{"id":"https://openalex.org/W4282930712","doi":"https://doi.org/10.3390/e24050606","title":"A Multi-Scale Entropy Approach to Study Collapse and Anomalous Diffusion in Shared Mobility Systems","display_name":"A Multi-Scale Entropy Approach to Study Collapse and Anomalous Diffusion in Shared Mobility Systems","publication_year":2022,"publication_date":"2022-04-27","ids":{"openalex":"https://openalex.org/W4282930712","doi":"https://doi.org/10.3390/e24050606","pmid":"https://pubmed.ncbi.nlm.nih.gov/35626491"},"language":"en","primary_location":{"id":"doi:10.3390/e24050606","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050606","pdf_url":"https://www.mdpi.com/1099-4300/24/5/606/pdf?version=1651054177","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/5/606/pdf?version=1651054177","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091452530","display_name":"Francisco Prieto\u2010Castrillo","orcid":"https://orcid.org/0000-0003-4709-772X"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Francisco Prieto-Castrillo","raw_affiliation_strings":["Facultad de Ciencias, Departamento de Matem\u00e1ticas, Universidad de Oviedo, Calle Federico Garc\u00eda Lorca 18, 33007 Oviedo, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4709-772X","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias, Departamento de Matem\u00e1ticas, Universidad de Oviedo, Calle Federico Garc\u00eda Lorca 18, 33007 Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049833846","display_name":"J. Borondo","orcid":"https://orcid.org/0000-0002-3774-2521"},"institutions":[{"id":"https://openalex.org/I96580804","display_name":"Universidad Pontificia Comillas","ror":"https://ror.org/017mdc710","country_code":"ES","type":"education","lineage":["https://openalex.org/I96580804"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Javier Borondo","raw_affiliation_strings":["Facultad de Ciencias Econ\u00f3micas y Empresariales (ICADE), Departamento de Gesti\u00f3n Empresarial, Universidad Pontificia Comillas, Calle Alberto Aguilera 23, 28015 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-3774-2521","affiliations":[{"raw_affiliation_string":"Facultad de Ciencias Econ\u00f3micas y Empresariales (ICADE), Departamento de Gesti\u00f3n Empresarial, Universidad Pontificia Comillas, Calle Alberto Aguilera 23, 28015 Madrid, Spain","institution_ids":["https://openalex.org/I96580804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005930808","display_name":"Rub\u00e9n Mart\u00edn Garc\u00eda","orcid":"https://orcid.org/0000-0001-8443-6108"},"institutions":[{"id":"https://openalex.org/I41382782","display_name":"Universidad Pontificia de Salamanca","ror":"https://ror.org/02jj93564","country_code":"ES","type":"education","lineage":["https://openalex.org/I41382782"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rub\u00e9n Mart\u00edn Garc\u00eda","raw_affiliation_strings":["Facultad de Inform\u00e1tica, Universidad Pontificia de Salamanca, Calle Compa\u00f1\u00eda, 5, 37002 Salamanca, Spain"],"raw_orcid":"https://orcid.org/0000-0001-8443-6108","affiliations":[{"raw_affiliation_string":"Facultad de Inform\u00e1tica, Universidad Pontificia de Salamanca, Calle Compa\u00f1\u00eda, 5, 37002 Salamanca, Spain","institution_ids":["https://openalex.org/I41382782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029099160","display_name":"R. M. Benito","orcid":"https://orcid.org/0000-0003-3949-8232"},"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":"Rosa M. Benito","raw_affiliation_strings":["Grupo de Sistemas Complejos, E.T.S. de Ingenier\u00eda Agron., Alim. y de Biosist., Universidad Polit\u00e9cnica de Madrid, Avda. Puerta de Hierro 2-4, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-3949-8232","affiliations":[{"raw_affiliation_string":"Grupo de Sistemas Complejos, E.T.S. de Ingenier\u00eda Agron., Alim. y de Biosist., Universidad Polit\u00e9cnica de Madrid, Avda. Puerta de Hierro 2-4, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091452530"],"corresponding_institution_ids":["https://openalex.org/I165339363"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2751,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47709873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"24","issue":"5","first_page":"606","last_page":"606"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9918000102043152,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.991100013256073,"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/anomalous-diffusion","display_name":"Anomalous diffusion","score":0.6027644276618958},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6005116701126099},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5469368696212769},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.5242310166358948},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5201026201248169},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.4773138463497162},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.46050119400024414},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.45593541860580444},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.45143088698387146},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.44213634729385376},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4258374571800232},{"id":"https://openalex.org/keywords/birth\u2013death-process","display_name":"Birth\u2013death process","score":0.4114152193069458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31661146879196167},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24909335374832153},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1694568395614624},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1380290389060974},{"id":"https://openalex.org/keywords/innovation-diffusion","display_name":"Innovation