{"id":"https://openalex.org/W1982058975","doi":"https://doi.org/10.1137/100802384","title":"Truth-Content and Phase Transitions of Random Boolean Networks with Generic Logics","display_name":"Truth-Content and Phase Transitions of Random Boolean Networks with Generic Logics","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1982058975","doi":"https://doi.org/10.1137/100802384","mag":"1982058975"},"language":"en","primary_location":{"id":"doi:10.1137/100802384","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100802384","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","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/A5077974832","display_name":"Dominik M. Wittmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominik M. Wittmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055276829","display_name":"Sabrina Hock","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabrina Hock","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083128670","display_name":"Fabian J. Theis","orcid":"https://orcid.org/0000-0002-2419-1943"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabian J. Theis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1496,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55659091,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"1","first_page":"315","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9707000255584717,"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":0.6742438077926636},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6321420073509216},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5204234719276428},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5152059197425842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5058652758598328},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.4978790283203125},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.48549702763557434},{"id":"https://openalex.org/keywords/boolean-model","display_name":"Boolean model","score":0.46752217411994934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43773525953292847},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4052931070327759},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.38538846373558044},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.343807190656662},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33359652757644653},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1034633219242096},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08951941132545471}],"concepts":[{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.6742438077926636},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6321420073509216},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5204234719276428},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5152059197425842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5058652758598328},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.4978790283203125},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.48549702763557434},{"id":"https://openalex.org/C67499762","wikidata":"https://www.wikidata.org/wiki/Q4943358","display_name":"Boolean model","level":2,"score":0.46752217411994934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43773525953292847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4052931070327759},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.38538846373558044},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.343807190656662},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33359652757644653},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1034633219242096},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08951941132545471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100802384","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100802384","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:opus-zb.helmholtz-muenchen.de:24281","is_oa":false,"landing_page_url":"https://push-zb.helmholtz-muenchen.de/frontdoor.php?source_opus=24281","pdf_url":null,"source":{"id":"https://openalex.org/S4377196115","display_name":"Site cant be reached","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":"SIAM J. Appl. Dyn. Syst. 12, 315-351 (2013)","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W138391281","https://openalex.org/W1573241742","https://openalex.org/W1581536631","https://openalex.org/W1599969036","https://openalex.org/W1886819223","https://openalex.org/W1970441315","https://openalex.org/W1971224531","https://openalex.org/W1980706331","https://openalex.org/W1985351346","https://openalex.org/W1990049347","https://openalex.org/W1991942070","https://openalex.org/W1994892791","https://openalex.org/W1995489344","https://openalex.org/W2003540754","https://openalex.org/W2008633581","https://openalex.org/W2009920385","https://openalex.org/W2028223005","https://openalex.org/W2044873481","https://openalex.org/W2046557303","https://openalex.org/W2053961182","https://openalex.org/W2064547210","https://openalex.org/W2065178468","https://openalex.org/W2076630162","https://openalex.org/W2081466838","https://openalex.org/W2096813836","https://openalex.org/W2097263107","https://openalex.org/W2097329148","https://openalex.org/W2099807710","https://openalex.org/W2108020239","https://openalex.org/W2118572979","https://openalex.org/W2121264243","https://openalex.org/W2125886217","https://openalex.org/W2126602684","https://openalex.org/W2130954044","https://openalex.org/W2134237864","https://openalex.org/W2142170851","https://openalex.org/W2160145365","https://openalex.org/W3101295759","https://openalex.org/W3102698487","https://openalex.org/W4211017114"],"related_works":["https://openalex.org/W1979056074","https://openalex.org/W3141532631","https://openalex.org/W2131164334","https://openalex.org/W4252281389","https://openalex.org/W2061512596","https://openalex.org/W1972685147","https://openalex.org/W3042206271","https://openalex.org/W1604438253","https://openalex.org/W2020667380","https://openalex.org/W2132980130"],"abstract_inverted_index":{"One":[0],"distinguishes":[1],"between":[2,210],"qualitative":[3],"and":[4,73,173,213],"Boolean":[5,29,38,63,84,156,191],"models":[6,12,30,57,64],"of":[7,33,46,71,106,109,119,125,189,216,235,247,252,261],"gene":[8],"regulatory":[9],"networks.":[10,207],"Qualitative":[11,56],"are":[13,89,158],"directed":[14],"graphs":[15],"with":[16,168,193],"signed":[17],"edges":[18],"according":[19,50],"to":[20,51,142,160,182,198],"whether":[21],"an":[22,77],"interaction":[23],"is":[24,36,101,122,218],"activating":[25,72],"or":[26],"inhibiting.":[27],"In":[28,129,220],"each":[31],"node":[32],"the":[34,44,47,107,116,126,132,187,214,233,245,250,258],"network":[35],"a":[37,52,102,135,165,174,200],"variable":[39],"whose":[40,86,150],"value":[41],"depends":[42],"on":[43],"values":[45],"node's":[48],"regulators":[49],"specific":[53],"update":[54,78,87],"rule.":[55,79],"can":[58],"be":[59],"systematically":[60],"converted":[61],"into":[62,76,244],"via":[65],"generic":[66,92,194],"logics,":[67],"which":[68,100,254],"allow":[69,196],"combination":[70],"inhibiting":[74],"influences":[75],"Here,":[80],"we":[81,223],"investigate":[82],"random":[83,190],"networks":[85,147,149,157,192],"rules":[88],"generated":[90],"using":[91],"logics.":[93],"We":[94,113,144],"begin":[95],"by":[96,178],"studying":[97],"their":[98],"truth-content,":[99],"mean":[103,237],"field":[104,238],"approximation":[105],"fraction":[108],"ones":[110],"(true":[111],"nodes).":[112],"prove":[114],"that":[115],"asymptotic":[117],"behavior":[118,138],"this":[120],"quantity":[121],"essentially":[123],"independent":[124],"initial":[127],"conditions.":[128],"numeric":[130,221],"analyses,":[131],"truth-content":[133,188],"exhibits":[134],"rich":[136],"dynamical":[137],"including":[139],"period-doublings":[140],"leading":[141],"chaos.":[143],"define":[145],"truth-stable":[146],"as":[148],"truth-contents":[151],"exhibit":[152],"non-chaotic":[153],"dynamics.":[154],"Random":[155],"known":[159],"exist":[161],"in":[162,205],"two":[163],"phases:":[164],"frozen":[166],"phase":[167,176,203,211],"stable":[169],"short":[170],"periodic":[171],"dynamics":[172],"chaotic":[175],"characterized":[177],"long-periodic":[179],"attractors":[180],"sensitive":[181],"perturbations.":[183],"Our":[184,240],"results":[185,241],"about":[186],"logics":[195],"us":[197],"derive":[199],"criterion":[201],"for":[202],"transitions":[204,212],"these":[206],"The":[208],"relation":[209],"concept":[215],"truth-stability":[217],"studied.":[219],"analyses":[222],"find":[224],"multiple,":[225],"intricately":[226],"shaped":[227],"critical":[228],"boundaries.":[229],"Simulations":[230],"further":[231],"strengthen":[232],"significance":[234],"our":[236],"results.":[239],"nicely":[242],"fit":[243],"theory":[246],"\u201cliving":[248],"at":[249,256],"edge":[251],"chaos,\u201d":[253],"aims":[255],"elucidating":[257],"crucial":[259],"properties":[260],"evolvable":[262],"biological":[263],"systems.":[264]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
