{"id":"https://openalex.org/W3157661465","doi":"https://doi.org/10.3390/axioms10020080","title":"Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps","display_name":"Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps","publication_year":2021,"publication_date":"2021-05-02","ids":{"openalex":"https://openalex.org/W3157661465","doi":"https://doi.org/10.3390/axioms10020080","mag":"3157661465"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10020080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020080","pdf_url":"https://www.mdpi.com/2075-1680/10/2/80/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/10/2/80/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017368871","display_name":"Sergey Kryzhevich","orcid":"https://orcid.org/0000-0002-1253-1015"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Sergey Kryzhevich","raw_affiliation_strings":["Mathematics and Mechanics Faculty, Saint Petersburg State University, 199034 St. Petersburg, Russia"],"raw_orcid":"https://orcid.org/0000-0002-1253-1015","affiliations":[{"raw_affiliation_string":"Mathematics and Mechanics Faculty, Saint Petersburg State University, 199034 St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081475028","display_name":"\u0412\u0438\u043a\u0442\u043e\u0440 \u0410\u0432\u0440\u0443\u0442\u0438\u043d","orcid":"https://orcid.org/0000-0001-7931-8844"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Viktor Avrutin","raw_affiliation_strings":["Institute for Systems Theory and Automatic Control, University of Stuttgart, 70174 Stuttgart, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Theory and Automatic Control, University of Stuttgart, 70174 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040271824","display_name":"Nikita Begun","orcid":"https://orcid.org/0000-0001-5148-9676"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nikita Begun","raw_affiliation_strings":["Mathematics and Mechanics Faculty, Saint Petersburg State University, 199034 St. Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Mechanics Faculty, Saint Petersburg State University, 199034 St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005880460","display_name":"\u0414\u043c\u0438\u0442\u0440\u0438\u0439 \u0420\u0430\u0447\u0438\u043d\u0441\u043a\u0438\u0439","orcid":"https://orcid.org/0000-0003-2786-7205"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dmitrii Rachinskii","raw_affiliation_strings":["Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USA","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059559267","display_name":"Khosro Tajbakhsh","orcid":"https://orcid.org/0000-0001-5489-0318"},"institutions":[{"id":"https://openalex.org/I1516879","display_name":"Tarbiat Modares University","ror":"https://ror.org/03mwgfy56","country_code":"IR","type":"education","lineage":["https://openalex.org/I1516879"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Khosro Tajbakhsh","raw_affiliation_strings":["Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran","institution_ids":["https://openalex.org/I1516879"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5017368871"],"corresponding_institution_ids":["https://openalex.org/I172901346"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.1602,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49833858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","issue":"2","first_page":"80","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9905999898910522,"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":0.9905999898910522,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9731000065803528,"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/invariant","display_name":"Invariant (physics)","score":0.7075955271720886},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.6629759073257446},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6457589268684387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.54807448387146},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5285652875900269},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4942188560962677},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.482148140668869},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.429020494222641},{"id":"https://openalex.org/keywords/hysteresis","display_name":"Hysteresis","score":0.4200735092163086},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36679506301879883},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3549550175666809},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32804954051971436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27698513865470886},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18064525723457336},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1373695433139801},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.11594417691230774},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08569732308387756},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0523381233215332}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7075955271720886},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.6629759073257446},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6457589268684387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.54807448387146},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5285652875900269},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4942188560962677},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.482148140668869},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.429020494222641},{"id":"https://openalex.org/C123299182