{"id":"https://openalex.org/W1998200279","doi":"https://doi.org/10.1109/tcns.2014.2357552","title":"Consensus and Coherence in Fractal Networks","display_name":"Consensus and Coherence in Fractal Networks","publication_year":2014,"publication_date":"2014-09-12","ids":{"openalex":"https://openalex.org/W1998200279","doi":"https://doi.org/10.1109/tcns.2014.2357552","mag":"1998200279"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2014.2357552","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2014.2357552","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control of Network 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/A5081738999","display_name":"Stacy Patterson","orcid":"https://orcid.org/0000-0001-7711-6018"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stacy Patterson","raw_affiliation_strings":["Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA","[Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]},{"raw_affiliation_string":"[Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA]","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071239059","display_name":"Bassam Bamieh","orcid":"https://orcid.org/0000-0001-9237-4613"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bassam Bamieh","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA","Dept. of Mech. Eng., Univ. of California Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dept. of Mech. Eng., Univ. of California Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081738999"],"corresponding_institution_ids":["https://openalex.org/I165799507"],"apc_list":null,"apc_paid":null,"fwci":3.1077,"has_fulltext":false,"cited_by_count":112,"citation_normalized_percentile":{"value":0.91721515,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"1","issue":"4","first_page":"338","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9993000030517578,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9987999796867371,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.6547893285751343},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.6181159019470215},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.5541884303092957},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5399072766304016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48926040530204773},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.4885726869106293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4822867214679718},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4728562831878662},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.4515877068042755},{"id":"https://openalex.org/keywords/fractal-analysis","display_name":"Fractal analysis","score":0.42479854822158813},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.39146706461906433},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3475499153137207},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.24235621094703674},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22923868894577026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12850245833396912},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11383578181266785},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10133853554725647},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0894339382648468}],"concepts":[{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.6547893285751343},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6181159019470215},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.5541884303092957},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5399072766304016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48926040530204773},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4885726869106293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4822867214679718},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4728562831878662},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.4515877068042755},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.42479854822158813},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39146706461906433},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3475499153137207},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.24235621094703674},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22923868894577026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12850245833396912},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11383578181266785},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10133853554725647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0894339382648468},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcns.2014.2357552","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2014.2357552","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control of Network Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6539152148","display_name":null,"funder_award_id":"1408442","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1536997931","https://openalex.org/W1547358136","https://openalex.org/W1586184796","https://openalex.org/W1723060524","https://openalex.org/W1965640670","https://openalex.org/W1980222794","https://openalex.org/W1985106274","https://openalex.org/W1992478204","https://openalex.org/W1992910095","https://openalex.org/W2006408461","https://openalex.org/W2006975882","https://openalex.org/W2010264617","https://openalex.org/W2024217986","https://openalex.org/W2043852692","https://openalex.org/W2046753759","https://openalex.org/W2048468225","https://openalex.org/W2048572907","https://openalex.org/W2052029349","https://openalex.org/W2063824659","https://openalex.org/W2071090652","https://openalex.org/W2071723512","https://openalex.org/W2081077061","https://openalex.org/W2086016772","https://openalex.org/W2099689250","https://openalex.org/W2107396783","https://openalex.org/W2123610102","https://openalex.org/W2129248505","https://openalex.org/W2129488612","https://openalex.org/W2138085462","https://openalex.org/W2151685478","https://openalex.org/W2165744313","https://openalex.org/W2266385647","https://openalex.org/W2318794083","https://openalex.org/W2601387062","https://openalex.org/W3104175967","https://openalex.org/W4247782380","https://openalex.org/W6693232038"],"related_works":["https://openalex.org/W2394117909","https://openalex.org/W2896054214","https://openalex.org/W2355197944","https://openalex.org/W2017118246","https://openalex.org/W2354661593","https://openalex.org/W2382240109","https://openalex.org/W2368475191","https://openalex.org/W2391311021","https://openalex.org/W1968412567","https://openalex.org/W1992756222"],"abstract_inverted_index":{"We":[0,12,36,93],"consider":[1],"first-":[2],"and":[3,83],"second-order":[4,103],"consensus":[5,17,82,105,147],"algorithms":[6,148],"in":[7,64,149],"networks":[8,42,112,151],"with":[9,113],"stochastic":[10,34,81,104,146],"disturbances.":[11],"quantify":[13],"the":[14,19,33,38,45,55,60,65,84,114,131,143,161],"deviation":[15],"from":[16],"using":[18],"notion":[20],"of":[21,32,40,47,62,90,130,141,145],"network":[22,124,132],"coherence,":[23],"which":[24],"can":[25,58,118,152],"be":[26,153],"expressed":[27],"as":[28,54,160],"an":[29],"$H_{2}$":[30],"norm":[31],"system.":[35],"use":[37],"setting":[39],"fractal":[41,56,116],"to":[43,97,101],"investigate":[44],"question":[46,140],"whether":[48,142],"a":[49],"purely":[50,156],"topological":[51,128,157],"measure,":[52],"such":[53,159],"dimension,":[57,163],"capture":[59],"asymptotics":[61],"coherence":[63,137],"large":[66,150],"system":[67],"size":[68],"limit.":[69],"Our":[70,107],"analysis":[71,108],"for":[72,123],"first-order":[73,80],"systems":[74],"is":[75],"facilitated":[76],"by":[77,155],"connections":[78],"between":[79],"global":[85],"mean":[86],"first":[87],"passage":[88],"time":[89],"random":[91],"walks.":[92],"then":[94],"show":[95],"how":[96],"apply":[98],"similar":[99],"techniques":[100],"analyze":[102],"systems.":[106],"reveals":[109],"that":[110],"two":[111],"same":[115],"dimension":[117],"exhibit":[119],"different":[120],"asymptotic":[121],"scalings":[122],"coherence.":[125],"Thus,":[126],"this":[127],"characterization":[129],"does":[133],"not":[134],"uniquely":[135],"determine":[136],"behavior.":[138],"The":[139],"performance":[144],"captured":[154],"measures,":[158],"spatial":[162],"remains":[164],"open.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3}],"updated_date":"2026-03-08T08:50:53.379069","created_date":"2025-10-10T00:00:00"}