{"id":"https://openalex.org/W2807069665","doi":"https://doi.org/10.1007/s00446-018-0335-5","title":"Noisy rumor spreading and plurality consensus","display_name":"Noisy rumor spreading and plurality consensus","publication_year":2018,"publication_date":"2018-06-06","ids":{"openalex":"https://openalex.org/W2807069665","doi":"https://doi.org/10.1007/s00446-018-0335-5","mag":"2807069665"},"language":"en","primary_location":{"id":"doi:10.1007/s00446-018-0335-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00446-018-0335-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00446-018-0335-5.pdf","source":{"id":"https://openalex.org/S139349430","display_name":"Distributed Computing","issn_l":"0178-2770","issn":["0178-2770","1432-0452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Distributed Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00446-018-0335-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110465085","display_name":"Pierre Fraigniaud","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre Fraigniaud","raw_affiliation_strings":["Institut de Recherche en Informatique Fondamentale, CNRS and University Paris Diderot, Paris, France","GANG - Networks, Graphs and Algorithms (France)","LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)"],"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Informatique Fondamentale, CNRS and University Paris Diderot, Paris, France","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"GANG - Networks, Graphs and Algorithms (France)","institution_ids":[]},{"raw_affiliation_string":"LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005769196","display_name":"Emanuele Natale","orcid":"https://orcid.org/0000-0002-8755-3892"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I4210106479","display_name":"Laboratoire d'Informatique, Signaux et Syst\u00e8mes de Sophia Antipolis","ror":"https://ror.org/01215r597","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I201841394","https://openalex.org/I4210106479","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I4210117840","display_name":"Institut de Biologie Valrose","ror":"https://ror.org/03bnma344","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I201841394","https://openalex.org/I4210096427","https://openalex.org/I4210117840"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"Emanuele Natale","raw_affiliation_strings":["Max Planck Institute for Informatics, Saarbr\u00fccken, 66123, Germany","COMUE UCA - COMUE Universit\u00e9 C\u00f4te d'Azur (2015-2019) (Parc Valrose, 28, avenue Valrose 06108 Nice Cedex 2  - France)","Max Planck Institute for Informatics [Saarbr\u00fccken] (Campus 4, 66123 Saarbr\u00fccken - Germany)","I3S - Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia Antipolis (2000, route des Lucioles - Les Algorithmes - b\u00e2t. Euclide B 06900 Sophia Antipolis - France)","COATI - Combinatorics, Optimization and Algorithms for Telecommunications (2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) - France)","CNRS - Centre National de la Recherche Scientifique (France)"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Informatics, Saarbr\u00fccken, 66123, Germany","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"COMUE UCA - COMUE Universit\u00e9 C\u00f4te d'Azur (2015-2019) (Parc Valrose, 28, avenue Valrose 06108 Nice Cedex 2  - France)","institution_ids":["https://openalex.org/I4210117840","https://openalex.org/I201841394"]},{"raw_affiliation_string":"Max Planck Institute for Informatics [Saarbr\u00fccken] (Campus 4, 66123 Saarbr\u00fccken - Germany)","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"I3S - Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia Antipolis (2000, route des Lucioles - Les Algorithmes - b\u00e2t. Euclide B 06900 Sophia Antipolis - France)","institution_ids":["https://openalex.org/I4210106479"]},{"raw_affiliation_string":"COATI - Combinatorics, Optimization and Algorithms for Telecommunications (2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) - France)","institution_ids":[]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110465085"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210117673","https://openalex.org/I4210144804"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.4654,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.63179078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"4","first_page":"257","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13052","display_name":"Molecular Communication and Nanonetworks","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rumor","display_name":"Rumor","score":0.8794432878494263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6971355080604553},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5277493596076965},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5154117345809937},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4856058955192566},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.42372721433639526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32820194959640503},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.23062655329704285},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21268680691719055},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13252604007720947}],"concepts":[{"id":"https://openalex.org/C2780469804","wikidata":"https://www.wikidata.org/wiki/Q878352","display_name":"Rumor","level":2,"score":0.8794432878494263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6971355080604553},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5277493596076965},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5154117345809937},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4856058955192566},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.42372721433639526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32820194959640503},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.23062655329704285},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21268680691719055},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13252604007720947},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C39549134","wikidata":"https://www.wikidata.org/wiki/Q133080","display_name":"Public relations","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00446-018-0335-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00446-018-0335-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00446-018-0335-5.pdf","source":{"id":"https://openalex.org/S139349430","display_name":"Distributed