{"id":"https://openalex.org/W2121881115","doi":"https://doi.org/10.1162/neco_a_00319","title":"Optimal Population Codes for Space: Grid Cells Outperform Place Cells","display_name":"Optimal Population Codes for Space: Grid Cells Outperform Place Cells","publication_year":2012,"publication_date":"2012-05-17","ids":{"openalex":"https://openalex.org/W2121881115","doi":"https://doi.org/10.1162/neco_a_00319","mag":"2121881115","pmid":"https://pubmed.ncbi.nlm.nih.gov/22594833"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_00319","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00319","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":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/handle/20.500.14299/173069","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013861606","display_name":"Alexander Mathis","orcid":"https://orcid.org/0000-0002-3777-2202"},"institutions":[{"id":"https://openalex.org/I4210134961","display_name":"Bernstein Center for Computational Neuroscience Munich","ror":"https://ror.org/04bz45c46","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210092532","https://openalex.org/I4210134961"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexander Mathis","raw_affiliation_strings":["Bernstein Center for Computational Neuroscience Munich; Graduate School of Systemic Neuroscience and Division of Neurobiology, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 82152 Martinsried, Germany"],"affiliations":[{"raw_affiliation_string":"Bernstein Center for Computational Neuroscience Munich; Graduate School of Systemic Neuroscience and Division of Neurobiology, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 82152 Martinsried, Germany","institution_ids":["https://openalex.org/I4210134961","https://openalex.org/I8204097"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029489554","display_name":"Andreas V. M. Herz","orcid":"https://orcid.org/0000-0002-3836-565X"},"institutions":[{"id":"https://openalex.org/I4210134961","display_name":"Bernstein Center for Computational Neuroscience Munich","ror":"https://ror.org/04bz45c46","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210092532","https://openalex.org/I4210134961"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas V. M. Herz","raw_affiliation_strings":["Bernstein Center for Computational Neuroscience Munich; Graduate School of Systemic Neuroscience and Division of Neurobiology, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 82152 Martinsried, Germany"],"affiliations":[{"raw_affiliation_string":"Bernstein Center for Computational Neuroscience Munich; Graduate School of Systemic Neuroscience and Division of Neurobiology, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 82152 Martinsried, Germany","institution_ids":["https://openalex.org/I4210134961","https://openalex.org/I8204097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044843006","display_name":"Martin Stemmler","orcid":"https://orcid.org/0000-0002-9040-0475"},"institutions":[{"id":"https://openalex.org/I4210134961","display_name":"Bernstein Center for Computational Neuroscience Munich","ror":"https://ror.org/04bz45c46","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210092532","https://openalex.org/I4210134961"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Stemmler","raw_affiliation_strings":["Bernstein Center for Computational Neuroscience Munich; Graduate School of Systemic Neuroscience and Division of Neurobiology, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 82152 Martinsried, Germany"],"affiliations":[{"raw_affiliation_string":"Bernstein Center for Computational Neuroscience Munich; Graduate School of Systemic Neuroscience and Division of Neurobiology, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 82152 Martinsried, Germany","institution_ids":["https://openalex.org/I4210134961","https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013861606","https://openalex.org/A5029489554","https://openalex.org/A5044843006"],"corresponding_institution_ids":["https://openalex.org/I4210134961","https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":4.0115,"has_fulltext":false,"cited_by_count":157,"citation_normalized_percentile":{"value":0.94351691,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"24","issue":"9","first_page":"2280","last_page":"2317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10448","display_name":"Memory and Neural Mechanisms","score":0.9997000098228455,"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/T10448","display_name":"Memory and Neural Mechanisms","score":0.9997000098228455,"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/T10077","display_name":"Neuroscience and Neuropharmacology Research","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2804","display_name":"Cellular and Molecular 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/T10581","display_name":"Neural dynamics and brain function","score":0.996999979019165,"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/grid","display_name":"Grid","score":0.7393178343772888},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6122415065765381},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4832635521888733},{"id":"https://openalex.org/keywords/hexagonal-tiling","display_name":"Hexagonal tiling","score":0.439432293176651},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4334205090999603},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4225383996963501},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4097546637058258},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3852996826171875},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27286043763160706},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25511670112609863}],"concepts":[{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.7393178343772888},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6122415065765381},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4832635521888733},{"id":"https://openalex.org/C35908053","wikidata":"https://www.wikidata.org/wiki/Q3063631","display_name":"Hexagonal tiling","level":3,"score":0.439432293176651},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4334205090999603},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4225383996963501},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4097546637058258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3852996826171875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27286043763160706},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25511670112609863},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[{"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":"D002540","descriptor_name":"Cerebral