{"id":"https://openalex.org/W2254662782","doi":"https://doi.org/10.1137/16m1060868","title":"Number of Fixed Points and Disjoint Cycles in Monotone Boolean Networks","display_name":"Number of Fixed Points and Disjoint Cycles in Monotone Boolean Networks","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2254662782","doi":"https://doi.org/10.1137/16m1060868","mag":"2254662782"},"language":"en","primary_location":{"id":"doi:10.1137/16m1060868","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1060868","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1602.03109","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110938098","display_name":"Julio Aracena","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Julio Aracena","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082953016","display_name":"Adrien Richard","orcid":"https://orcid.org/0000-0003-3360-5869"},"institutions":[{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Adrien Richard","raw_affiliation_strings":["Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia-Antipolis (I3S) / Equipe BIOINFO"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signaux, et Syst\u00e8mes de Sophia-Antipolis (I3S) / Equipe BIOINFO","institution_ids":["https://openalex.org/I4210106479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021672782","display_name":"Lilian Salinas","orcid":"https://orcid.org/0000-0002-6368-3035"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lilian Salinas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0009189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"3","first_page":"1702","last_page":"1725"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9976000189781189,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9976000189781189,"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/T13991","display_name":"Nuclear Receptors and Signaling","score":0.9800999760627747,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11266","display_name":"Neuroinflammation and Neurodegeneration Mechanisms","score":0.9700999855995178,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8339349031448364},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.7022303938865662},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6572490930557251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6466779112815857},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.638769268989563},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6223436594009399},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.532486617565155},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4719502031803131},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41386598348617554}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8339349031448364},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.7022303938865662},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6572490930557251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6466779112815857},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.638769268989563},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6223436594009399},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.532486617565155},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4719502031803131},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41386598348617554},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/16m1060868","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1060868","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1602.03109","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.03109","pdf_url":"https://arxiv.org/pdf/1602.03109","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":"mag:2254662782","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1602.03109v2","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-01630477v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01630477","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":"SIAM Journal on Discrete Mathematics, 2017, 31 (3), pp.1702 - 1725. &#x27E8;10.1137/16M1060868&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1602.03109","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1602.03109","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-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1602.03109","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.03109","pdf_url":"https://arxiv.org/pdf/1602.03109","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":[],"awards":[{"id":"https://openalex.org/G4847901217","display_name":"R\u00e9seau orient\u00e9 utilisateur","funder_award_id":"ANR-11-LABX-0031","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5872740503","display_name":null,"funder_award_id":"1151265","funder_id":"https://openalex.org/F4320338073","funder_display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico"},{"id":"https://openalex.org/G8874607686","display_name":null,"funder_award_id":"PICS06718","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320338073","display_name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W143489896","https://openalex.org/W1563286165","https://openalex.org/W1964031838","https://openalex.org/W1971224531","https://openalex.org/W1995341919","https://openalex.org/W2003003919","https://openalex.org/W2007062164","https://openalex.org/W2014485295","https://openalex.org/W2040831377","https://openalex.org/W2046538693","https://openalex.org/W2065782501","https://openalex.org/W2079566953","https://openalex.org/W2083759184","https://openalex.org/W2096113666","https://openalex.org/W2104130992","https://openalex.org/W2105831729","https://openalex.org/W2128084896","https://openalex.org/W2131045899","https://openalex.org/W2136670370","https://openalex.org/W2142400903","https://openalex.org/W2151919492","https://openalex.org/W2157825915","https://openalex.org/W4210751359","https://openalex.org/W4248867122"],"related_works":["https://openalex.org/W3025294703","https://openalex.org/W2950186946","https://openalex.org/W2883118335","https://openalex.org/W3101837034","https://openalex.org/W3205249760","https://openalex.org/W2097029176","https://openalex.org/W2950953989","https://openalex.org/W2620189872","https://openalex.org/W2999454811","https://openalex.org/W2951139953","https://openalex.org/W3100625388","https://openalex.org/W2606224933","https://openalex.org/W1595929008","https://openalex.org/W2952049531","https://openalex.org/W2582851771","https://openalex.org/W2952539738","https://openalex.org/W2949660516","https://openalex.org/W2896652362","https://openalex.org/W2951224376","https://openalex.org/W2741509757"],"abstract_inverted_index":{"Given":[0],"a":[1,17,28,52,71,173,199],"digraph":[2],"$G$,":[3,203],"much":[4],"attention":[5],"has":[6],"focused":[7],"on":[8,86,90,217],"the":[9,37,40,48,63,91,100,104,112,126,137,177,195,209,218],"maximum":[10,64,105,113,196],"number":[11,65,106,114,219],"$\\phi(G)$":[12],"of":[13,39,51,56,67,94,108,116,140,144,157,198,202,220,223],"fixed":[14,68,221],"points":[15,69,222],"in":[16,31,35,70],"Boolean":[18,73,225],"network":[19,32,74,226],"$f:\\{0,1\\}^n\\to\\{0,1\\}^n$":[20],"with":[21,75,208],"$G$":[22],"as":[23],"interaction":[24,76,231],"graph.":[25,232],"In":[26,58,96],"particular,":[27],"central":[29],"problem":[30],"coding":[33],"consists":[34],"studying":[36],"optimality":[38],"feedback":[41,53,127],"bound":[42,128,216],"$\\phi(G)\\leq":[43],"2^{\\tau}$,":[44],"where":[45],"$\\tau$":[46],"is":[47,134,194],"minimum":[49],"size":[50,145,158],"vertex":[54],"set":[55],"$G$.":[57,78,95],"this":[59],"paper,":[60],"we":[61,161,175,189,212],"study":[62],"$\\phi_m(G)$":[66,87,133],"monotone":[72],"graph":[77],"We":[79,124],"establish":[80,213],"new":[81],"upper":[82,215],"and":[83,111,147,169,182],"lower":[84,165],"bounds":[85],"that":[88,132,191],"depend":[89],"cycle":[92,201],"structure":[93],"addition":[97],"to":[98,228],"$\\tau$,":[99],"involved":[101],"parameters":[102],"are":[103],"$\\nu$":[107],"vertex-disjoint":[109,117],"cycles,":[110],"$\\nu^*$":[115],"cycles":[118],"verifying":[119],"some":[120],"additional":[121],"technical":[122],"conditions.":[123],"improve":[125],"$2^\\tau$":[129],"by":[130,153],"proving":[131],"at":[135],"most":[136],"largest":[138],"sublattice":[139],"$\\{0,1\\}^\\tau$":[141],"without":[142,148],"chain":[143],"$\\nu+2$,":[146],"another":[149,187],"forbidden":[150],"pattern":[151],"described":[152],"two":[154,163],"disjoint":[155],"antichains":[156],"$\\nu^*+1$.":[159],"Then,":[160],"prove":[162],"optimal":[164],"bounds:":[166],"$\\phi_m(G)\\geq":[167,170],"\\nu+1$":[168],"2^{\\nu^*}$.":[171],"As":[172,186],"consequence,":[174,188],"get":[176,190],"following":[178],"characterization:":[179],"$\\phi_m(G)=2^\\tau$":[180],"if":[181,184,192],"only":[183],"$\\nu^*=\\tau$.":[185],"$c$":[193],"length":[197],"chordless":[200],"then":[204],"$2^{\\nu/3^c}\\leq\\phi_m(G)\\leq":[205],"2^{c\\nu}$.":[206],"Finally,":[207],"techniques":[210],"introduced,":[211],"an":[214],"any":[224],"according":[227],"its":[229],"signed":[230]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
