{"id":"https://openalex.org/W1987476191","doi":"https://doi.org/10.1002/scj.4690221010","title":"Set partition of real numbers by hopfield neural network","display_name":"Set partition of real numbers by hopfield neural network","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W1987476191","doi":"https://doi.org/10.1002/scj.4690221010","mag":"1987476191"},"language":"en","primary_location":{"id":"doi:10.1002/scj.4690221010","is_oa":false,"landing_page_url":"https://doi.org/10.1002/scj.4690221010","pdf_url":null,"source":{"id":"https://openalex.org/S58208175","display_name":"Systems and Computers in Japan","issn_l":"0882-1666","issn":["0882-1666","1520-684X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems and Computers in Japan","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/A5077643817","display_name":"Yutaka Hisanaga","orcid":null},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yutaka Hisanaga","raw_affiliation_strings":["Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 724","Yutaka Hisanaga graduated in 1988 from the Dept. Electronic Eng., Fac. Eng., Yamaguchi University, and enrolled in the doctoral program at Hiroshima University. Presently, he is a Research Associate, Fac. Eng., Yamaguchi University. He is interested in research on neural networks. He is a member of Inf. Proc. SOC., Japan"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 724","institution_ids":["https://openalex.org/I113306721"]},{"raw_affiliation_string":"Yutaka Hisanaga graduated in 1988 from the Dept. Electronic Eng., Fac. Eng., Yamaguchi University, and enrolled in the doctoral program at Hiroshima University. Presently, he is a Research Associate, Fac. Eng., Yamaguchi University. He is interested in research on neural networks. He is a member of Inf. Proc. SOC., Japan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111575379","display_name":"Masafumi Yamashita","orcid":null},"institutions":[{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masafumi Yamashita","raw_affiliation_strings":["Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 724","Masafumi Yamashita graduated in 1974 from the Dept. Inf. Eng., Fac. Eng., Kyoto University, where he obtained a Master's degree in 1977. He obtained a Dr. of Eng. degree in 1980 from Nagoya University. He was a Research Associate at Toyohashi University of Technology and is presently an Assoc. Prof. in the 2nd Dept., Fac. Eng., Hiroshima University. He was a Visiting Assoc. Prof. at Simon-Fraser University, Canada, for one year from 1986. He is engaged in research on load balancing of multiprocessor systems, the basis of distributed networks, and combinational problems. He is a member of the Inf. Proc. SOC., Japan"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 724","institution_ids":["https://openalex.org/I113306721"]},{"raw_affiliation_string":"Masafumi Yamashita graduated in 1974 from the Dept. Inf. Eng., Fac. Eng., Kyoto University, where he obtained a Master's degree in 1977. He obtained a Dr. of Eng. degree in 1980 from Nagoya University. He was a Research Associate at Toyohashi University of Technology and is presently an Assoc. Prof. in the 2nd Dept., Fac. Eng., Hiroshima University. He was a Visiting Assoc. Prof. at Simon-Fraser University, Canada, for one year from 1986. He is engaged in research on load balancing of multiprocessor systems, the basis of distributed networks, and combinational problems. He is a member of the Inf. Proc. SOC., Japan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112678545","display_name":"Tadashi Ae","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]},{"id":"https://openalex.org/I113306721","display_name":"Hiroshima University","ror":"https://ror.org/03t78wx29","country_code":"JP","type":"education","lineage":["https://openalex.org/I113306721"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR","JP"],"is_corresponding":false,"raw_author_name":"Tadashi Ae","raw_affiliation_strings":["Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 724","Tadashi Ae graduated in 1964 from the Dept. Comm. Eng., Fac. Eng., Tohoku University, where he obtained a Dr. of Eng. degree in 1969. He was a Research Associate at Tohoku Uni- versity and an Assoc. Prof. at Hiroshima University. Since 1982, he has beena Prof. at Hiroshima University (Educ. Computer Sci., 2nd Dept., Fac. Eng.). He was a Visiting Researcher at Grenoble University, France, for one year from 1974. Presently, he is engaged mainly in research on the design, construction and performance evaluation of distributed processing sys tems (multiprocessor and LAN). He is a member of the Inf. Proc. SOC., Japan; ACM; and IEEE","IEEE","Tadashi Ae graduated in 1964 from the Dept. Comm. Eng., Fac. Eng., Tohoku University, where he obtained a Dr. of Eng. degree in 1969. He was a Research Associate at Tohoku Uni- versity and an Assoc. Prof. at Hiroshima University. Since 1982, he has beena Prof. at Hiroshima University (Educ. Computer Sci., 2nd Dept., Fac. Eng.). He was a Visiting Researcher at Grenoble University, France, for one year from 1974. Presently, he is engaged mainly in research on the design, construction and performance evaluation of distributed processing sys tems (multiprocessor and LAN). He is a member of the Inf. Proc. SOC., Japan"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Hiroshima University, Higashi-Hiroshima, Japan 724","institution_ids":["https://openalex.org/I113306721"]},{"raw_affiliation_string":"Tadashi Ae graduated in 1964 from the Dept. Comm. Eng., Fac. Eng., Tohoku University, where he obtained a Dr. of Eng. degree in 1969. He was a Research Associate at Tohoku Uni- versity and an Assoc. Prof. at Hiroshima University. Since 1982, he has beena Prof. at Hiroshima University (Educ. Computer Sci., 2nd Dept., Fac. Eng.). He was a Visiting Researcher at Grenoble University, France, for one year from 1974. Presently, he is engaged mainly in research on the design, construction and performance evaluation of distributed processing sys tems (multiprocessor and LAN). He is a member of the Inf. Proc. SOC., Japan; ACM; and IEEE","institution_ids":[]},{"raw_affiliation_string":"IEEE","institution_ids":[]},{"raw_affiliation_string":"Tadashi