{"id":"https://openalex.org/W2072483224","doi":"https://doi.org/10.1142/s0218127409025043","title":"ON THE MONOTONICITY OF ENTROPY FOR MULTILAYER CELLULAR NEURAL NETWORKS","display_name":"ON THE MONOTONICITY OF ENTROPY FOR MULTILAYER CELLULAR NEURAL NETWORKS","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W2072483224","doi":"https://doi.org/10.1142/s0218127409025043","mag":"2072483224"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409025043","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409025043","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5022934610","display_name":"Jung\u2010Chao Ban","orcid":"https://orcid.org/0000-0002-4920-6945"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]},{"id":"https://openalex.org/I33096239","display_name":"National Dong Hwa University","ror":"https://ror.org/00mng9617","country_code":"TW","type":"education","lineage":["https://openalex.org/I33096239"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"JUNG-CHAO BAN","raw_affiliation_strings":["Department of Applied Mathematics, National Dong Hwa University, Hualian, 97063, Taiwan, R.O.C","Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, 10617, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Dong Hwa University, Hualian, 97063, Taiwan, R.O.C","institution_ids":["https://openalex.org/I33096239"]},{"raw_affiliation_string":"Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, 10617, Taiwan, R.O.C","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044246659","display_name":"Chih-Hung Chang","orcid":"https://orcid.org/0000-0001-7352-5148"},"institutions":[{"id":"https://openalex.org/I4210119858","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210119858"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"CHIH-HUNG CHANG","raw_affiliation_strings":["National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu, 30043, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Center for Theoretical Sciences, National Tsing Hua University, Hsinchu, 30043, Taiwan, R.O.C","institution_ids":["https://openalex.org/I4210119858"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3562,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.63596143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"11","first_page":"3657","last_page":"3670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9922999739646912,"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/monotonic-function","display_name":"Monotonic function","score":0.9171701669692993},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.7049641013145447},{"id":"https://openalex.org/keywords/template","display_name":"Template","score":0.6388055682182312},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6032020449638367},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5460801124572754},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4807819724082947},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.47642287611961365},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.46152228116989136},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4206593334674835},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35408228635787964},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3448695242404938},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.343940794467926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27267032861709595},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2210325002670288},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21652963757514954},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09235873818397522},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08473306894302368}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.9171701669692993},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.7049641013145447},{"id":"https://openalex.org/C82714645","wikidata":"https://www.wikidata.org/wiki/Q438331","display_name":"Template","level":2,"score":0.6388055682182312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6032020449638367},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5460801124572754},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4807819724082947},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.47642287611961365},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.46152228116989136},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4206593334674835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35408228635787964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3448695242404938},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.343940794467926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27267032861709595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2210325002670288},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21652963757514954},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09235873818397522},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08473306894302368},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409025043","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409025043","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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":18,"referenced_works":["https://openalex.org/W1509576544","https://openalex.org/W1537935065","https://openalex.org/W1565611252","https://openalex.org/W1981987846","https://openalex.org/W1988314658","https://openalex.org/W2011216071","https://openalex.org/W2046738125","https://openalex.org/W2056717940","https://openalex.org/W2081379625","https://openalex.org/W2102892532","https://openalex.org/W2107025852","https://openalex.org/W2133225357","https://openalex.org/W2137668463","https://openalex.org/W2148514738","https://openalex.org/W2160121923","https://openalex.org/W4206252072","https://openalex.org/W4234409395","https://openalex.org/W4294830154"],"related_works":["https://openalex.org/W2121300814","https://openalex.org/W1886613375","https://openalex.org/W4236081792","https://openalex.org/W4250583430","https://openalex.org/W2077314575","https://openalex.org/W4234406076","https://openalex.org/W2010731026","https://openalex.org/W4311328601","https://openalex.org/W2360893094","https://openalex.org/W2044673172"],"abstract_inverted_index":{"This":[0],"work":[1],"investigates":[2],"the":[3,30,48,51,90,99,102,108],"monotonicity":[4,92],"of":[5,19,28,32,50,53,62,74,80,84,93,101],"topological":[6,33,54,94],"entropy":[7,95],"for":[8],"one-dimensional":[9],"multilayer":[10],"cellular":[11],"neural":[12],"networks.":[13],"The":[14],"interacting":[15,76],"radius":[16,77],"and":[17,57,71,104],"number":[18,79],"layers":[20],"are":[21,60,110],"treated":[22],"as":[23,36,107],"parameters.":[24],"Fix":[25],"either":[26],"one":[27,44],"them;":[29],"set":[31,52],"entropies":[34],"grows":[35],"a":[37,63],"strictly":[38],"nested":[39],"sequence":[40],"with":[41],"respect":[42],"to":[43],"another.":[45],"Apart":[46],"from":[47],"comparison":[49,100],"entropies,":[55],"maximal":[56,70,103],"minimal":[58,72,105],"templates":[59,73,106],"indicators":[61],"dynamical":[64],"system.":[65],"Our":[66],"results":[67],"demonstrate":[68],"that":[69],"larger":[75],"(respectively":[78],"layers)":[81],"dominate":[82],"those":[83],"smaller":[85],"one.":[86],"To":[87],"be":[88],"precise,":[89],"strict":[91],"is":[96],"demonstrated":[97],"through":[98],"parameters":[109],"varied.":[111]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}