diffusion","score":0.1327853500843048},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09884220361709595},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09882920980453491}],"concepts":[{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.6027644276618958},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6005116701126099},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5469368696212769},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5242310166358948},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5201026201248169},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.4773138463497162},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.46050119400024414},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.45593541860580444},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.45143088698387146},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.44213634729385376},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4258374571800232},{"id":"https://openalex.org/C65990518","wikidata":"https://www.wikidata.org/wiki/Q1456275","display_name":"Birth\u2013death process","level":3,"score":0.4114152193069458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31661146879196167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24909335374832153},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1694568395614624},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1380290389060974},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.1327853500843048},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09884220361709595},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09882920980453491},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24050606","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050606","pdf_url":"https://www.mdpi.com/1099-4300/24/5/606/pdf?version=1651054177","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:35626491","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35626491","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:doaj.org/article:8efa97a4944449dda80cbcf60e3e0857","is_oa":true,"landing_page_url":"https://doaj.org/article/8efa97a4944449dda80cbcf60e3e0857","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 5, p 606 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/5/606/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24050606","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; Volume 24; Issue 5; Pages: 606","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9141931","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9141931","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"}],"best_oa_location":{"id":"doi:10.3390/e24050606","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050606","pdf_url":"https://www.mdpi.com/1099-4300/24/5/606/pdf?version=1651054177","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":[{"display_name":"Sustainable cities and communities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4282930712.pdf","grobid_xml":"https://content.openalex.org/works/W4282930712.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1521862445","https://openalex.org/W1776514298","https://openalex.org/W1854151356","https://openalex.org/W1971827710","https://openalex.org/W1982300822","https://openalex.org/W2006957610","https://openalex.org/W2012324282","https://openalex.org/W2013598124","https://openalex.org/W2017053662","https://openalex.org/W2047525231","https://openalex.org/W2059851411","https://openalex.org/W2077204677","https://openalex.org/W2093266575","https://openalex.org/W2109708078","https://openalex.org/W2135616346","https://openalex.org/W2156767060","https://openalex.org/W2299288249","https://openalex.org/W2339589496","https://openalex.org/W2471731606","https://openalex.org/W2523951014","https://openalex.org/W2539308428","https://openalex.org/W2558177690","https://openalex.org/W2760942449","https://openalex.org/W2793018423","https://openalex.org/W2803156588","https://openalex.org/W2963775138","https://openalex.org/W4205419457","https://openalex.org/W4248273320","https://openalex.org/W6638355978","https://openalex.org/W6665389906","https://openalex.org/W6669699252"],"related_works":["https://openalex.org/W1996593003","https://openalex.org/W2964190585","https://openalex.org/W2803757496","https://openalex.org/W2033402214","https://openalex.org/W1618612856","https://openalex.org/W2379959577","https://openalex.org/W2026946703","https://openalex.org/W4318606473","https://openalex.org/W2032935596","https://openalex.org/W2924070052"],"abstract_inverted_index":{"In":[0,16],"this":[1],"paper,":[2],"we":[3,18,51,60,78],"study":[4],"the":[5,32,63,74,88],"phenomena":[6],"of":[7,23,34,90,99],"collapse":[8],"and":[9,30,59],"anomalous":[10],"diffusion":[11],"in":[12,36,87],"shared":[13],"mobility":[14],"systems.":[15],"particular,":[17],"focus":[19],"on":[20],"a":[21,27,40,47,84,94,100,104,108],"fleet":[22,86],"vehicles":[24],"moving":[25],"through":[26],"stations":[28],"network":[29],"analyse":[31],"effect":[33],"self-journeys":[35],"system":[37,64,106],"stability,":[38],"using":[39],"mathematical":[41],"simplex":[42],"under":[43,69],"stochastic":[44],"flows.":[45],"With":[46],"birth-death":[48],"process":[49],"approach,":[50],"find":[52],"analytical":[53],"upper":[54],"bounds":[55],"for":[56],"random":[57],"walk":[58],"monitor":[61],"how":[62],"collapses":[65],"by":[66],"super":[67],"diffusing":[68],"different":[70],"randomization":[71],"conditions.":[72],"Using":[73],"multi-scale":[75],"entropy":[76],"metric,":[77],"show":[79],"that":[80],"real":[81],"data":[82],"from":[83],"bike-sharing":[85],"city":[89],"Salamanca":[91],"(Spain)":[92],"present":[93],"complex":[95],"behaviour":[96],"with":[97,107],"more":[98],"1/f":[101],"signal":[102],"than":[103],"disorganized":[105],"white":[109],"noise":[110],"signal.":[111]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
