssler":[184,260],"systems.":[185],"Notably,":[186],"find":[188],"not":[193,266],"allows":[195],"us":[196],"detect":[198],"threshold":[200],"synchronization":[202,225],"but":[203,264],"it":[204],"provides":[206],"non-trivial":[207],"insight":[208],"into":[209],"structure":[211],"transient":[214,255],"regime":[215],"exists":[217],"region":[220],"chaotic":[222],"correlations":[223],"threshold.":[226],"addition,":[228],"entropy,":[232],"could":[234],"reliably":[235],"infer":[236],"direction":[238],"coupling":[240,246],"and,":[241],"hence,":[242],"causality,":[243],"strengths":[247],"smaller":[248],"than":[249],"onset":[251],"value":[252],"regime,":[256],"i.e.,":[257],"when":[258],"systems":[261],"have":[265],"yet":[267],"entered":[268],"synchronization.":[269]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2022-04-03T00:00:00"}