{"id":"https://openalex.org/W2131816943","doi":"https://doi.org/10.1109/ijcnn.2010.5596509","title":"Learning nonlinearly separable mod k addition problem using a single multi-valued neuron with a periodic activation function","display_name":"Learning nonlinearly separable mod k addition problem using a single multi-valued neuron with a periodic activation function","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W2131816943","doi":"https://doi.org/10.1109/ijcnn.2010.5596509","mag":"2131816943"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2010.5596509","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2010.5596509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 2010 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-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/A5052101553","display_name":"Igor Aizenberg","orcid":"https://orcid.org/0000-0002-5994-6568"},"institutions":[{"id":"https://openalex.org/I51380931","display_name":"Texas A&M University \u2013 Texarkana","ror":"https://ror.org/01x3z9745","country_code":"US","type":"education","lineage":["https://openalex.org/I51380931"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Igor Aizenberg","raw_affiliation_strings":["Texas A and M University, Texarkana, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A and M University, Texarkana, TX, USA","institution_ids":["https://openalex.org/I51380931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033282504","display_name":"Matthew Caudill","orcid":null},"institutions":[{"id":"https://openalex.org/I51380931","display_name":"Texas A&M University \u2013 Texarkana","ror":"https://ror.org/01x3z9745","country_code":"US","type":"education","lineage":["https://openalex.org/I51380931"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Caudill","raw_affiliation_strings":["Texas A and M University, Texarkana, Texarkana, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A and M University, Texarkana, Texarkana, TX, USA","institution_ids":["https://openalex.org/I51380931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102143022","display_name":"Jacob Jackson","orcid":null},"institutions":[{"id":"https://openalex.org/I51380931","display_name":"Texas A&M University \u2013 Texarkana","ror":"https://ror.org/01x3z9745","country_code":"US","type":"education","lineage":["https://openalex.org/I51380931"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jacob Jackson","raw_affiliation_strings":["Texas A and M University, Texarkana, Texarkana, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A and M University, Texarkana, Texarkana, TX, USA","institution_ids":["https://openalex.org/I51380931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082860420","display_name":"Shane Alexander","orcid":"https://orcid.org/0009-0001-2614-7233"},"institutions":[{"id":"https://openalex.org/I51380931","display_name":"Texas A&M University \u2013 Texarkana","ror":"https://ror.org/01x3z9745","country_code":"US","type":"education","lineage":["https://openalex.org/I51380931"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shane Alexander","raw_affiliation_strings":["Texas A and M University, Texarkana, Texarkana, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A and M University, Texarkana, Texarkana, TX, USA","institution_ids":["https://openalex.org/I51380931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8646,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.88178044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"196","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9995999932289124,"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":0.9995999932289124,"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/T11236","display_name":"Control Systems and Identification","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9642000198364258,"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/activation-function","display_name":"Activation function","score":0.7486698627471924},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.7439575791358948},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5755802989006042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46143507957458496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45479682087898254},{"id":"https://openalex.org/keywords/artificial-neuron","display_name":"Artificial neuron","score":0.4375099241733551},{"id":"https://openalex.org/keywords/neuron","display_name":"Neuron","score":0.42704808712005615},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28157997131347656},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.24127182364463806},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19598394632339478},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.061566054821014404}],"concepts":[{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.7486698627471924},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.7439575791358948},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5755802989006042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46143507957458496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45479682087898254},{"id":"https://openalex.org/C2776990819","wikidata":"https://www.wikidata.org/wiki/Q177058","display_name":"Artificial neuron","level":3,"score":0.4375099241733551},{"id":"https://openalex.org/C2778794669","wikidata":"https://www.wikidata.org/wiki/Q43054","display_name":"Neuron","level":2,"score":0.42704808712005615},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28157997131347656},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.24127182364463806},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19598394632339478},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.061566054821014404},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2010.5596509","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2010.5596509","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 2010 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W142384176","https://openalex.org/W1594058661","https://openalex.org/W1764686324","https://openalex.org/W1894035673","https://openalex.org/W2003151924","https://openalex.org/W2047515252","https://openalex.org/W2087834767","https://openalex.org/W2104870463","https://openalex.org/W2105050785","https://openalex.org/W2126944419","https://openalex.org/W2136892987","https://openalex.org/W2161694749","https://openalex.org/W2161780063","https://openalex.org/W2476841360","https://openalex.org/W2487295360","https://openalex.org/W2549243812","https://openalex.org/W4292692317","https://openalex.org/W6630894543"],"related_works":["https://openalex.org/W2362890678","https://openalex.org/W2792268997","https://openalex.org/W3137729713","https://openalex.org/W3010570736","https://openalex.org/W4250465769","https://openalex.org/W4319264491","https://openalex.org/W2789860659","https://openalex.org/W2743204949","https://openalex.org/W4312133802","https://openalex.org/W4213197948"],"abstract_inverted_index":{"In":[0],"this":[1,56,85],"paper,":[2],"we":[3],"further":[4],"develop":[5],"a":[6,14,19,59,68,73],"complex-valued":[7],"neuron":[8,17],"paradigm.":[9],"It":[10,47],"is":[11,43,48,64],"shown":[12,49],"how":[13],"single":[15,60],"multi-valued":[16,61],"with":[18],"periodic":[20,69],"activation":[21,70,86],"function":[22,71],"may":[23],"learn":[24,55],"multiple-valued":[25],"nonlinearly":[26,33],"separable":[27,34],"problems.":[28],"One":[29],"of":[30,40],"the":[31,78],"classical":[32],"problems":[35],"-":[36],"mod":[37],"k":[38],"addition":[39],"n":[41],"variables":[42],"considered":[44],"in":[45],"detail.":[46],"that":[50],"to":[51,54,66,84],"be":[52],"able":[53],"problem":[57],"using":[58],"neuron,":[62],"it":[63],"necessary":[65],"use":[67],"and":[72,82],"learning":[74,80],"algorithm":[75],"based":[76],"on":[77],"error-correction":[79],"rule":[81],"adapted":[83],"function.":[87]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}