{"id":"https://openalex.org/W2112246162","doi":"https://doi.org/10.1073/pnas.81.10.3088","title":"Neurons with graded response have collective computational properties like those of two-state neurons.","display_name":"Neurons with graded response have collective computational properties like those of two-state neurons.","publication_year":1984,"publication_date":"1984-05-01","ids":{"openalex":"https://openalex.org/W2112246162","doi":"https://doi.org/10.1073/pnas.81.10.3088","mag":"2112246162","pmid":"https://pubmed.ncbi.nlm.nih.gov/6587342"},"language":"en","primary_location":{"id":"doi:10.1073/pnas.81.10.3088","doi":"https://doi.org/10.1073/pnas.81.10.3088","is_oa":false,"landing_page_url":"https://doi.org/10.1073/pnas.81.10.3088","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","erih-plus","jufo-3","ki-jl-3","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/345226","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001584643","display_name":"J. J. Hopfield","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J J Hopfield","raw_affiliation_strings":["Bell Laboratories, Murray Hill, NJ 07974","Divisions of Chemistry and Biology, California Institute of Technology, Pasadena, CA 91125; and"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Murray Hill, NJ 07974","institution_ids":[]},{"raw_affiliation_string":"Divisions of Chemistry and Biology, California Institute of Technology, Pasadena, CA 91125; and","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001584643"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":26.6397,"has_fulltext":false,"cited_by_count":6906,"citation_normalized_percentile":{"value":0.99905762,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"81","issue":"10","first_page":"3088","last_page":"3092"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.5737000107765198,"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":0.5737000107765198,"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/T10320","display_name":"Neural Networks and Applications","score":0.39579999446868896,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.006500000134110451,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mcculloch-pitts-neuron","display_name":"McCulloch-Pitts neuron","score":0.8980000019073486},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"content-addressable memory","score":0.8849999904632568},{"id":"https://openalex.org/keywords/deterministic-neural-networks","display_name":"deterministic neural networks","score":0.6439999938011169},{"id":"https://openalex.org/keywords/action-potential","display_name":"action potential","score":0.9020000100135803},{"id":"https://openalex.org/keywords/neural-network-model","display_name":"neural network model","score":0.5099999904632568}],"concepts":[{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.7331700325012207},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6238055229187012},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.5620788335800171},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5444314479827881},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5438232421875},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5213778614997864},{"id":"https://openalex.org/C100339178","wikidata":"https://www.wikidata.org/wiki/Q2548752","display_name":"Collective behavior","level":2,"score":0.5164147019386292},{"id":"https://openalex.org/C2779513410","wikidata":"https://www.wikidata.org/wiki/Q25351567","display_name":"Credence","level":2,"score":0.4697701632976532},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4410936236381531},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.37742146849632263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2921622097492218},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2708166241645813},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26015645265579224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.17098477482795715},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.13593009114265442},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08455908298492432},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004553","descriptor_name":"Electric Conductivity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004553","descriptor_name":"Electric Conductivity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004553","descriptor_name":"Electric Conductivity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008433","descriptor_name":"Mathematics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false}],"locations_count":4,"locations":[{"id":"doi:10.1073/pnas.81.10.3088","doi":"https://doi.org/10.1073/pnas.81.10.3088","is_oa":false,"landing_page_url":"https://doi.org/10.1073/pnas.81.10.3088","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","erih-plus","jufo-3","ki-jl-3","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},{"id":"pmid:6587342","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/6587342","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,"listed_in":[],"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":"Proceedings of the National Academy of Sciences of the United States of America","raw_type":"Comparative Study"},{"id":"pmh:oai:pubmedcentral.nih.gov:345226","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/345226","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc Natl Acad Sci U S A","raw_type":"Text"},{"id":"pmh:oai:authors.library.caltech.edu:7748","doi":null,"is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:HOPpnas84","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:345226","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/345226","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc Natl Acad Sci U S A","raw_type":"Text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W582196039","https://openalex.org/W1504026171","https://openalex.org/W1973108021","https://openalex.org/W1986759597","https://openalex.org/W2024060531","https://openalex.org/W2031369606","https://openalex.org/W2128084896"],"related_works":["https://openalex.org/W2324869209","https://openalex.org/W4385957115","https://openalex.org/W2061372042","https://openalex.org/W3047779762","https://openalex.org/W2304903823","https://openalex.org/W2212640847","https://openalex.org/W4236768710","https://openalex.org/W2513089610","https://openalex.org/W2079637762","https://openalex.org/W2341378690"],"abstract_inverted_index":{"A":[0],"model":[1,32,51,111],"for":[2,82,117],"a":[3,9,106],"large":[4],"network":[5],"of":[6,48,79,91,101,133],"\"neurons\"":[7],"with":[8,28],"graded":[10,57,123,138],"response":[11,58,124,139],"(or":[12],"sigmoid":[13],"input-output":[14],"relation)":[15],"is":[16,71,126],"studied.":[17],"This":[18],"deterministic":[19],"system":[20,140],"has":[21],"collective":[22,46,64,99],"properties":[23,47,65,81],"in":[24,55,68,136],"very":[25],"close":[26],"correspondence":[27],"the":[29,49,56,76,92,102,131,137],"earlier":[30],"stochastic":[31],"based":[33],"on":[34],"McCulloch":[35],"-":[36],"Pitts":[37],"neurons.":[38],"The":[39,60,98,109],"content-":[40],"addressable":[41],"memory":[42],"and":[43],"other":[44],"emergent":[45],"original":[50,110],"also":[52,142],"are":[53,66,141],"present":[54],"model.":[59],"idea":[61],"that":[62,129],"such":[63,80],"used":[67],"biological":[69,85],"systems":[70,125],"given":[72],"added":[73],"credence":[74],"by":[75],"continued":[77],"presence":[78],"more":[83],"nearly":[84],"\"neurons.\"":[86],"Collective":[87],"analog":[88],"electrical":[89],"circuits":[90],"kind":[93],"described":[94],"will":[95,112],"certainly":[96],"function.":[97],"states":[100],"two":[103],"models":[104],"have":[105],"simple":[107],"correspondence.":[108],"continue":[113],"to":[114,122],"be":[115],"useful":[116],"simulations,":[118],"because":[119],"its":[120],"connection":[121],"established.":[127],"Equations":[128],"include":[130],"effect":[132],"action":[134],"potentials":[135],"developed.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":116},{"year":2025,"cited_by_count":213},{"year":2024,"cited_by_count":147},{"year":2023,"cited_by_count":180},{"year":2022,"cited_by_count":152},{"year":2021,"cited_by_count":146},{"year":2020,"cited_by_count":163},{"year":2019,"cited_by_count":120},{"year":2018,"cited_by_count":142},{"year":2017,"cited_by_count":123},{"year":2016,"cited_by_count":130},{"year":2015,"cited_by_count":123},{"year":2014,"cited_by_count":156},{"year":2013,"cited_by_count":201},{"year":2012,"cited_by_count":166}],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2025-10-10T00:00:00"}