Ae graduated in 1964 from the Dept. Comm. Eng., Fac. Eng., Tohoku University, where he obtained a Dr. of Eng. degree in 1969. He was a Research Associate at Tohoku Uni- versity and an Assoc. Prof. at Hiroshima University. Since 1982, he has beena Prof. at Hiroshima University (Educ. Computer Sci., 2nd Dept., Fac. Eng.). He was a Visiting Researcher at Grenoble University, France, for one year from 1974. Presently, he is engaged mainly in research on the design, construction and performance evaluation of distributed processing sys tems (multiprocessor and LAN). He is a member of the Inf. Proc. SOC., Japan","institution_ids":["https://openalex.org/I201537933","https://openalex.org/I113306721","https://openalex.org/I899635006"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077643817"],"corresponding_institution_ids":["https://openalex.org/I113306721"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11717999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"10","first_page":"88","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9930999875068665,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9775999784469604,"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/hopfield-network","display_name":"Hopfield network","score":0.8108091354370117},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.683715283870697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6174407601356506},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6156015992164612},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5202537775039673},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5136436820030212},{"id":"https://openalex.org/keywords/partition-problem","display_name":"Partition problem","score":0.4761210083961487},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46346062421798706},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.4619581699371338},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.45887529850006104},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4439029097557068},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4150785207748413},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.327892541885376},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2952503561973572},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2597372531890869},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10903707146644592}],"concepts":[{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.8108091354370117},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.683715283870697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6174407601356506},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6156015992164612},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5202537775039673},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5136436820030212},{"id":"https://openalex.org/C35995877","wikidata":"https://www.wikidata.org/wiki/Q1065968","display_name":"Partition problem","level":3,"score":0.4761210083961487},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46346062421798706},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.4619581699371338},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.45887529850006104},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4439029097557068},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4150785207748413},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.327892541885376},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2952503561973572},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2597372531890869},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10903707146644592},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/scj.4690221010","is_oa":false,"landing_page_url":"https://doi.org/10.1002/scj.4690221010","pdf_url":null,"source":{"id":"https://openalex.org/S58208175","display_name":"Systems and Computers in Japan","issn_l":"0882-1666","issn":["0882-1666","1520-684X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Systems and Computers in Japan","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1597286183","https://openalex.org/W2036270456","https://openalex.org/W2044462412","https://openalex.org/W2102227134","https://openalex.org/W2112246162","https://openalex.org/W2149943625","https://openalex.org/W2502339760"],"related_works":["https://openalex.org/W2025912669","https://openalex.org/W2057299700","https://openalex.org/W1549987457","https://openalex.org/W2014615094","https://openalex.org/W1977789739","https://openalex.org/W2351778335","https://openalex.org/W4240458717","https://openalex.org/W2497180562","https://openalex.org/W2379495598","https://openalex.org/W2047470742"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Hopfield":[2,65],"neural":[3,66],"network":[4,25,95,107],"is":[5,45,57,100,103,125,137],"attracting":[6],"attention":[7],"as":[8],"a":[9,20,37,61,85,119],"high\u2010speed":[10],"solver":[11],"for":[12],"optimization":[13],"and":[14],"other":[15,49],"problems.":[16],"However,":[17],"it":[18],"contains":[19],"problem":[21,62,77,99,136],"in":[22,59],"that":[23,105],"the":[24,30,42,51,54,64,71,76,80,106,110,115,132,134],"may":[26],"not":[27],"arrive":[28],"at":[29,36,109],"globally":[31,111],"optimal":[32,39,112],"solution":[33,40,113],"but":[34],"stops":[35],"locally":[38],"unless":[41],"initial":[43,55,116],"state":[44,56,117],"selected":[46],"appropriately.":[47],"In":[48],"words,":[50],"selection":[52],"of":[53,78,88,131],"important":[58],"solving":[60],"using":[63],"network.":[67],"This":[68],"paper":[69],"considers":[70],"real":[72,89],"number":[73],"partition":[74],"problem,":[75],"finding":[79],"k":[81],"largest":[82],"elements":[83],"from":[84],"given":[86,91],"set":[87],"numbers,":[90],"integer":[92],"k.":[93],"A":[94],"to":[96],"solve":[97],"this":[98],"constructed.":[101],"It":[102],"shown":[104],"arrives":[108],"if":[114],"satisfies":[118],"certain":[120],"condition.":[121],"Its":[122],"basin":[123],"also":[124],"examined.":[126],"As":[127],"an":[128],"application":[129],"example":[130],"network,":[133],"sorting":[135],"considered.":[138]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}