{"id":"https://openalex.org/W2953826417","doi":"https://doi.org/10.3390/e21070630","title":"Stationary-State Statistics of a Binary Neural Network Model with Quenched Disorder","display_name":"Stationary-State Statistics of a Binary Neural Network Model with Quenched Disorder","publication_year":2019,"publication_date":"2019-06-26","ids":{"openalex":"https://openalex.org/W2953826417","doi":"https://doi.org/10.3390/e21070630","mag":"2953826417","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267344"},"language":"en","primary_location":{"id":"doi:10.3390/e21070630","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070630","pdf_url":"https://www.mdpi.com/1099-4300/21/7/630/pdf?version=1562128561","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/7/630/pdf?version=1562128561","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Diego Fasoli","orcid":"https://orcid.org/0000-0003-4278-6630"},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]},{"id":"https://openalex.org/I4210127676","display_name":"Center for Neuroscience and Cognitive Systems","ror":"https://ror.org/045yf0774","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210127676"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Diego Fasoli","raw_affiliation_strings":["Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy"],"raw_orcid":"https://orcid.org/0000-0003-4278-6630","affiliations":[{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I30771326"]}]},{"author_position":"last","author":{"id":null,"display_name":"Stefano Panzeri","orcid":"https://orcid.org/0000-0003-1700-8909"},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]},{"id":"https://openalex.org/I4210127676","display_name":"Center for Neuroscience and Cognitive Systems","ror":"https://ror.org/045yf0774","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210127676"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Panzeri","raw_affiliation_strings":["Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1700-8909","affiliations":[{"raw_affiliation_string":"Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia, 38068 Rovereto, Italy","institution_ids":["https://openalex.org/I4210127676","https://openalex.org/I30771326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I30771326","https://openalex.org/I4210127676"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1246,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.47338462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"7","first_page":"630","last_page":"630"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.6000000238418579,"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"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.6000000238418579,"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"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.13899999856948853,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.07800000160932541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.6148999929428101},{"id":"https://openalex.org/keywords/multistability","display_name":"Multistability","score":0.6097000241279602},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4927000105381012},{"id":"https://openalex.org/keywords/gumbel-distribution","display_name":"Gumbel distribution","score":0.4675999879837036},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.43560001254081726},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3955000042915344},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.3792000114917755},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3619999885559082}],"concepts":[{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.6148999929428101},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.6097000241279602},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5835000276565552},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5789999961853027},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4927000105381012},{"id":"https://openalex.org/C137610916","wikidata":"https://www.wikidata.org/wiki/Q1096862","display_name":"Gumbel distribution","level":3,"score":0.4675999879837036},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41359999775886536},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.3792000114917755},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3562999963760376},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C1602530","wikidata":"https://www.wikidata.org/wiki/Q1472677","display_name":"Heavy-tailed distribution","level":3,"score":0.273499995470047},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.27250000834465027},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26570001244544983},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C158557763","wikidata":"https://www.wikidata.org/wiki/Q5166603","display_name":"Convolution of probability distributions","level":4,"score":0.2540999948978424},{"id":"https://openalex.org/C166921843","wikidata":"https://www.wikidata.org/wiki/Q3776487","display_name":"Statistical parameter","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e21070630","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070630","pdf_url":"https://www.mdpi.com/1099-4300/21/7/630/pdf?version=1562128561","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33267344","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267344","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:1811.12153","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.12153","pdf_url":"https://arxiv.org/pdf/1811.12153","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":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:7c470c500da842b5ae24f7b00947bd80","is_oa":true,"landing_page_url":"https://doaj.org/article/7c470c500da842b5ae24f7b00947bd80","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 21, Iss 7, p 630 