{"id":"https://openalex.org/W2113146504","doi":"https://doi.org/10.1162/089976603321780308","title":"Ergodicity of Spike Trains: When Does Trial Averaging Make Sense?","display_name":"Ergodicity of Spike Trains: When Does Trial Averaging Make Sense?","publication_year":2003,"publication_date":"2003-05-22","ids":{"openalex":"https://openalex.org/W2113146504","doi":"https://doi.org/10.1162/089976603321780308","mag":"2113146504","pmid":"https://pubmed.ncbi.nlm.nih.gov/12816576"},"language":"en","primary_location":{"id":"doi:10.1162/089976603321780308","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976603321780308","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/A5086073834","display_name":"Naoki Masuda","orcid":"https://orcid.org/0000-0003-1567-801X"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Naoki Masuda","raw_affiliation_strings":["Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan,","Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo , Japan"],"affiliations":[{"raw_affiliation_string":"Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan,","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo , Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113676858","display_name":"Kazuyuki Aihara","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086780","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19","country_code":"JP","type":"government","lineage":["https://openalex.org/I4210086780"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuyuki Aihara","raw_affiliation_strings":["Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan, and CREST, Japan Science and Technology Corporation, Saitama, Japan,"],"affiliations":[{"raw_affiliation_string":"Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan, and CREST, Japan Science and Technology Corporation, Saitama, Japan,","institution_ids":["https://openalex.org/I4210086780","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086073834"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":1.0117,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.7316326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"6","first_page":"1341","last_page":"1372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":1.0,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/spike-train","display_name":"Spike train","score":0.5691993832588196},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.5573992729187012},{"id":"https://openalex.org/keywords/spike","display_name":"Spike (software development)","score":0.5194553732872009},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.49434638023376465},{"id":"https://openalex.org/keywords/stimulus","display_name":"Stimulus (psychology)","score":0.47453463077545166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45383432507514954},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.44904765486717224},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3853272497653961},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36121866106987},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.32661473751068115},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2605198919773102},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.2498987317085266},{"id":"https://openalex.org/keywords/cognitive-psychology","display_name":"Cognitive psychology","score":0.09456494450569153}],"concepts":[{"id":"https://openalex.org/C2909946758","wikidata":"https://www.wikidata.org/wiki/Q194277","display_name":"Spike train","level":3,"score":0.5691993832588196},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.5573992729187012},{"id":"https://openalex.org/C2781390188","wikidata":"https://www.wikidata.org/wiki/Q25203449","display_name":"Spike (software development)","level":2,"score":0.5194553732872009},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.49434638023376465},{"id":"https://openalex.org/C2779918689","wikidata":"https://www.wikidata.org/wiki/Q3771842","display_name":"Stimulus (psychology)","level":2,"score":0.47453463077545166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45383432507514954},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.44904765486717224},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3853272497653961},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36121866106987},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.32661473751068115},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2605198919773102},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.2498987317085266},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.09456494450569153},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005246","descriptor_name":"Feedback","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D005246","descriptor_name":"Feedback","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":"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":"D010507","descriptor_name":"Periodicity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010507","descriptor_name":"Periodicity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D010507","descriptor_name":"Periodicity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013569","descriptor_name":"Synapses","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013569","descriptor_name