{"id":"https://openalex.org/W2125805354","doi":"https://doi.org/10.1162/neco.2007.07-06-297","title":"Design of Continuous Attractor Networks with Monotonic Tuning Using a Symmetry Principle","display_name":"Design of Continuous Attractor Networks with Monotonic Tuning Using a Symmetry Principle","publication_year":2007,"publication_date":"2007-11-29","ids":{"openalex":"https://openalex.org/W2125805354","doi":"https://doi.org/10.1162/neco.2007.07-06-297","mag":"2125805354","pmid":"https://pubmed.ncbi.nlm.nih.gov/18047414"},"language":"en","primary_location":{"id":"doi:10.1162/neco.2007.07-06-297","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2007.07-06-297","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/A5024887903","display_name":"Christian K. Machens","orcid":"https://orcid.org/0000-0003-1717-1562"},"institutions":[{"id":"https://openalex.org/I2750212522","display_name":"Cold Spring Harbor Laboratory","ror":"https://ror.org/02qz8b764","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2750212522"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christian K. Machens","raw_affiliation_strings":["Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A","Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A. machens@zi.biologie.uni-muenchen.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A","institution_ids":["https://openalex.org/I2750212522"]},{"raw_affiliation_string":"Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A. machens@zi.biologie.uni-muenchen.de#TAB#","institution_ids":["https://openalex.org/I2750212522"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032177255","display_name":"Carlos D. Brody","orcid":"https://orcid.org/0000-0002-4201-561X"},"institutions":[{"id":"https://openalex.org/I2750212522","display_name":"Cold Spring Harbor Laboratory","ror":"https://ror.org/02qz8b764","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2750212522"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carlos D. Brody","raw_affiliation_strings":["Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A","Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A. brody@princeton.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A","institution_ids":["https://openalex.org/I2750212522"]},{"raw_affiliation_string":"Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, U.S.A. brody@princeton.edu#TAB#","institution_ids":["https://openalex.org/I2750212522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6949,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.90949128,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"20","issue":"2","first_page":"452","last_page":"485"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9919000267982483,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9919000267982483,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9907000064849854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.8148851990699768},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6760760545730591},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.647343099117279},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4284559488296509},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.42772117257118225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4211067855358124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41987860202789307},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38528409600257874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35712623596191406},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3354093134403229},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33264803886413574},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3277534246444702},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26817166805267334},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26028719544410706},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.19571909308433533},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16853025555610657}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8148851990699768},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6760760545730591},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.647343099117279},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4284559488296509},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.42772117257118225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4211067855358124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41987860202789307},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38528409600257874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35712623596191406},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3354093134403229},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33264803886413574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3277534246444702},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26817166805267334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26028719544410706},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.19571909308433533},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16853025555610657},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","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":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013028","descriptor_name":"Space Perception","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013028","descriptor_name":"Space Perception","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013028","descriptor_name":"Space