{"id":"https://openalex.org/W2050076528","doi":"https://doi.org/10.1162/neco_c_00526","title":"Some Remarks on \u201cAlmost Periodic Dynamics of a Class of Delayed Neural Networks with Discontinuous Activations\u201d","display_name":"Some Remarks on \u201cAlmost Periodic Dynamics of a Class of Delayed Neural Networks with Discontinuous Activations\u201d","publication_year":2013,"publication_date":"2013-09-18","ids":{"openalex":"https://openalex.org/W2050076528","doi":"https://doi.org/10.1162/neco_c_00526","mag":"2050076528","pmid":"https://pubmed.ncbi.nlm.nih.gov/24047325"},"language":"en","primary_location":{"id":"doi:10.1162/neco_c_00526","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_c_00526","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"erratum","indexed_in":["crossref","pubmed"],"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/A5062509066","display_name":"Tianping Chen","orcid":"https://orcid.org/0000-0001-6117-6673"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tianping Chen","raw_affiliation_strings":["Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R.C"],"affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Mathematics Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R.C","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062509066"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":0.3624,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.65589381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"12","first_page":"3340","last_page":"3342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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/T10320","display_name":"Neural Networks and Applications","score":0.9966999888420105,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9937000274658203,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dominated-convergence-theorem","display_name":"Dominated convergence theorem","score":0.7488187551498413},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.743842363357544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.704422116279602},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5602155327796936},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5241361260414124},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5119434595108032},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.4990992546081543},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4841190278530121},{"id":"https://openalex.org/keywords/lp-space","display_name":"Lp space","score":0.4760432243347168},{"id":"https://openalex.org/keywords/dual-space","display_name":"Dual space","score":0.4439212679862976},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4169294834136963},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4110843241214752},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4085431396961212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28912150859832764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12461903691291809},{"id":"https://openalex.org/keywords/convergence-tests","display_name":"Convergence tests","score":0.11138147115707397},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.08598843216896057}],"concepts":[{"id":"https://openalex.org/C38487692","wikidata":"https://www.wikidata.org/wiki/Q1067156","display_name":"Dominated convergence theorem","level":5,"score":0.7488187551498413},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.743842363357544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.704422116279602},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5602155327796936},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5241361260414124},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5119434595108032},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.4990992546081543},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4841190278530121},{"id":"https://openalex.org/C172294467","wikidata":"https://www.wikidata.org/wiki/Q305936","display_name":"Lp space","level":3,"score":0.4760432243347168},{"id":"https://openalex.org/C45633534","wikidata":"https://www.wikidata.org/wiki/Q752487","display_name":"Dual space","level":2,"score":0.4439212679862976},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4169294834136963},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4110843241214752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4085431396961212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28912150859832764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12461903691291809},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.11138147115707397},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.08598843216896057},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1162/neco_c_00526","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_c_00526","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:24047325","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24047325","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2121385949","https://openalex.org/W2142389098","https://openalex.org/W4229840834"],"related_works":["https://openalex.org/W2027251766","https://openalex.org/W2592171298","https://openalex.org/W4244092693","https://openalex.org/W2115522651","https://openalex.org/W1986582885","https://openalex.org/W2335720052","https://openalex.org/W4297823889","https://openalex.org/W2600309243","https://openalex.org/W3000799397","https://openalex.org/W4288065319"],"abstract_inverted_index":{"There":[0],"are":[1,38,43,55],"some":[2,39,44,64],"incorrect":[3],"uses":[4],"of":[5,29,66,116,162,171,190,248,271,288],"mathematical":[6,67],"terminology":[7,68],"and":[8,21,53,73,117,172,194,219,253,275],"typos":[9],"in":[10,69,94,152,201,211,238],"previous":[11,71],"papers.":[12],"We":[13,137],"rewrite":[14,74],"them":[15,75],"precisely":[16,76],"here.In":[17],"Lu,":[18,191,272],"Wenlian,":[19,192,273],"Chen,":[20,193,274],"Tianping":[22,195,276],"(2008),":[23,277],"we":[24,109,123,166,177],"studied":[25],"the":[26,95,101,112,118,130,153,159,184,202,212,239,245,255],"following":[27,78,203],"class":[28],"delayed":[30],"differential":[31],"equations:":[32],"1where":[33],"di(t),":[34],"aij(t),":[35],"Ii(t),":[36],",":[37,41,42,50,54,108,156,242],"functions;":[40],"nondecreasing":[45],"discontinuous":[46],"functions":[47],"for":[48,106,146],"any":[49],"dKij(t,":[51],"s);":[52],"Lebesgue-Stieljies":[56],"measures":[57],"with":[58],"respect":[59],"to":[60,88,128,141,182,226,261],"s.We":[61],"have":[62,110,167],"noticed":[63],"misuse":[65],"this":[70],"letter,":[72],"here.The":[77],"paragraph":[79],"is":[80,92,100,150,158,198,209,220,236,244,254,284],"from":[81],"that":[82,125,149,179,208,235],"letter":[83],"(pp.":[84],"1075\u20131076):":[85],"weakly":[86,126,139,180,224,259],"converges":[87,127,140,181,225,260],"on":[89,129,142,183,187,227,262,268,291],"space":[90,97,103,131,143,155,161,185,214,241,247],".":[91],"dense":[93,151,210,237],"Banach":[96,154,213,240],"),":[98],"which":[99,157,243],"conjugate":[102],").":[104],"Therefore,":[105,223,258],"each":[107,147,206,233],"By":[111,168],"uniform":[113,169],"essential":[114],"boundedness":[115,170],"Lebesgue":[119,173],"dominant":[120,174],"convergence":[121,175],"theorem,":[122,176],"conclude":[124,178],".It":[132],"should":[133,278],"be":[134,279],"rewritten":[135],"as:":[136],"claim":[138],".In":[144],"fact,":[145],"(noting":[148],"dual":[160,246],"L1([0,":[163,215,249,263],"T],":[164,216,250,264],"Rn)),":[165,217,251],".Similarly,":[186],"page":[188,269,292],"696":[189],"(2006),":[196],"there":[197],"a":[199,285],"problem":[200],"paragraph:":[204],"For":[205,232],"(noticing":[207,234],"holds":[218,252],"uniformly":[221,256],"bounded.":[222,257],".The":[228],"correct":[229],"wording":[230],"is:":[231],"Rn).Moreover,":[265],"inequality":[266,289],"4.3":[267],"1085":[270],"replaced":[280],"by":[281],"because":[282],"it":[283],"special":[286],"case":[287],"3.1":[290],"1072:":[293]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-02-24T19:35:01.260952","created_date":"2025-10-10T00:00:00"}