{"id":"https://openalex.org/W2075126249","doi":"https://doi.org/10.1142/s0218127405013277","title":"REALIZATION AND BIFURCATION OF BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS","display_name":"REALIZATION AND BIFURCATION OF BOOLEAN FUNCTIONS VIA CELLULAR NEURAL NETWORKS","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2075126249","doi":"https://doi.org/10.1142/s0218127405013277","mag":"2075126249"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405013277","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013277","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/A5088079072","display_name":"Fangyue Chen","orcid":"https://orcid.org/0000-0002-5440-3206"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FANGYUE CHEN","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"GUANRONG CHEN","raw_affiliation_strings":["Department of Electronic Engineering, City University of Hong Kong, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4619,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.91209394,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"15","issue":"07","first_page":"2109","last_page":"2129"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.8295842409133911},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.8091025352478027},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.6563061475753784},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5354004502296448},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.5308939814567566},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.5229742527008057},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.49729683995246887},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.45506972074508667},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4512729048728943},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4436595141887665},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4420086443424225},{"id":"https://openalex.org/keywords/binary-function","display_name":"Binary function","score":0.4262385666370392},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4244208335876465},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.41062912344932556},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4087934195995331},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3258296847343445},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3223038911819458},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.17417269945144653},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14411014318466187},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13860121369361877},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0634327232837677}],"concepts":[{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.8295842409133911},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.8091025352478027},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.6563061475753784},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5354004502296448},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.5308939814567566},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.5229742527008057},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.49729683995246887},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.45506972074508667},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4512729048728943},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4436595141887665},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4420086443424225},{"id":"https://openalex.org/C105462591","wikidata":"https://www.wikidata.org/wiki/Q3737844","display_name":"Binary function","level":3,"score":0.4262385666370392},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4244208335876465},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.41062912344932556},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4087934195995331},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3258296847343445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3223038911819458},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.17417269945144653},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14411014318466187},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13860121369361877},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0634327232837677},{"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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127405013277","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405013277","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.622.9816","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.622.9816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ee.cityu.edu.hk/~gchen/pdf/LSBF.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1509576544","https://openalex.org/W1570173134","https://openalex.org/W1606202192","https://openalex.org/W1971768740","https://openalex.org/W1974011730","https://openalex.org/W2004315890","https://openalex.org/W2056717940","https://openalex.org/W2107025852","https://openalex.org/W2109812597","https://openalex.org/W2126137056","https://openalex.org/W2130416988","https://openalex.org/W2151162785","https://openalex.org/W2156484806","https://openalex.org/W2160121923","https://openalex.org/W2164046457","https://openalex.org/W2292208776","https://openalex.org/W2894564506","https://openalex.org/W3122808755","https://openalex.org/W4240240399"],"related_works":["https://openalex.org/W155681467","https://openalex.org/W2735569833","https://openalex.org/W64805845","https://openalex.org/W2995617542","https://openalex.org/W4243221174","https://openalex.org/W3141532631","https://openalex.org/W2131164334","https://openalex.org/W4383066791","https://openalex.org/W4231391991","https://openalex.org/W4322827077"],"abstract_inverted_index":{"In":[0],"this":[1,122],"work,":[2,123],"we":[3,51,124],"study":[4],"the":[5,23,27,30,39,42,49,110,128,152],"realization":[6],"and":[7,29,67,98,134],"bifurcation":[8],"of":[9,12,32,41,64,86,114,146,154],"Boolean":[10,62,77,89,107],"functions":[11,63,78],"four":[13,65,115],"variables":[14],"via":[15,79],"a":[16],"Cellular":[17],"Neural":[18],"Network":[19],"(CNN).":[20],"We":[21],"characterize":[22],"basic":[24],"relations":[25],"between":[26],"genes":[28,101],"offsets":[31],"an":[33,69,80,95],"uncoupled":[34,81,96],"CNN":[35,100,111,130],"as":[36,38],"well":[37],"basis":[40],"binary":[43],"input":[44],"vectors":[45],"set.":[46],"Based":[47],"on":[48],"analysis,":[50],"have":[52],"rigorously":[53],"proved":[54],"that":[55,102,127],"there":[56],"are":[57,103],"exactly":[58],"1882":[59],"linearly":[60,75,87],"separable":[61,76,88],"variables,":[66,116],"found":[68],"effective":[70],"method":[71],"for":[72],"realizing":[73],"all":[74,99],"CNN.":[82],"Consequently,":[83],"any":[84],"kind":[85],"function":[90],"can":[91,117],"be":[92,118],"implemented":[93],"by":[94,132],"CNN,":[97],"associated":[104],"with":[105],"these":[106],"functions,":[108],"called":[109],"gene":[112],"bank":[113],"easily":[119],"determined.":[120],"Through":[121],"will":[125],"show":[126],"standard":[129],"invented":[131],"Chua":[133],"Yang":[135],"in":[136,144,151],"1988":[137],"indeed":[138],"is":[139],"very":[140],"essential":[141],"not":[142],"only":[143],"terms":[145],"engineering":[147],"applications":[148],"but":[149],"also":[150],"sense":[153],"fundamental":[155],"mathematics.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}