Perception","qualifier_ui":"Q000502","qualifier_name":"physiology","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},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":4,"locations":[{"id":"doi:10.1162/neco.2007.07-06-297","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2007.07-06-297","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:18047414","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18047414","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:repository.cshl.edu:27513","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402288","display_name":"Cold Spring Harbor Laboratory Institutional Repository (Cold Spring Harbor Laboratory)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2750212522","host_organization_name":"Cold Spring Harbor Laboratory","host_organization_lineage":["https://openalex.org/I2750212522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.333.9826","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.9826","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cns.upf.edu/jclub/machens_brody_neco2008.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6308269507","display_name":null,"funder_award_id":"R01 MH 067991","funder_id":"https://openalex.org/F4320337346","funder_display_name":"National Institute of Mental Health"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337346","display_name":"National Institute of Mental Health","ror":"https://ror.org/04xeg9z08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W637551875","https://openalex.org/W1491547160","https://openalex.org/W1608745771","https://openalex.org/W1740170058","https://openalex.org/W1804362150","https://openalex.org/W1950306692","https://openalex.org/W1966841546","https://openalex.org/W1968903256","https://openalex.org/W1978287828","https://openalex.org/W1989512479","https://openalex.org/W1992476998","https://openalex.org/W2008240154","https://openalex.org/W2025891204","https://openalex.org/W2029374903","https://openalex.org/W2047807449","https://openalex.org/W2051682114","https://openalex.org/W2052296894","https://openalex.org/W2060841481","https://openalex.org/W2070447195","https://openalex.org/W2076145339","https://openalex.org/W2076208166","https://openalex.org/W2079600283","https://openalex.org/W2094488329","https://openalex.org/W2101620490","https://openalex.org/W2115168690","https://openalex.org/W2119599269","https://openalex.org/W2119899403","https://openalex.org/W2122186032","https://openalex.org/W2129618392","https://openalex.org/W2131330930","https://openalex.org/W2131659116","https://openalex.org/W2137700545","https://openalex.org/W2147199905","https://openalex.org/W2149422514","https://openalex.org/W2150439267","https://openalex.org/W2156985666","https://openalex.org/W2157518752","https://openalex.org/W2161983882","https://openalex.org/W2165443127","https://openalex.org/W2166507263","https://openalex.org/W2167809052","https://openalex.org/W2170120409","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W2960434112","https://openalex.org/W3049714198","https://openalex.org/W2036805113","https://openalex.org/W2592279130","https://openalex.org/W2049158118","https://openalex.org/W2123827981","https://openalex.org/W1499880030","https://openalex.org/W4205994410","https://openalex.org/W34461864","https://openalex.org/W30029751"],"abstract_inverted_index":{"Neurons":[0],"that":[1,122,159,185],"sustain":[2,23],"elevated":[3],"firing":[4,24,102],"in":[5,13,36,55,76,86,98,126],"the":[6,73,87,100,123,127,154,190,198],"absence":[7],"of":[8,33,44,47,52,58,103,115,139,175,193,200],"stimuli":[9],"have":[10,160],"been":[11,72],"found":[12,31],"many":[14,26,187],"neural":[15],"systems.":[16],"In":[17,167],"graded":[18],"persistent":[19,101],"activity,":[20],"neurons":[21,60,104],"can":[22,39,131],"at":[25],"levels,":[27],"suggesting":[28],"a":[29,45,78,106,111,116,136,161,171,176,201],"widely":[30],"type":[32],"network":[34,88,130,179],"dynamics":[35],"which":[37,77,99],"networks":[38,57,158],"relax":[40],"to":[41,64,134,157,197],"any":[42],"one":[43],"continuum":[46],"stationary":[48],"states.":[49],"The":[50],"reproduction":[51],"these":[53],"findings":[54],"model":[56,70],"nonlinear":[59],"has":[61,71],"turned":[62],"out":[63],"be":[65,132],"nontrivial.":[66],"A":[67],"particularly":[68],"insightful":[69],"\"bump":[74],"attractor,\"":[75],"continuous":[79,140],"attractor":[80,129,141,178],"emerges":[81],"through":[82],"an":[83],"underlying":[84],"symmetry":[85,124],"connectivity":[89,162],"matrix.":[90],"This":[91],"model,":[92],"however,":[93],"cannot":[94],"account":[95],"for":[96,186],"data":[97],"is":[105,150],"monotonic":[107,146,181],"--":[108,113],"rather":[109],"than":[110],"bell-shaped":[112],"function":[114],"stored":[117],"variable.":[118],"Here,":[119],"we":[120,169],"show":[121,184],"used":[125],"bump":[128],"employed":[133],"create":[135],"whole":[137],"family":[138],"networks,":[142,189],"including":[143],"those":[144],"with":[145,164,180],"tuning.":[147],"Our":[148],"design":[149],"based":[151],"on":[152],"tuning":[153,182,192],"external":[155],"inputs":[156],"matrix":[163],"Toeplitz":[165],"symmetry.":[166],"particular,":[168],"provide":[170],"complete":[172],"analytical":[173],"solution":[174],"line":[177],"and":[183],"other":[188],"numerical":[191],"synaptic":[194],"weights":[195],"reduces":[196],"computation":[199],"single":[202],"parameter.":[203]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-24T13:16:06.693445","created_date":"2025-10-10T00:00:00"}