{"id":"https://openalex.org/W2144579655","doi":"https://doi.org/10.1109/acc.2007.4282958","title":"On Recurrence of Graph Connectivity in Vicsek's Model of Motion Coordination for Mobile Autonomous Agents","display_name":"On Recurrence of Graph Connectivity in Vicsek's Model of Motion Coordination for Mobile Autonomous Agents","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2144579655","doi":"https://doi.org/10.1109/acc.2007.4282958","mag":"2144579655"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282958","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282958","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-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/A5003432485","display_name":"Alireza Tahbaz-Salehi","orcid":"https://orcid.org/0000-0002-6860-1836"},"institutions":[{"id":"https://openalex.org/I922845939","display_name":"Philadelphia University","ror":"https://ror.org/03zzmyz63","country_code":"US","type":"education","lineage":["https://openalex.org/I922845939"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alireza Tahbaz-Salehi","raw_affiliation_strings":["GRASP Laboratory and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA","University of Pennsylvania , Philadelphia"],"affiliations":[{"raw_affiliation_string":"GRASP Laboratory and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"University of Pennsylvania , Philadelphia","institution_ids":["https://openalex.org/I922845939","https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078288116","display_name":"Ali Jadbabaie","orcid":"https://orcid.org/0000-0003-1122-3069"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]},{"id":"https://openalex.org/I922845939","display_name":"Philadelphia University","ror":"https://ror.org/03zzmyz63","country_code":"US","type":"education","lineage":["https://openalex.org/I922845939"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Jadbabaie","raw_affiliation_strings":["GRASP Laboratory and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA","University of Pennsylvania , Philadelphia"],"affiliations":[{"raw_affiliation_string":"GRASP Laboratory and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"University of Pennsylvania , Philadelphia","institution_ids":["https://openalex.org/I922845939","https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003432485"],"corresponding_institution_ids":["https://openalex.org/I79576946","https://openalex.org/I922845939"],"apc_list":null,"apc_paid":null,"fwci":2.2034,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88473308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"699","last_page":"704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994000196456909,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994000196456909,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9990000128746033,"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.7074960470199585},{"id":"https://openalex.org/keywords/heading","display_name":"Heading (navigation)","score":0.6787953972816467},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5045500993728638},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4825546145439148},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4756740629673004},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4730229377746582},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.46301954984664917},{"id":"https://openalex.org/keywords/kuramoto-model","display_name":"Kuramoto model","score":0.45308059453964233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4418872594833374},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41757458448410034},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.41736865043640137},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4121691882610321},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.32971182465553284},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.24850785732269287},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20723602175712585},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1609145700931549},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.14929768443107605},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1296236515045166},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.10491117835044861}],"concepts":[{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.7074960470199585},{"id":"https://openalex.org/C2776937971","wikidata":"https://www.wikidata.org/wiki/Q4384217","display_name":"Heading (navigation)","level":2,"score":0.6787953972816467},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5045500993728638},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4825546145439148},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4756740629673004},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4730229377746582},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.46301954984664917},{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.45308059453964233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4418872594833374},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41757458448410034},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.41736865043640137},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4121691882610321},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32971182465553284},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.24850785732269287},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20723602175712585},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1609145700931549},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.14929768443107605},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1296236515045166},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.10491117835044861},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2007.4282958","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282958","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.331.9487","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.331.9487","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.seas.upenn.edu/~jadbabai/papers/ACC07_final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W150267902","https://openalex.org/W1508718255","https://openalex.org/W1537368336","https://openalex.org/W1547358136","https://openalex.org/W1685087528","https://openalex.org/W1894990513","https://openalex.org/W1998692453","https://openalex.org/W2006746073","https://openalex.org/W2015410655","https://openalex.org/W2018800107","https://openalex.org/W2026304610","https://openalex.org/W2075032588","https://openalex.org/W2076597612","https://openalex.org/W2077055049","https://openalex.org/W2098863504","https://openalex.org/W2101517602","https://openalex.org/W2107396783","https://openalex.org/W2114871659","https://openalex.org/W2115428923","https://openalex.org/W2125668987","https://openalex.org/W2130518506","https://openalex.org/W2137642864","https://openalex.org/W2151063922","https://openalex.org/W2154834860","https://openalex.org/W2161522176","https://openalex.org/W2165744313","https://openalex.org/W2172252395","https://openalex.org/W2781725465","https://openalex.org/W3142756138","https://openalex.org/W3175367423","https://openalex.org/W4244375620","https://openalex.org/W4247555059","https://openalex.org/W4250134109","https://openalex.org/W6639381414","https://openalex.org/W6674727558","https://openalex.org/W6681857541","https://openalex.org/W6684092557","https://openalex.org/W7034029160","https://openalex.org/W7061399666"],"related_works":["https://openalex.org/W4244052565","https://openalex.org/W2358719579","https://openalex.org/W4252778923","https://openalex.org/W2385042721","https://openalex.org/W2367929022","https://openalex.org/W2351754530","https://openalex.org/W2378649906","https://openalex.org/W2391014597","https://openalex.org/W2350113401","https://openalex.org/W2978007058"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,57],"complete":[4],"the":[5,55,70,73,115,123],"analysis":[6],"of":[7,10,30,75,101,106,109,126],"Vicsek's":[8],"model":[9,18,125],"distributed":[11],"coordination":[12],"among":[13],"kinematic":[14,31],"planar":[15],"agents.":[16],"The":[17],"is":[19,95,119],"a":[20,28,43,98],"simple":[21],"discrete":[22],"time":[23],"heading":[24,90],"update":[25,71,117],"rule":[26],"for":[27,82],"set":[29],"agents":[32,76],"(or":[33],"self-propelled":[34],"particles":[35],"as":[36],"referred":[37],"to":[38,51,122],"by":[39],"Vicsek)":[40],"moving":[41],"in":[42,54,88],"finite":[44],"plane":[45],"with":[46],"periodic":[47],"boundary":[48],"conditions.":[49],"Contrary":[50],"existing":[52],"results":[53],"literature,":[56],"do":[58],"not":[59],"make":[60],"any":[61],"assumptions":[62],"on":[63,104],"connectivity":[64],"but":[65],"instead":[66],"prove":[67],"that":[68,114],"under":[69],"scheme,":[72],"network":[74],"stays":[77],"jointly":[78],"connected":[79],"infinitely":[80],"often":[81],"almost":[83],"all":[84],"initial":[85],"conditions,":[86],"resulting":[87],"global":[89],"alignment.":[91],"Our":[92],"main":[93],"result":[94],"derived":[96],"using":[97],"famous":[99],"theorem":[100],"Hermann":[102],"Weyl":[103],"equidistribution":[105],"fractional":[107],"parts":[108],"sequences.":[110],"We":[111],"also":[112],"show":[113],"Vicsek":[116],"scheme":[118],"closely":[120],"related":[121],"Kuramoto":[124],"coupled":[127],"nonlinear":[128],"oscillators.":[129]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
