{"id":"https://openalex.org/W2008831431","doi":"https://doi.org/10.1142/s0218127403006765","title":"FINDING CYCLES IN SYNCHRONOUS BOOLEAN NETWORKS WITH APPLICATIONS TO BIOCHEMICAL SYSTEMS","display_name":"FINDING CYCLES IN SYNCHRONOUS BOOLEAN NETWORKS WITH APPLICATIONS TO BIOCHEMICAL SYSTEMS","publication_year":2003,"publication_date":"2003-03-01","ids":{"openalex":"https://openalex.org/W2008831431","doi":"https://doi.org/10.1142/s0218127403006765","mag":"2008831431"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127403006765","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403006765","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5052400301","display_name":"Jack Heidel","orcid":null},"institutions":[{"id":"https://openalex.org/I122266389","display_name":"University of Nebraska at Omaha","ror":"https://ror.org/04yrkc140","country_code":"US","type":"education","lineage":["https://openalex.org/I122266389"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JACK HEIDEL","raw_affiliation_strings":["Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA","institution_ids":["https://openalex.org/I122266389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110618719","display_name":"John Maloney","orcid":null},"institutions":[{"id":"https://openalex.org/I122266389","display_name":"University of Nebraska at Omaha","ror":"https://ror.org/04yrkc140","country_code":"US","type":"education","lineage":["https://openalex.org/I122266389"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JOHN MALONEY","raw_affiliation_strings":["Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA","institution_ids":["https://openalex.org/I122266389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020819966","display_name":"Christopher L. Farrow","orcid":"https://orcid.org/0000-0001-5768-6654"},"institutions":[{"id":"https://openalex.org/I122266389","display_name":"University of Nebraska at Omaha","ror":"https://ror.org/04yrkc140","country_code":"US","type":"education","lineage":["https://openalex.org/I122266389"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"CHRISTOPHER FARROW","raw_affiliation_strings":["Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, USA","institution_ids":["https://openalex.org/I122266389"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112648342","display_name":"Jim Rogers","orcid":"https://orcid.org/0000-0001-9327-1245"},"institutions":[{"id":"https://openalex.org/I59130452","display_name":"University of Nebraska Medical Center","ror":"https://ror.org/00thqtb16","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I59130452"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. A. ROGERS","raw_affiliation_strings":["Department of Cell Biology and Anatomy, University of Nebraska Medical Center, Omaha, NE 68198-6395, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Cell Biology and Anatomy, University of Nebraska Medical Center, Omaha, NE 68198-6395, USA","institution_ids":["https://openalex.org/I59130452"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052400301"],"corresponding_institution_ids":["https://openalex.org/I122266389"],"apc_list":null,"apc_paid":null,"fwci":1.0308,"has_fulltext":false,"cited_by_count":186,"citation_normalized_percentile":{"value":0.73824006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"13","issue":"03","first_page":"535","last_page":"552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9988999962806702,"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":0.9988999962806702,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.9866999983787537,"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/T10932","display_name":"Microbial Metabolic Engineering and Bioproduction","score":0.9800999760627747,"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/boolean-network","display_name":"Boolean network","score":0.7533395886421204},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.668121337890625},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6139540076255798},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5791923999786377},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5644670724868774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5269508957862854},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48950421810150146},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.46683183312416077},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4268845021724701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.408571720123291},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35367822647094727},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27402058243751526},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10119068622589111},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08220738172531128}],"concepts":[{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.7533395886421204},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.668121337890625},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6139540076255798},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5791923999786377},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5644670724868774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5269508957862854},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