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/7/630/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21070630","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7515124","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515124","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21070630","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070630","pdf_url":"https://www.mdpi.com/1099-4300/21/7/630/pdf?version=1562128561","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2774275927","display_name":null,"funder_award_id":"602849","funder_id":"https://openalex.org/F4320315019","funder_display_name":"Simons Foundation Autism Research Initiative"},{"id":"https://openalex.org/G4505578710","display_name":null,"funder_award_id":"SFARI, Explorer Grant No. 602849","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G481323486","display_name":null,"funder_award_id":"602849","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320315019","display_name":"Simons Foundation Autism Research Initiative","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2953826417.pdf","grobid_xml":"https://content.openalex.org/works/W2953826417.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W216098040","https://openalex.org/W810648723","https://openalex.org/W1498550271","https://openalex.org/W1622584740","https://openalex.org/W1640265418","https://openalex.org/W1981045909","https://openalex.org/W1983272724","https://openalex.org/W1991904924","https://openalex.org/W1997387342","https://openalex.org/W2000567868","https://openalex.org/W2001102481","https://openalex.org/W2001170284","https://openalex.org/W2003894833","https://openalex.org/W2005686453","https://openalex.org/W2006912660","https://openalex.org/W2015780784","https://openalex.org/W2019016101","https://openalex.org/W2022494241","https://openalex.org/W2022820481","https://openalex.org/W2023970549","https://openalex.org/W2025205831","https://openalex.org/W2025604508","https://openalex.org/W2026119411","https://openalex.org/W2027802883","https://openalex.org/W2037707772","https://openalex.org/W2041533382","https://openalex.org/W2042192623","https://openalex.org/W2043725560","https://openalex.org/W2047900759","https://openalex.org/W2059668389","https://openalex.org/W2062657255","https://openalex.org/W2063294564","https://openalex.org/W2064512219","https://openalex.org/W2068227019","https://openalex.org/W2086841290","https://openalex.org/W2096886711","https://openalex.org/W2097311594","https://openalex.org/W2097965856","https://openalex.org/W2101954189","https://openalex.org/W2103934527","https://openalex.org/W2115354531","https://openalex.org/W2117144089","https://openalex.org/W2122456939","https://openalex.org/W2123042723","https://openalex.org/W2128084896","https://openalex.org/W2137101191","https://openalex.org/W2137761603","https://openalex.org/W2162717455","https://openalex.org/W2206067236","https://openalex.org/W2257652304","https://openalex.org/W2324099123","https://openalex.org/W2486232056","https://openalex.org/W2588583345","https://openalex.org/W2616843507","https://openalex.org/W2904683338","https://openalex.org/W3111293759","https://openalex.org/W4206502013","https://openalex.org/W4213382999","https://openalex.org/W4214712351","https://openalex.org/W4234536451","https://openalex.org/W4236154753","https://openalex.org/W4237925847","https://openalex.org/W6638945058","https://openalex.org/W6785693436","https://openalex.org/W6940179681"],"related_works":[],"abstract_inverted_index":{"In":[0,184],"this":[1,185],"paper,":[2],"we":[3,143,154,188,214],"study":[4,146],"the":[5,9,34,37,40,57,61,65,70,75,78,83,87,93,97,101,107,114,133,140,161,170,179,191,204,211,219,226,232,250,254],"statistical":[6],"properties":[7],"of":[8,13,39,56,60,69,74,77,82,96,100,113,116,132,139,150,164,199,202,218,222,231,243,249],"stationary":[10,62,102],"firing-rate":[11],"states":[12,63,103],"a":[14,194,240],"neural":[15],"network":[16,134],"model":[17,22],"with":[18,104],"quenched":[19],"disorder.":[20],"The":[21],"has":[23],"arbitrary":[24],"size,":[25],"discrete-time":[26],"evolution":[27],"equations":[28],"and":[29,36,64,81,135,172,176,246],"binary":[30],"firing":[31],"rates,":[32],"while":[33],"topology":[35],"strength":[38],"synaptic":[41,79,141,181],"connections":[42,80,166],"are":[43,127],"randomly":[44],"generated":[45,252],"from":[46],"known,":[47],"generally":[48],"arbitrary,":[49],"probability":[50,59,94,162],"distributions.":[51],"We":[52,237],"derived":[53,215],"semi-analytical":[54,125],"expressions":[55,126,217],"occurrence":[58],"mean":[66],"multistability":[67],"diagram":[68],"model,":[71],"in":[72,111,225,229],"terms":[73,112,230],"distribution":[76,95,138,163],"external":[84,108],"stimuli":[85],"to":[86,106,158],"network.":[88],"Our":[89],"calculations":[90],"rely":[91],"on":[92,147,169,178],"bifurcation":[98],"points":[99],"respect":[105],"stimuli,":[109],"calculated":[110,189],"permanent":[115],"special":[117],"matrices":[118],"using":[119],"extreme":[120],"value":[121],"theory.":[122],"While":[123],"our":[124,145,244],"exact":[128],"for":[129,136],"any":[130,137],"size":[131],"connections,":[142],"focus":[144],"networks":[148,224],"made":[149],"several":[151,200],"populations,":[152],"that":[153,160,197],"term":[155],"\"statistically":[156],"homogeneous\"":[157],"indicate":[159],"their":[165],"depends":[167],"only":[168],"pre-":[171],"post-synaptic":[173],"population":[174],"indexes,":[175],"not":[177],"individual":[180],"pair":[182],"indexes.":[183],"specific":[186],"case,":[187],"analytically":[190],"permanent,":[192],"obtaining":[193],"compact":[195],"formula":[196],"outperforms":[198],"orders":[201],"magnitude":[203],"Balasubramanian-Bax-Franklin-Glynn":[205],"algorithm.":[206],"To":[207],"conclude,":[208],"by":[209,253],"applying":[210],"Fisher-Tippett-Gnedenko":[212],"theorem,":[213],"asymptotic":[216],"stationary-state":[220],"statistics":[221],"multi-population":[223],"large-network-size":[227],"limit,":[228],"Gumbel":[233],"(double":[234],"exponential)":[235],"distribution.":[236],"also":[238],"provide":[239],"Python":[241],"implementation":[242],"formulas":[245],"some":[247],"examples":[248],"results":[251],"code.":[255]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2019-07-12T00:00:00"}
