{"id":"https://openalex.org/W1991883237","doi":"https://doi.org/10.1007/s11063-007-9070-9","title":"Constructive Approximation of Discontinuous Functions by Neural Networks","display_name":"Constructive Approximation of Discontinuous Functions by Neural Networks","publication_year":2008,"publication_date":"2008-01-17","ids":{"openalex":"https://openalex.org/W1991883237","doi":"https://doi.org/10.1007/s11063-007-9070-9","mag":"1991883237"},"language":"en","primary_location":{"id":"doi:10.1007/s11063-007-9070-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11063-007-9070-9","pdf_url":null,"source":{"id":"https://openalex.org/S140962798","display_name":"Neural Processing Letters","issn_l":"1370-4621","issn":["1370-4621","1573-773X"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Processing Letters","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/A5067073804","display_name":"B. Llanas","orcid":null},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"B. Llanas","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain","Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain 28040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain 28040#TAB#","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":null,"display_name":"S. Lantar\u00f3n","orcid":null},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. Lantar\u00f3n","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain","Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain 28040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain 28040#TAB#","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089116457","display_name":"Francisco Javier S\u00e1inz","orcid":null},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"F. J. S\u00e1inz","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain","Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain 28040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Ciudad Universitaria s/n, 28040, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, E.T.S.I. de Caminos, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain 28040#TAB#","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.351,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.89553193,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"27","issue":"3","first_page":"209","last_page":"226"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/constructive","display_name":"Constructive","score":0.7964786291122437},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7301846742630005},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6558941602706909},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.6519731283187866},{"id":"https://openalex.org/keywords/feedforward-neural-network","display_name":"Feedforward neural network","score":0.6192778944969177},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5820475220680237},{"id":"https://openalex.org/keywords/feed-forward","display_name":"Feed forward","score":0.5628282427787781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5178604125976562},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5098263621330261},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4656800627708435},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4492711126804352},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4058290421962738},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35451316833496094},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29703885316848755},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19287866353988647},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17175889015197754}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7964786291122437},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7301846742630005},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6558941602706909},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.6519731283187866},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.6192778944969177},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5820475220680237},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.5628282427787781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5178604125976562},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5098263621330261},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4656800627708435},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4492711126804352},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4058290421962738},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35451316833496094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29703885316848755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19287866353988647},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17175889015197754},{"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11063-007-9070-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11063-007-9070-9","pdf_url":null,"source":{"id":"https://openalex.org/S140962798","display_name":"Neural Processing Letters","issn_l":"1370-4621","issn":["1370-4621","1573-773X"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.7300000190734863,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W655548073","https://openalex.org/W1562562553","https://openalex.org/W1565170927","https://openalex.org/W1565485340","https://openalex.org/W1647470094","https://openalex.org/W1964699038","https://openalex.org/W1968369729","https://openalex.org/W1969304434","https://openalex.org/W1979836930","https://openalex.org/W1980149518","https://openalex.org/W1981798406","https://openalex.org/W1985618715","https://openalex.org/W1988459307","https://openalex.org/W1989572515","https://openalex.org/W2002797051","https://openalex.org/W2011153164","https://openalex.org/W2012358490","https://openalex.org/W2014253464","https://openalex.org/W2021148839","https://openalex.org/W2036808929","https://openalex.org/W2041557168","https://openalex.org/W2054914424","https://openalex.org/W2066462711","https://openalex.org/W2089455490","https://openalex.org/W2092104635","https://openalex.org/W2098413769","https://openalex.org/W2103496339","https://openalex.org/W2109504624","https://openalex.org/W2116490015","https://openalex.org/W2136003379","https://openalex.org/W2137983211","https://openalex.org/W2146842127","https://openalex.org/W2158581396","https://openalex.org/W2169997788","https://openalex.org/W2798683100","https://openalex.org/W3146803896","https://openalex.org/W4230227726","https://openalex.org/W4249676513","https://openalex.org/W4251776825"],"related_works":["https://openalex.org/W2365402722","https://openalex.org/W2096285364","https://openalex.org/W2525162253","https://openalex.org/W2369505716","https://openalex.org/W1584826867","https://openalex.org/W2157965928","https://openalex.org/W2152966207","https://openalex.org/W2114873881","https://openalex.org/W4237191926","https://openalex.org/W2156433922"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}