{"id":"https://openalex.org/W2158348181","doi":"https://doi.org/10.1155/2012/571358","title":"Hopfield Neural Networks with Unbounded Monotone Activation Functions","display_name":"Hopfield Neural Networks with Unbounded Monotone Activation Functions","publication_year":2012,"publication_date":"2012-12-31","ids":{"openalex":"https://openalex.org/W2158348181","doi":"https://doi.org/10.1155/2012/571358","mag":"2158348181"},"language":"en","primary_location":{"id":"doi:10.1155/2012/571358","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/571358","pdf_url":"https://downloads.hindawi.com/archive/2012/571358.pdf","source":{"id":"https://openalex.org/S202405347","display_name":"Advances in Artificial Neural Systems","issn_l":"1687-7594","issn":["1687-7594","1687-7608"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Artificial Neural Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2012/571358.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038108964","display_name":"Nasser\u2010eddine Tatar","orcid":"https://orcid.org/0000-0003-3467-230X"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Nasser-eddine Tatar","raw_affiliation_strings":["Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038108964"],"corresponding_institution_ids":["https://openalex.org/I134085113"],"apc_list":null,"apc_paid":null,"fwci":1.2844,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84168846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.965499997138977,"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/monotone-polygon","display_name":"Monotone polygon","score":0.8478472232818604},{"id":"https://openalex.org/keywords/hopfield-network","display_name":"Hopfield network","score":0.6920912861824036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6809056997299194},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6739532351493835},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.6441330909729004},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6147301197052002},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.521992564201355},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3613011837005615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3436703681945801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.296875},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19686388969421387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08750289678573608}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.8478472232818604},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.6920912861824036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6809056997299194},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6739532351493835},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6441330909729004},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6147301197052002},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.521992564201355},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3613011837005615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3436703681945801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.296875},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19686388969421387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08750289678573608},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1155/2012/571358","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/571358","pdf_url":"https://downloads.hindawi.com/archive/2012/571358.pdf","source":{"id":"https://openalex.org/S202405347","display_name":"Advances in Artificial Neural Systems","issn_l":"1687-7594","issn":["1687-7594","1687-7608"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Artificial Neural Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1155/2012/571358","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/571358","pdf_url":"https://downloads.hindawi.com/archive/2012/571358.pdf","source":{"id":"https://openalex.org/S202405347","display_name":"Advances in Artificial Neural Systems","issn_l":"1687-7594","issn":["1687-7594","1687-7608"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Artificial Neural Systems","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G4287841813","display_name":null,"funder_award_id":"IN111052","funder_id":"https://openalex.org/F4320322323","funder_display_name":"King Fahd University of Petroleum and Minerals"}],"funders":[{"id":"https://openalex.org/F4320322323","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2158348181.pdf","grobid_xml":"https://content.openalex.org/works/W2158348181.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W590529998","https://openalex.org/W1487844866","https://openalex.org/W1501162218","https://openalex.org/W1964083743","https://openalex.org/W1964285465","https://openalex.org/W1973151461","https://openalex.org/W1976105407","https://openalex.org/W2010526455","https://openalex.org/W2015699835","https://openalex.org/W2021810924","https://openalex.org/W2026566421","https://openalex.org/W2054640988","https://openalex.org/W2067662365","https://openalex.org/W2071288341","https://openalex.org/W2077619904","https://openalex.org/W2084820442","https://openalex.org/W2084985498","https://openalex.org/W2087637266","https://openalex.org/W2089808022","https://openalex.org/W2090844246","https://openalex.org/W2109218509","https://openalex.org/W2121752938","https://openalex.org/W2128084896","https://openalex.org/W2128332575","https://openalex.org/W2137613323","https://openalex.org/W2166588786","https://openalex.org/W2167293229","https://openalex.org/W3021623482","https://openalex.org/W3099372094"],"related_works":["https://openalex.org/W3110577345","https://openalex.org/W2946235959","https://openalex.org/W2902935192","https://openalex.org/W3134817226","https://openalex.org/W4318066384","https://openalex.org/W2122248524","https://openalex.org/W2113105772","https://openalex.org/W2063554202","https://openalex.org/W3203467549","https://openalex.org/W1991653136"],"abstract_inverted_index":{"For":[0],"the":[1],"Hopfield":[2],"Neural":[3],"Network":[4],"problem":[5],"we":[6,24],"consider":[7],"unbounded":[8],"monotone":[9],"nondecreasing":[10],"activation":[11],"functions.":[12],"We":[13],"prove":[14],"convergence":[15],"to":[16],"zero":[17],"in":[18],"an":[19],"exponential":[20],"manner":[21],"provided":[22],"that":[23],"start":[25],"with":[26],"sufficiently":[27],"small":[28],"initial":[29],"data.":[30]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}