{"id":"https://openalex.org/W2159396213","doi":"https://doi.org/10.1162/08997660152469378","title":"Recurrence Methods in the Analysis of Learning Processes","display_name":"Recurrence Methods in the Analysis of Learning Processes","publication_year":2001,"publication_date":"2001-08-01","ids":{"openalex":"https://openalex.org/W2159396213","doi":"https://doi.org/10.1162/08997660152469378","mag":"2159396213","pmid":"https://pubmed.ncbi.nlm.nih.gov/11506673"},"language":"en","primary_location":{"id":"doi:10.1162/08997660152469378","is_oa":false,"landing_page_url":"https://doi.org/10.1162/08997660152469378","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":"article","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/A5053455526","display_name":"Shahar Mendelson","orcid":"https://orcid.org/0000-0002-5673-7576"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"S. Mendelson","raw_affiliation_strings":["Department of Mathematics, Technion, and Institute of Computer Science, Hebrew University, Jerusalem 91120, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technion, and Institute of Computer Science, Hebrew University, Jerusalem 91120, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031217617","display_name":"Israel Nelken","orcid":"https://orcid.org/0000-0002-6645-107X"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"I. Nelken","raw_affiliation_strings":["Department of Physiology, Hebrew University-Hadassah Medical School, and the Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem 91120, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physiology, Hebrew University-Hadassah Medical School, and the Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem 91120, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5467,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79525391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"8","first_page":"1839","last_page":"1861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9818999767303467,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.972000002861023,"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/artificial-intelligence","display_name":"Artificial intelligence","score":0.655086100101471},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6268757581710815},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6109903454780579},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5794805884361267},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5785405039787292},{"id":"https://openalex.org/keywords/perceptron","display_name":"Perceptron","score":0.5564847588539124},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.47813427448272705},{"id":"https://openalex.org/keywords/unsupervised-learning","display_name":"Unsupervised learning","score":0.476043701171875},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.40577590465545654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22382158041000366}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.655086100101471},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6268757581710815},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6109903454780579},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5794805884361267},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5785405039787292},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.5564847588539124},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.47813427448272705},{"id":"https://openalex.org/C8038995","wikidata":"https://www.wikidata.org/wiki/Q1152135","display_name":"Unsupervised learning","level":2,"score":0.476043701171875},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.40577590465545654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22382158041000366},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008960","descriptor_name":"Models, Psychological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008960","descriptor_name":"Models, Psychological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008960","descriptor_name":"Models, Psychological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"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":3,"locations":[{"id":"doi:10.1162/08997660152469378","is_oa":false,"landing_page_url":"https://doi.org/10.1162/08997660152469378","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:11506673","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11506673","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},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.6656","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.6656","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://axiom.anu.edu.au/~shahar/recurrence.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W23758216","https://openalex.org/W1967121925","https://openalex.org/W1971836751","https://openalex.org/W1991848143","https://openalex.org/W2006346143","https://openalex.org/W2124776405","https://openalex.org/W2165924120"],"related_works":["https://openalex.org/W3196155444","https://openalex.org/W3209574120","https://openalex.org/W4386462264","https://openalex.org/W4285260836","https://openalex.org/W3046775127","https://openalex.org/W3123344745","https://openalex.org/W4245248941","https://openalex.org/W3208099188","https://openalex.org/W4297022372","https://openalex.org/W2941320171"],"abstract_inverted_index":{"The":[0],"goal":[1],"of":[2,14,68,77],"most":[3],"learning":[4,62,78,82],"processes":[5],"is":[6,52,57],"to":[7,24,54,74],"bring":[8],"a":[9,12,35],"machine":[10],"into":[11],"set":[13,45],"\"correct\"":[15],"states.":[16],"In":[17],"practice,":[18],"however,":[19],"it":[20,73],"may":[21],"be":[22],"difficult":[23],"show":[25],"that":[26,37,39],"the":[27,40,43,66,80,89,93],"process":[28,41],"enters":[29],"this":[30,69],"target":[31,44],"set.":[32],"We":[33],"present":[34],"condition":[36,51],"ensures":[38],"visits":[42],"infinitely":[46],"often":[47],"almost":[48],"surely.":[49],"This":[50],"easy":[53],"verify":[55],"and":[56,92],"true":[58],"for":[59],"many":[60],"well-known":[61],"rules.":[63],"To":[64],"demonstrate":[65],"utility":[67],"method,":[70],"we":[71],"apply":[72],"four":[75],"types":[76],"processes:":[79],"perceptron,":[81],"rules":[83],"governed":[84],"by":[85],"continuous":[86],"energy":[87],"functions,":[88],"Kohonen":[90],"rule,":[91],"committee":[94],"machine.":[95]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}