{"id":"https://openalex.org/W2039649494","doi":"https://doi.org/10.1142/s0218127400001043","title":"MOSAIC SOLUTIONS AND SPATIAL ENTROPY FOR A CLASS OF NEURAL NETWORK MODELS","display_name":"MOSAIC SOLUTIONS AND SPATIAL ENTROPY FOR A CLASS OF NEURAL NETWORK MODELS","publication_year":2000,"publication_date":"2000-07-01","ids":{"openalex":"https://openalex.org/W2039649494","doi":"https://doi.org/10.1142/s0218127400001043","mag":"2039649494"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127400001043","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127400001043","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/A5049473396","display_name":"Barbara Jennings","orcid":null},"institutions":[{"id":"https://openalex.org/I167576493","display_name":"Colorado School of Mines","ror":"https://ror.org/04raf6v53","country_code":"US","type":"education","lineage":["https://openalex.org/I167576493"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"BARBARA JENNINGS","raw_affiliation_strings":["Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401-1887, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401-1887, USA","institution_ids":["https://openalex.org/I167576493"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012033652","display_name":"Erik S. Van Vleck","orcid":"https://orcid.org/0000-0001-9203-8345"},"institutions":[{"id":"https://openalex.org/I167576493","display_name":"Colorado School of Mines","ror":"https://ror.org/04raf6v53","country_code":"US","type":"education","lineage":["https://openalex.org/I167576493"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ERIK S. VAN VLECK","raw_affiliation_strings":["Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401-1887, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401-1887, USA","institution_ids":["https://openalex.org/I167576493"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049473396"],"corresponding_institution_ids":["https://openalex.org/I167576493"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.20601978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"07","first_page":"1661","last_page":"1675"},"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/T10320","display_name":"Neural Networks and Applications","score":0.9944000244140625,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9850000143051147,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5470763444900513},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5027816295623779},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4998323917388916},{"id":"https://openalex.org/keywords/mosaic","display_name":"Mosaic","score":0.49262887239456177},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4747113287448883},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45740842819213867},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4475909173488617},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4203546643257141},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4180452823638916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3606957495212555},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26780593395233154},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16556859016418457},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14678239822387695},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.11333861947059631}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5470763444900513},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5027816295623779},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4998323917388916},{"id":"https://openalex.org/C110739175","wikidata":"https://www.wikidata.org/wiki/Q133067","display_name":"Mosaic","level":2,"score":0.49262887239456177},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4747113287448883},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45740842819213867},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4475909173488617},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4203546643257141},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4180452823638916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3606957495212555},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26780593395233154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16556859016418457},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14678239822387695},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.11333861947059631},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127400001043","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127400001043","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":8,"referenced_works":["https://openalex.org/W2031157874","https://openalex.org/W2034476467","https://openalex.org/W2046738125","https://openalex.org/W2064006517","https://openalex.org/W2105830015","https://openalex.org/W2112246162","https://openalex.org/W2131391582","https://openalex.org/W2160121923"],"related_works":["https://openalex.org/W2493552207","https://openalex.org/W2397874377","https://openalex.org/W2027673787","https://openalex.org/W4249026204","https://openalex.org/W2327982655","https://openalex.org/W428377179","https://openalex.org/W1483215156","https://openalex.org/W2796222479","https://openalex.org/W2074553785","https://openalex.org/W3027773099"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"present":[4],"a":[5,11,48],"lattice":[6],"differential":[7],"equation":[8],"model":[9],"for":[10,34],"class":[12],"of":[13,18,39,50,53,64],"neural":[14],"networks.":[15],"A":[16],"subset":[17],"the":[19,51,54,62],"equilibrium":[20,24,36],"solutions":[21,25],"called":[22],"mosaic":[23,35],"is":[26],"defined.":[27],"Existence":[28],"and":[29,43],"stability":[30,40],"theorems":[31],"are":[32,41,56],"proved":[33],"solutions.":[37],"Regions":[38],"defined":[42],"spatial":[44,65],"entropy":[45],"calculations,":[46],"as":[47],"measure":[49],"complexity":[52],"system,":[55],"presented":[57],"that":[58],"give":[59],"insights":[60],"into":[61],"effects":[63],"coupling.":[66]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