":"Synapses","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D013569","descriptor_name":"Synapses","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1162/089976603321780308","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976603321780308","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:12816576","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12816576","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":61,"referenced_works":["https://openalex.org/W25946478","https://openalex.org/W60166153","https://openalex.org/W566656105","https://openalex.org/W1539683305","https://openalex.org/W1582051163","https://openalex.org/W1947144830","https://openalex.org/W1964309659","https://openalex.org/W1966740449","https://openalex.org/W1969049552","https://openalex.org/W1976027541","https://openalex.org/W1984931175","https://openalex.org/W1990305461","https://openalex.org/W1992084652","https://openalex.org/W1992919184","https://openalex.org/W1995747963","https://openalex.org/W2003743055","https://openalex.org/W2010714529","https://openalex.org/W2011459128","https://openalex.org/W2014339193","https://openalex.org/W2017209122","https://openalex.org/W2017444605","https://openalex.org/W2028356170","https://openalex.org/W2028546686","https://openalex.org/W2029342452","https://openalex.org/W2035051040","https://openalex.org/W2036231165","https://openalex.org/W2039755641","https://openalex.org/W2049244667","https://openalex.org/W2054430476","https://openalex.org/W2057733436","https://openalex.org/W2058691103","https://openalex.org/W2062899906","https://openalex.org/W2063810326","https://openalex.org/W2065345648","https://openalex.org/W2066703464","https://openalex.org/W2073512103","https://openalex.org/W2074993220","https://openalex.org/W2079948225","https://openalex.org/W2080041388","https://openalex.org/W2084793648","https://openalex.org/W2093305345","https://openalex.org/W2111239915","https://openalex.org/W2119443761","https://openalex.org/W2130168752","https://openalex.org/W2130305130","https://openalex.org/W2138704896","https://openalex.org/W2142373488","https://openalex.org/W2144263190","https://openalex.org/W2148342982","https://openalex.org/W2153201079","https://openalex.org/W2154953441","https://openalex.org/W2156146528","https://openalex.org/W2159492611","https://openalex.org/W2160667172","https://openalex.org/W2172294131","https://openalex.org/W2294880175","https://openalex.org/W2341008280","https://openalex.org/W2497735908","https://openalex.org/W2989827627","https://openalex.org/W4250384672","https://openalex.org/W4255770584"],"related_works":["https://openalex.org/W2383615955","https://openalex.org/W2056756835","https://openalex.org/W2062974934","https://openalex.org/W2187212244","https://openalex.org/W2775582103","https://openalex.org/W2329992713","https://openalex.org/W1558157446","https://openalex.org/W2173049006","https://openalex.org/W2014837149","https://openalex.org/W2114811586"],"abstract_inverted_index":{"Neuronal":[0],"information":[1],"processing":[2],"is":[3,48,53,74],"often":[4],"studied":[5],"on":[6],"the":[7,21,51,55,59,66,78,111,175,190],"basis":[8],"of":[9,95,113,130,149,164],"spiking":[10,29],"patterns.":[11,115],"The":[12,162],"relevant":[13],"statistics":[14,57,112],"such":[15,100],"as":[16,101],"firing":[17,114,169],"rates":[18],"calculated":[19],"with":[20,138,181],"peri-stimulus":[22],"time":[23],"histogram":[24],"are":[25,157,170,185],"obtained":[26],"by":[27],"averaging":[28,70],"patterns":[30],"over":[31,159],"many":[32,160],"experimental":[33,41],"runs.":[34],"However,":[35],"animals":[36],"should":[37],"respond":[38],"to":[39,50,126,132,174,188],"one":[40],"stimulation":[42],"in":[43,77,153],"real":[44],"situations,":[45],"and":[46,71,107,141,145,167,172],"what":[47],"available":[49],"brain":[52],"not":[54,84],"trial":[56,69],"but":[58],"population":[60,72],"statistics.":[61],"Consequently,":[62],"physiological":[63],"ergodicity,":[64],"namely,":[65],"consistency":[67],"between":[68],"averaging,":[73],"implicitly":[75],"assumed":[76],"data":[79],"analyses,":[80],"although":[81],"it":[82],"does":[83],"trivially":[85],"hold":[86],"true.":[87],"In":[88,116],"this":[89],"letter,":[90],"we":[91,118],"investigate":[92],"how":[93,121],"characteristics":[94],"noisy":[96],"neural":[97,182],"network":[98,183],"models,":[99],"single":[102],"neuron":[103],"properties,":[104],"external":[105,136],"stimuli,":[106],"synaptic":[108,150],"inputs,":[109,135],"affect":[110],"particular,":[117],"show":[119],"that":[120,156],"high":[122],"membrane":[123],"potential":[124],"sensitivity":[125],"input":[127],"fluctuations,":[128],"inability":[129],"neurons":[131],"remember":[133],"past":[134],"stimuli":[137],"large":[139],"variability":[140],"temporally":[142],"separated":[143],"peaks,":[144],"relatively":[146],"few":[147],"contributions":[148],"inputs":[151],"result":[152],"spike":[154,165],"trains":[155,166],"reproducible":[158],"trials.":[161],"reproducibility":[163],"synchronous":[168],"contrasted":[171],"related":[173],"ergodicity":[176],"issue.":[177],"Several":[178],"numerical":[179],"calculations":[180],"examples":[184],"carried":[186],"out":[187],"support":[189],"theoretical":[191],"results.":[192]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