Computing","issn_l":"0178-2770","issn":["0178-2770","1432-0452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Distributed Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02001830v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02001830","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Distributed Computing, 2019, 32 (4), pp.257-276. ⟨10.1007/s00446-018-0335-5⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-02433482v1","is_oa":false,"landing_page_url":"https://hal.inria.fr/hal-02433482","pdf_url":null,"source":{"id":"https://openalex.org/S4406922276","display_name":"INRIA a CCSD electronic archive server","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0178-2770","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-03100192v1","is_oa":false,"landing_page_url":"https://hal.inria.fr/hal-03100192","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0178-2770","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00446-018-0335-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00446-018-0335-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00446-018-0335-5.pdf","source":{"id":"https://openalex.org/S139349430","display_name":"Distributed Computing","issn_l":"0178-2770","issn":["0178-2770","1432-0452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Distributed Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2683614276","display_name":null,"funder_award_id":"DISPLEXITY","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2807069665.pdf","grobid_xml":"https://content.openalex.org/works/W2807069665.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W283401411","https://openalex.org/W764739102","https://openalex.org/W1494099594","https://openalex.org/W1501097462","https://openalex.org/W1595409123","https://openalex.org/W1975481739","https://openalex.org/W1984727163","https://openalex.org/W1984977694","https://openalex.org/W1989274820","https://openalex.org/W1993649018","https://openalex.org/W2016657432","https://openalex.org/W2032452511","https://openalex.org/W2034681107","https://openalex.org/W2038562061","https://openalex.org/W2043683320","https://openalex.org/W2044234510","https://openalex.org/W2059505795","https://openalex.org/W2079583100","https://openalex.org/W2094761309","https://openalex.org/W2097610718","https://openalex.org/W2110100895","https://openalex.org/W2112238803","https://openalex.org/W2121061285","https://openalex.org/W2121696574","https://openalex.org/W2123429492","https://openalex.org/W2142465565","https://openalex.org/W2150600684","https://openalex.org/W2157004711","https://openalex.org/W2161305294","https://openalex.org/W2162775152","https://openalex.org/W2171414281","https://openalex.org/W2198935850","https://openalex.org/W2472645009","https://openalex.org/W2483628663","https://openalex.org/W2512254926","https://openalex.org/W2546217121","https://openalex.org/W2551916216","https://openalex.org/W2568091325","https://openalex.org/W2612730318","https://openalex.org/W2625096483","https://openalex.org/W2793492460","https://openalex.org/W2899702797","https://openalex.org/W2911824201","https://openalex.org/W2949361955","https://openalex.org/W2962973060","https://openalex.org/W2963943319","https://openalex.org/W4251519439","https://openalex.org/W4300840296"],"related_works":["https://openalex.org/W2372853429","https://openalex.org/W2793319716","https://openalex.org/W3110636174","https://openalex.org/W4210503589","https://openalex.org/W2810386322","https://openalex.org/W2908713064","https://openalex.org/W2801267666","https://openalex.org/W4213140416","https://openalex.org/W2188429085","https://openalex.org/W2886888575"],"abstract_inverted_index":{"Error-correcting":[0],"codes":[1],"are":[2,29],"efficient":[3],"methods":[4,19],"for":[5,161,190,206,259],"handling":[6,191],"noisy":[7,65],"communication":[8,66],"channels":[9,192],"in":[10,60,110,144,217],"the":[11,24,98,111,137,145,186,201,218,229,233,239,250,260],"context":[12],"of":[13,97,113,174,188,203,228,231,241,274],"technological":[14],"networks.":[15],"However,":[16],"such":[17,49],"elaborate":[18],"differ":[20],"a":[21,73,90,94,121,172,213,242,255],"lot":[22],"from":[23,237],"unsophisticated":[25],"way":[26,99],"biological":[27,61,100],"entities":[28,101],"supposed":[30],"to":[31,64,124,135,158,170,183,249,266],"communicate.":[32],"Yet,":[33],"it":[34],"has":[35,105],"been":[36,107],"recently":[37],"shown":[38],"by":[39,221,253,269],"Feinerman":[40,222],"et":[41,223],"al.":[42,224],"(PODC":[43],"2014)":[44],"that":[45,140,263,272],"complex":[46],"coordination":[47],"tasks":[48],"as":[50],"rumor":[51,116],"spreading":[52,117],"and":[53,127,271],"majority":[54,128],"consensus":[55,129,209],"can":[56],"plausibly":[57],"be":[58,267],"achieved":[59],"systems":[62],"subject":[63],"channels,":[67],"where":[68],"every":[69],"message":[70],"transferred":[71],"through":[72],"channel":[74],"remains":[75],"intact":[76],"with":[77,147],"small":[78,243],"probability":[79,230],"$$\\frac{1}{2}+\\epsilon":[80],"$$":[81],",":[82],"without":[83],"using":[84],"coding":[85],"techniques.":[86],"This":[87],"result":[88,215,248],"is":[89,210,225,264,273],"considerable":[91],"step":[92],"towards":[93],"better":[95],"understanding":[96],"may":[102],"cooperate.":[103],"It":[104],"nevertheless":[106],"established":[108],"only":[109],"case":[112,220,252,262],"2-valued":[114],"opinions:":[115],"aims":[118,130],"at":[119,131],"broadcasting":[120],"single-bit":[122,138],"opinion":[123,139,236],"all":[125,133],"nodes,":[126],"leading":[132],"nodes":[134],"adopt":[136],"was":[141],"initially":[142],"present":[143],"system":[146],"(relative)":[148],"majority.":[149],"In":[150,196],"this":[151,155,247],"paper,":[152],"we":[153,198],"extend":[154],"previous":[156],"work":[157],"k-valued":[159,194],"opinions,":[160],"any":[162],"constant":[163],"$$k\\ge":[164],"2$$":[165],".":[166],"Our":[167],"extension":[168],"requires":[169],"address":[171],"series":[173],"important":[175],"issues,":[176],"some":[177],"conceptual,":[178],"others":[179],"technical.":[180],"We":[181,245],"had":[182],"entirely":[184],"revisit":[185],"notion":[187],"noise,":[189],"carrying":[193],"messages.":[195],"fact,":[197],"precisely":[199],"characterize":[200],"type":[202],"noise":[204],"patterns":[205],"which":[207],"plurality":[208],"solvable.":[211],"Also,":[212],"key":[214],"employed":[216],"bivalued":[219,261],"an":[226],"estimate":[227],"observing":[232,238],"most":[234],"frequent":[235],"mode":[240],"sample.":[244],"generalize":[246],"multivalued":[251],"providing":[254],"new":[256],"analytical":[257],"proof":[258],"amenable":[265],"extended,":[268],"induction,":[270],"independent":[275],"interest.":[276]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}