48950421810150146},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.46683183312416077},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4268845021724701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.408571720123291},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35367822647094727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27402058243751526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10119068622589111},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08220738172531128},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127403006765","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403006765","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W38710637","https://openalex.org/W577890094","https://openalex.org/W985433685","https://openalex.org/W1491459594","https://openalex.org/W1514205146","https://openalex.org/W1540439229","https://openalex.org/W1556027180","https://openalex.org/W1572584518","https://openalex.org/W1968863900","https://openalex.org/W1971224531","https://openalex.org/W1979239128","https://openalex.org/W1981369758","https://openalex.org/W1988602492","https://openalex.org/W2015869454","https://openalex.org/W2020097836","https://openalex.org/W2027634124","https://openalex.org/W2027789855","https://openalex.org/W2031369606","https://openalex.org/W2043186887","https://openalex.org/W2050303734","https://openalex.org/W2053004995","https://openalex.org/W2054013790","https://openalex.org/W2078834769","https://openalex.org/W2092182389","https://openalex.org/W2100416355","https://openalex.org/W2102240278","https://openalex.org/W2105291362","https://openalex.org/W2106916378","https://openalex.org/W2109677752","https://openalex.org/W2112175922","https://openalex.org/W2160077776","https://openalex.org/W2167652445","https://openalex.org/W2323658858","https://openalex.org/W4233002499","https://openalex.org/W4251606455","https://openalex.org/W4252639814","https://openalex.org/W4388252848"],"related_works":["https://openalex.org/W2075451905","https://openalex.org/W2075126249","https://openalex.org/W2105128170","https://openalex.org/W2918709778","https://openalex.org/W2012388690","https://openalex.org/W1991822629","https://openalex.org/W3141532631","https://openalex.org/W52722086","https://openalex.org/W2495550620","https://openalex.org/W2995277268"],"abstract_inverted_index":{"This":[0,153,201],"paper":[1],"is":[2,11,41,113,154,202,226,265],"an":[3],"analytical":[4],"study":[5],"of":[6,47,78,105,117,147,160,220],"Boolean":[7,44,71,97],"networks.":[8,28],"The":[9,29,108,261],"motivation":[10],"our":[12],"desire":[13],"to":[14,91,210,250],"understand":[15],"the":[16,42,53,101,114,123,144,158,161,172,177,183,212,231,243,255],"large,":[17],"complicated":[18],"and":[19,103,215,271],"interconnected":[20],"pathways":[21],"which":[22,79,170,175,253],"comprise":[23],"intracellular":[24],"biochemical":[25,276],"signal":[26,36],"transduction":[27,37],"simplest":[30],"possible":[31],"conceptual":[32],"model":[33],"that":[34,206,242],"mimics":[35],"with":[38],"sigmoidal":[39],"kinetics":[40],"n-node":[43],"network":[45,72,98,162,244],"each":[46,180],"whose":[48],"elements":[49],"or":[50,57,88,131],"nodes":[51],"has":[52,73],"value":[54],"0":[55],"(off)":[56],"1":[58],"(on)":[59],"at":[60,179,187],"any":[61,221],"given":[62],"time":[63,189],"T":[64],"=":[65],"0,":[66],"1,":[67],"2,":[68],"\u2026.":[69],"A":[70],"2":[74,150],"n":[75,120,140,151,167],"states":[76,118],"all":[77,149,191],"are":[80,126,278],"either":[81],"on":[82,137],"periodic":[83,218],"cycles":[84,219,233],"(including":[85,274],"fixed":[86,192,213],"points)":[87],"transients":[89],"leading":[90],"cycles.":[92,107],"Thus":[93,134],"one":[94,110,185],"understands":[95],"a":[96,188,203,235,266],"by":[99,166],"determining":[100],"number":[102,116],"length":[104],"its":[106],"problem":[109],"must":[111],"circumvent":[112],"large":[115,217,236],"(2":[119],")":[121],"since":[122],"networks":[124],"we":[125,135,239],"interested":[127],"in":[128,229,234],"have":[129],"100":[130],"more":[132,259],"elements.":[133],"concentrate":[136],"developing":[138],"size":[139,222],"methods":[141],"rather":[142],"than":[143],"impossible":[145],"task":[146],"enumerating":[148],"states.":[152],"done":[155],"as":[156],"follows:":[157],"dynamics":[159],"can":[163,207,246],"be":[164,208,248],"described":[165],"polynomial":[168],"equations":[169,184,245,263],"describe":[171],"logical":[173],"function":[174],"determines":[176],"interaction":[178],"node.":[181],"Iterating":[182],"step":[186],"finds":[190],"points,":[193],"period":[194,197],"two":[195],"cycles,":[196,199],"three":[198],"etc.":[200],"general":[204],"method":[205,264,270],"used":[209],"determine":[211],"points":[214],"moderately":[216],"network,":[223],"but":[224],"it":[225],"not":[227],"useful":[228],"finding":[230],"largest":[232],"network.":[237],"However,":[238],"also":[240],"show":[241],"often":[247],"reduced":[249],"scalar":[251,262],"form,":[252],"makes":[254],"cycle":[256],"structure":[257],"much":[258],"transparent.":[260],"true":[267],"\"size":[268],"n\"":[269],"several":[272],"examples":[273],"nontrivial":[275],"systems)":[277],"examined.":[279]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":9}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}