{"id":"https://openalex.org/W2150417341","doi":"https://doi.org/10.1007/978-3-540-72383-7_130","title":"Uniform Approximation Capabilities of Sum-of-Product and Sigma-Pi-Sigma Neural Networks","display_name":"Uniform Approximation Capabilities of Sum-of-Product and Sigma-Pi-Sigma Neural Networks","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2150417341","doi":"https://doi.org/10.1007/978-3-540-72383-7_130","mag":"2150417341"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-72383-7_130","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72383-7_130","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5103929725","display_name":"Jinling Long","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinling Long","raw_affiliation_strings":["Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China"],"affiliations":[{"raw_affiliation_string":"Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101622926","display_name":"Wei Wu","orcid":"https://orcid.org/0000-0002-3137-4086"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Wu","raw_affiliation_strings":["Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China"],"affiliations":[{"raw_affiliation_string":"Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101601579","display_name":"Nan Dong","orcid":"https://orcid.org/0009-0009-5166-8290"},"institutions":[{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]},{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong Nan","raw_affiliation_strings":["Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China"],"affiliations":[{"raw_affiliation_string":"Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China","institution_ids":["https://openalex.org/I4210092944","https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103929725"],"corresponding_institution_ids":["https://openalex.org/I27357992","https://openalex.org/I4210092944"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.17624309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1110","last_page":"1116"},"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":0.9976000189781189,"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":0.9556999802589417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.796978771686554},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.7150430679321289},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6710559725761414},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.597617506980896},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5862117409706116},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.532450795173645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5201205015182495},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5064674615859985},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.422243595123291},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4113916754722595},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38399043679237366},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3275752663612366},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19814354181289673},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1542486548423767},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09569329023361206},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0624241828918457},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05763113498687744}],"concepts":[{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.796978771686554},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.7150430679321289},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6710559725761414},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.597617506980896},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5862117409706116},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.532450795173645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5201205015182495},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5064674615859985},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.422243595123291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4113916754722595},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38399043679237366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3275752663612366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19814354181289673},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1542486548423767},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09569329023361206},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0624241828918457},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05763113498687744},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-72383-7_130","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72383-7_130","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1525762998","https://openalex.org/W1601499986","https://openalex.org/W1983776716","https://openalex.org/W1988115241","https://openalex.org/W1994818536","https://openalex.org/W1998242011","https://openalex.org/W2006544021","https://openalex.org/W2009323003","https://openalex.org/W2019247511","https://openalex.org/W2025259401","https://openalex.org/W2047161049","https://openalex.org/W2062430377","https://openalex.org/W2103496339","https://openalex.org/W2113442785","https://openalex.org/W2122040390","https://openalex.org/W2137365657","https://openalex.org/W2141695047","https://openalex.org/W2157890204","https://openalex.org/W3125537303"],"related_works":["https://openalex.org/W2030762054","https://openalex.org/W3157618815","https://openalex.org/W2401345448","https://openalex.org/W255820224","https://openalex.org/W3110660489","https://openalex.org/W2278807000","https://openalex.org/W2964228179","https://openalex.org/W2252718650","https://openalex.org/W2628590989","https://openalex.org/W2785371485"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}