{"id":"https://openalex.org/W1670128905","doi":"https://doi.org/10.1109/cdc.1993.325904","title":"The tight upper bound on the number of stationary points in Hopfield networks","display_name":"The tight upper bound on the number of stationary points in Hopfield networks","publication_year":2002,"publication_date":"2002-12-30","ids":{"openalex":"https://openalex.org/W1670128905","doi":"https://doi.org/10.1109/cdc.1993.325904","mag":"1670128905"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.1993.325904","doi":"https://doi.org/10.1109/cdc.1993.325904","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.1993.325904","pdf_url":null,"source":{"id":"https://openalex.org/S4210221977","display_name":"IEEE Conference on Decision and Control (CDC)","issn_l":"0191-2216","issn":["0191-2216"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of 32nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","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/A5110044239","display_name":"Y. Shrivastava","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y. Shrivastava","raw_affiliation_strings":["Industrial Control Systems, Newcastle, NSW, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Control Systems, Newcastle, NSW, Australia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003042086","display_name":"Soura Dasgupta","orcid":"https://orcid.org/0000-0001-6633-2938","observed_orcids":["https://orcid.org/0000-0001-6633-2938"]},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Dasgupta","raw_affiliation_strings":["Department Of Electrical And Computer Engineering, University of Iowa, IA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Of Electrical And Computer Engineering, University of Iowa, IA, USA","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.07462598,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"3682","last_page":"3687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10581","display_name":"Neural dynamics and brain function","score":0.00019999999494757503,"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/hopfield-neural-network","display_name":"Hopfield neural network","score":0.9580000042915344},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.9800000190734863},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.6570000052452087},{"id":"https://openalex.org/keywords/graph-theoretic-characterization","display_name":"graph-theoretic characterization","score":0.878000020980835}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7803231477737427},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.7631679773330688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5572322010993958},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5092364549636841},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49493879079818726},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4898931384086609},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46033984422683716},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.45048025250434875},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4346253275871277},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42410194873809814},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.40569543838500977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3796752691268921},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23953291773796082},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0692327618598938},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0687873363494873},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.1993.325904","doi":"https://doi.org/10.1109/cdc.1993.325904","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.1993.325904","pdf_url":null,"source":{"id":"https://openalex.org/S4210221977","display_name":"IEEE Conference on Decision and Control (CDC)","issn_l":"0191-2216","issn":["0191-2216"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of 32nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1543281322","https://openalex.org/W1980769375","https://openalex.org/W1983197517","https://openalex.org/W1984431842","https://openalex.org/W2000133822","https://openalex.org/W2059146732","https://openalex.org/W2064817282","https://openalex.org/W2087567316","https://openalex.org/W2103543018","https://openalex.org/W2112246162","https://openalex.org/W2128084896"],"related_works":["https://openalex.org/W3161249958","https://openalex.org/W1868759028","https://openalex.org/W1535472682","https://openalex.org/W2014897004","https://openalex.org/W4417520224","https://openalex.org/W2206753421","https://openalex.org/W2128299841","https://openalex.org/W1559492231","https://openalex.org/W1674138889","https://openalex.org/W1767641048"],"abstract_inverted_index":{"This":[0],"paper":[1],"derives":[2],"the":[3,8,44,49,65],"tight":[4,45],"upper":[5,46],"bound":[6,47],"on":[7,48],"number":[9,50],"of":[10,25,51,54,64],"stationary":[11,52],"points":[12,53],"that":[13,29,39],"an":[14,55],"nth":[15],"order":[16],"Hopfield":[17,57],"network":[18,32],"can":[19],"have,":[20],"and":[21],"provides":[22],"a":[23,31],"characterization":[24,63],"synaptic":[26],"sign":[27],"patterns":[28],"allow":[30],"to":[33],"achieve":[34],"this":[35],"capacity.":[36],"We":[37],"show":[38],"n/sup":[40],"C//sub":[41],"[/n/2]":[42],"is":[43,69],"n-order":[56],"network.":[58],"A":[59],"simple":[60],"graph":[61],"theoretic":[62],"maximum":[66],"capacity":[67],"networks":[68],"given.>":[70]},"counts_by_year":[],"updated_date":"2026-10-26T11:51:55.731654","created_date":"2016-06-24T00:00:00"}