","wikidata":"https://www.wikidata.org/wiki/Q190837","display_name":"Hysteresis","level":2,"score":0.4200735092163086},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36679506301879883},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3549550175666809},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32804954051971436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27698513865470886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18064525723457336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1373695433139801},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.11594417691230774},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08569732308387756},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0523381233215332},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/axioms10020080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020080","pdf_url":"https://www.mdpi.com/2075-1680/10/2/80/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.11825","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.11825","pdf_url":"https://arxiv.org/pdf/2104.11825","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":"mag:3157661465","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2104.11825","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:e4a850e077fc44f9b1f6c38fcee7d5b9","is_oa":true,"landing_page_url":"https://doaj.org/article/e4a850e077fc44f9b1f6c38fcee7d5b9","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":"Axioms, Vol 10, Iss 2, p 80 (2021)","raw_type":"article"},{"id":"pmh:oai:elib.uni-stuttgart.de:11682/12894","is_oa":true,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-128942","pdf_url":null,"source":{"id":"https://openalex.org/S4306401556","display_name":"OPUS Publication Server of the University of Stuttgart (University of Stuttgart)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I100066346","host_organization_name":"University of Stuttgart","host_organization_lineage":["https://openalex.org/I100066346"],"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":null,"raw_type":"article"},{"id":"doi:10.48550/arxiv.2104.11825","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.11825","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"},{"id":"doi:10.18419/opus-12875","is_oa":true,"landing_page_url":"https://doi.org/10.18419/opus-12875","pdf_url":null,"source":{"id":"https://openalex.org/S7407052998","display_name":"Universit\u00e4tsbibliothek Stuttgart","issn_l":null,"issn":[],"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms10020080","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020080","pdf_url":"https://www.mdpi.com/2075-1680/10/2/80/pdf","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G888371005","display_name":null,"funder_award_id":"AV 111/2-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324521","display_name":"Freie Universit\u00e4t Berlin","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3157661465.pdf","grobid_xml":"https://content.openalex.org/works/W3157661465.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W38868731","https://openalex.org/W595325313","https://openalex.org/W638757554","https://openalex.org/W1488052276","https://openalex.org/W1980908043","https://openalex.org/W1988277584","https://openalex.org/W2040152993","https://openalex.org/W2041209262","https://openalex.org/W2049595302","https://openalex.org/W2081817659","https://openalex.org/W2082843460","https://openalex.org/W2083694129","https://openalex.org/W2087100765","https://openalex.org/W2113092129","https://openalex.org/W2127074104","https://openalex.org/W2137520423","https://openalex.org/W2138434353","https://openalex.org/W2159859228","https://openalex.org/W2170408787","https://openalex.org/W2328754094","https://openalex.org/W2497597089","https://openalex.org/W2963219729","https://openalex.org/W2963890502","https://openalex.org/W2964290925","https://openalex.org/W3011951839","https://openalex.org/W3021856834","https://openalex.org/W3133146829","https://openalex.org/W3177529379","https://openalex.org/W4230143057","https://openalex.org/W6629132800"],"related_works":["https://openalex.org/W3162874841","https://openalex.org/W2162757367","https://openalex.org/W1978191167","https://openalex.org/W3120195731","https://openalex.org/W2963370994","https://openalex.org/W2314215021","https://openalex.org/W3099991590","https://openalex.org/W2151268547","https://openalex.org/W1974497962","https://openalex.org/W2171082407","https://openalex.org/W2094219191","https://openalex.org/W1453318738","https://openalex.org/W1983180908","https://openalex.org/W3198524820","https://openalex.org/W1573241742","https://openalex.org/W3199914982","https://openalex.org/W2912771066","https://openalex.org/W2012475956","https://openalex.org/W3124432067","https://openalex.org/W1994472061"],"abstract_inverted_index":{"We":[0],"studied":[1],"topological":[2],"and":[3,22],"metric":[4],"properties":[5],"of":[6,37],"the":[7,18,30,35,38],"so-called":[8],"interval":[9,54],"translation":[10,55],"maps":[11,56],"(ITMs).":[12],"For":[13],"these":[14],"maps,":[15],"we":[16,27],"introduced":[17],"maximal":[19],"invariant":[20,31],"measure":[21],"study":[23,28],"its":[24],"properties.":[25],"Further,":[26],"how":[29],"measures":[32],"depend":[33],"on":[34],"parameters":[36],"system.":[39],"These":[40],"results":[41],"were":[42],"illustrated":[43],"by":[44],"a":[45,49],"simple":[46],"example":[47],"or":[48],"risk":[50],"management":[51],"model":[52],"where":[53],"appear":[57],"naturally.":[58]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}