{"id":"https://openalex.org/W2084488670","doi":"https://doi.org/10.1109/tac.2014.2304369","title":"The Forest Consensus Theorem","display_name":"The Forest Consensus Theorem","publication_year":2014,"publication_date":"2014-02-03","ids":{"openalex":"https://openalex.org/W2084488670","doi":"https://doi.org/10.1109/tac.2014.2304369","mag":"2084488670"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2014.2304369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2304369","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1301.1848","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050459701","display_name":"Pavel Chebotarev","orcid":"https://orcid.org/0000-0001-8232-847X"},"institutions":[{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Pavel Chebotarev","raw_affiliation_strings":["Institute of Control Sciences of RAS, Moscow, Russia","Inst. of Control Sci., Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Control Sciences of RAS, Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]},{"raw_affiliation_string":"Inst. of Control Sci., Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015837598","display_name":"Rafig Agaev","orcid":null},"institutions":[{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Rafig Agaev","raw_affiliation_strings":["Institute of Control Sciences of RAS, Moscow, Russia","Inst. of Control Sci., Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Control Sciences of RAS, Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]},{"raw_affiliation_string":"Inst. of Control Sci., Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050459701"],"corresponding_institution_ids":["https://openalex.org/I4210157430"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15851421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"9","first_page":"2475","last_page":"2479"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9995999932289124,"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":0.9995999932289124,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9957000017166138,"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/pooling","display_name":"Pooling","score":0.7586280107498169},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.7113496661186218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5859442949295044},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.48638537526130676},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.42165204882621765},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4191031754016876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4187888503074646},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3841429650783539},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.371481716632843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3491952121257782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.277640700340271},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1259995996952057},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0920664370059967}],"concepts":[{"id":"https://openalex.org/C70437156","wikidata":"https://www.wikidata.org/wiki/Q7228652","display_name":"Pooling","level":2,"score":0.7586280107498169},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.7113496661186218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5859442949295044},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.48638537526130676},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.42165204882621765},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4191031754016876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4187888503074646},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3841429650783539},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.371481716632843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3491952121257782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.277640700340271},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1259995996952057},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0920664370059967},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2014.2304369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2304369","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1301.1848","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.1848","pdf_url":"https://arxiv.org/pdf/1301.1848","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.1301.1848","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1301.1848","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":"mag:2084488670","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1301.1848","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.1848","pdf_url":"https://arxiv.org/pdf/1301.1848","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":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7900000214576721,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G3088282334","display_name":null,"funder_award_id":"13-07-13167","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G3635241424","display_name":null,"funder_award_id":"13-07-00990","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G6926803369","display_name":null,"funder_award_id":"13-01-13105","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084488670.pdf","grobid_xml":"https://content.openalex.org/works/W2084488670.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W193717806","https://openalex.org/W613360614","https://openalex.org/W1479963817","https://openalex.org/W1483030393","https://openalex.org/W1483804921","https://openalex.org/W1536228023","https://openalex.org/W1992856221","https://openalex.org/W1998692453","https://openalex.org/W2001864568","https://openalex.org/W2011872397","https://openalex.org/W2028192443","https://openalex.org/W2029741811","https://openalex.org/W2036807120","https://openalex.org/W2055576996","https://openalex.org/W2055796072","https://openalex.org/W2081595203","https://openalex.org/W2093520943","https://openalex.org/W2107396783","https://openalex.org/W2122702058","https://openalex.org/W2128978199","https://openalex.org/W2131705730","https://openalex.org/W2138764986","https://openalex.org/W2142285137","https://openalex.org/W2167805812","https://openalex.org/W2484117929","https://openalex.org/W3099358910","https://openalex.org/W3102419163","https://openalex.org/W4250134109","https://openalex.org/W6631993146","https://openalex.org/W6683107235","https://openalex.org/W6983305780"],"related_works":["https://openalex.org/W2343176593","https://openalex.org/W2187188731","https://openalex.org/W3200230063","https://openalex.org/W2884116131","https://openalex.org/W2248553123","https://openalex.org/W3101721269"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,8,21,24,28,31,37,41,48,55,68,72,82],"limiting":[4],"state":[5],"vector":[6,32],"of":[7,23,27,33,44,47,84],"continuous-time":[9],"consensus":[10,57,77,85],"protocol":[11],"with":[12,40],"an":[13],"arbitrary":[14],"communication":[15,50],"digraph":[16],"is":[17,79],"obtained":[18],"by":[19,30],"multiplying":[20],"eigenprojection":[22,38],"Laplacian":[25],"matrix":[26,43],"model":[29,66],"initial":[34],"states.":[35],"Furthermore,":[36],"coincides":[39],"stochastic":[42],"maximum":[45],"out-forests":[46],"weighted":[49],"digraph.":[51],"These":[52],"statements":[53],"make":[54],"forest":[56,76],"theorem.":[58],"A":[59],"similar":[60],"result":[61],"for":[62,81],"DeGroot's":[63],"iterative":[64],"pooling":[65],"requires":[67],"Ces\u00e0ro":[69],"limit":[70],"in":[71],"general":[73],"case.":[74],"The":[75],"theorem":[78],"useful":[80],"analysis":[83],"algorithms.":[86]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
