{"id":"https://openalex.org/W4285173968","doi":"https://doi.org/10.1109/tac.2022.3175931","title":"Stability Analysis of Probabilistic Boolean Networks With Switching Discrete Probability Distribution","display_name":"Stability Analysis of Probabilistic Boolean Networks With Switching Discrete Probability Distribution","publication_year":2022,"publication_date":"2022-05-19","ids":{"openalex":"https://openalex.org/W4285173968","doi":"https://doi.org/10.1109/tac.2022.3175931"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3175931","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3175931","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5102798047","display_name":"Xinrong Yang","orcid":"https://orcid.org/0000-0002-1151-4686"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinrong Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100453276","display_name":"Haitao Li","orcid":"https://orcid.org/0000-0001-5322-5375"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haitao Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102798047"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":null,"apc_paid":null,"fwci":1.544,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82713675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"68","issue":"4","first_page":"2506","last_page":"2512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":1.0,"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":1.0,"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/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9824000000953674,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9603999853134155,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.7701190710067749},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.655890703201294},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.564974844455719},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5572195053100586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5199562311172485},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4620456397533417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3590221405029297},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35171955823898315},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3206910490989685},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09843552112579346}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.7701190710067749},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.655890703201294},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.564974844455719},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5572195053100586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5199562311172485},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4620456397533417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3590221405029297},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35171955823898315},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3206910490989685},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09843552112579346},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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":1,"locations":[{"id":"doi:10.1109/tac.2022.3175931","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3175931","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2533198692","display_name":null,"funder_award_id":"62073202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W821019010","https://openalex.org/W1494628843","https://openalex.org/W1971318969","https://openalex.org/W2006811029","https://openalex.org/W2041443351","https://openalex.org/W2049480816","https://openalex.org/W2052873276","https://openalex.org/W2063896427","https://openalex.org/W2073775042","https://openalex.org/W2073902307","https://openalex.org/W2090997347","https://openalex.org/W2146917465","https://openalex.org/W2160533336","https://openalex.org/W2166384194","https://openalex.org/W2188238115","https://openalex.org/W2337379798","https://openalex.org/W2486512961","https://openalex.org/W2582212316","https://openalex.org/W2594786382","https://openalex.org/W2598182031","https://openalex.org/W2610723735","https://openalex.org/W2619974965","https://openalex.org/W2753793742","https://openalex.org/W2801151173","https://openalex.org/W2801370262","https://openalex.org/W2904868358","https://openalex.org/W2911854602","https://openalex.org/W2946477357","https://openalex.org/W2947430442","https://openalex.org/W2954808819","https://openalex.org/W2963258918","https://openalex.org/W2965903271","https://openalex.org/W2967826606","https://openalex.org/W2997622225","https://openalex.org/W3002009436","https://openalex.org/W3011204164","https://openalex.org/W3037018960","https://openalex.org/W3049548713","https://openalex.org/W3104286328","https://openalex.org/W3122366485","https://openalex.org/W3129739660","https://openalex.org/W3140409016","https://openalex.org/W3141467375","https://openalex.org/W3159128651","https://openalex.org/W3159860971","https://openalex.org/W3181786550"],"related_works":["https://openalex.org/W2943623134","https://openalex.org/W2494523064","https://openalex.org/W2215759665","https://openalex.org/W2030292806","https://openalex.org/W2960358116","https://openalex.org/W4287727129","https://openalex.org/W3041172967","https://openalex.org/W2749065928","https://openalex.org/W2147155098","https://openalex.org/W2009776842"],"abstract_inverted_index":{"This":[0],"article":[1],"analyzes":[2],"the":[3,17,32,40,66,80,93,96,110],"stability":[4,68,71],"of":[5,19,35,49,51,72,82,95,112],"probabilistic":[6],"Boolean":[7],"networks":[8],"(PBNs)":[9],"with":[10,21,74,118],"switching":[11,22,75,119],"discrete":[12],"probability":[13],"distribution":[14],"(DPD).":[15],"First,":[16],"dynamics":[18],"PBNs":[20,73,117],"DPD":[23,76],"is":[24,102],"converted":[25],"to":[26,79,91,115],"an":[27],"algebraic":[28,41],"form":[29],"by":[30,77],"using":[31],"semitensor":[33],"product":[34],"matrices.":[36],"Second,":[37],"based":[38],"on":[39],"form,":[42],"two":[43,85],"essential":[44],"concepts,":[45],"that":[46],"is,":[47],"expectation":[48,56],"number":[50],"trajectories":[52],"(ENT)":[53],"and":[54,69],"state":[55],"matrix,":[57],"are":[58,63,88],"proposed.":[59],"Third,":[60],"some":[61],"criteria":[62],"presented":[64],"for":[65,105],"finite-time":[67],"asymptotical":[70],"resorting":[78],"properties":[81],"ENT.":[83],"Finally,":[84],"illustrative":[86],"examples":[87],"worked":[89],"out":[90],"show":[92],"effectiveness":[94],"obtained":[97],"new":[98],"results.":[99],"Computational":[100],"complexity":[101],"still":[103],"challenging":[104],"this":[106],"article,":[107],"which":[108],"limits":[109],"application":[111],"ENT-based":[113],"framework":[114],"large-size":[116],"DPD.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}