Cortex","qualifier_ui":"Q000166","qualifier_name":"cytology","is_major_topic":false},{"descriptor_ui":"D002540","descriptor_name":"Cerebral Cortex","qualifier_ui":"Q000166","qualifier_name":"cytology","is_major_topic":false},{"descriptor_ui":"D002540","descriptor_name":"Cerebral Cortex","qualifier_ui":"Q000166","qualifier_name":"cytology","is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006624","descriptor_name":"Hippocampus","qualifier_ui":"Q000166","qualifier_name":"cytology","is_major_topic":false},{"descriptor_ui":"D006624","descriptor_name":"Hippocampus","qualifier_ui":"Q000166","qualifier_name":"cytology","is_major_topic":false},{"descriptor_ui":"D006624","descriptor_name":"Hippocampus","qualifier_ui":"Q000166","qualifier_name":"cytology","is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","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":"Q000145","qualifier_name":"classification","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000145","qualifier_name":"classification","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000145","qualifier_name":"classification","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":"D009949","descriptor_name":"Orientation","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009949","descriptor_name":"Orientation","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009949","descriptor_name":"Orientation","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D011157","descriptor_name":"Population Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011157","descriptor_name":"Population Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011157","descriptor_name":"Population Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D011336","descriptor_name":"Probability","qualifier_ui":null,"qualifier_name":null,"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}],"locations_count":4,"locations":[{"id":"doi:10.1162/neco_a_00319","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_00319","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:22594833","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22594833","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:epub.ub.uni-muenchen.de:15117","is_oa":false,"landing_page_url":"http://nbn-resolving.de/urn:nbn:de:bvb:19-epub-15117-0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401845","display_name":"Open access LMU (Ludwid Maxmilian's Universitat Munchen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neural Computation","raw_type":"doc-type:article"},{"id":"pmh:oai:infoscience.epfl.ch:281453","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/173069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:281453","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/173069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":87,"referenced_works":["https://openalex.org/W1653233231","https://openalex.org/W1864097855","https://openalex.org/W1965585960","https://openalex.org/W1966446573","https://openalex.org/W1969769253","https://openalex.org/W1970792572","https://openalex.org/W1971452080","https://openalex.org/W1975778127","https://openalex.org/W1978213775","https://openalex.org/W1978385102","https://openalex.org/W1980576528","https://openalex.org/W1984871000","https://openalex.org/W1988887771","https://openalex.org/W1994490999","https://openalex.org/W1995257611","https://openalex.org/W2003836944","https://openalex.org/W2008936540","https://openalex.org/W2021394691","https://openalex.org/W2022246269","https://openalex.org/W2027914336","https://openalex.org/W2030805642","https://openalex.org/W2033221285","https://openalex.org/W2037628926","https://openalex.org/W2043956739","https://openalex.org/W2045353501","https://openalex.org/W2051440620","https://openalex.org/W2052515926","https://openalex.org/W2052918792","https://openalex.org/W2055339690","https://openalex.org/W2058838930","https://openalex.org/W2060489187","https://openalex.org/W2067337882","https://openalex.org/W2067497461","https://openalex.org/W2067933183","https://openalex.org/W2071335965","https://openalex.org/W2078575897","https://openalex.org/W2080994882","https://openalex.org/W2081197259","https://openalex.org/W2086967399","https://openalex.org/W2087298647","https://openalex.org/W2089097360","https://openalex.org/W2092580449","https://openalex.org/W2093018428","https://openalex.org/W2097765403","https://openalex.org/W2099755474","https://openalex.org/W2100273034","https://openalex.org/W2101028262","https://openalex.org/W2103234826","https://openalex.org/W2103236816","https://openalex.org/W2103692957","https://openalex.org/W2105918394","https://openalex.org/W2107852368","https://openalex.org/W2107894771","https://openalex.org/W2110161683","https://openalex.org/W2117443520","https://openalex.org/W2117985192","https://openalex.org/W2119565218","https://openalex.org/W2120127728","https://openalex.org/W2122741244","https://openalex.org/W2122759946","https://openalex.org/W2125928414","https://openalex.org/W2127275707","https://openalex.org/W2127389037","https://openalex.org/W2127806105","https://openalex.org/W2128189925","https://openalex.org/W2131861377","https://openalex.org/W2132238259","https://openalex.org/W2138704896","https://openalex.org/W2139475683","https://openalex.org/W2147142551","https://openalex.org/W2151239423","https://openalex.org/W2157052947","https://openalex.org/W2160947738","https://openalex.org/W2165400927","https://openalex.org/W2166092475","https://openalex.org/W2166405697","https://openalex.org/W2167403166","https://openalex.org/W2169262669","https://openalex.org/W2172294131","https://openalex.org/W2178512648","https://openalex.org/W2318741562","https://openalex.org/W2319882402","https://openalex.org/W2322148641","https://openalex.org/W2322181608","https://openalex.org/W2914478155","https://openalex.org/W4298161877","https://openalex.org/W4298298962"],"related_works":["https://openalex.org/W2042377693","https://openalex.org/W2137398591","https://openalex.org/W2187906575","https://openalex.org/W2393841986","https://openalex.org/W2112164326","https://openalex.org/W4313445046","https://openalex.org/W2609286172","https://openalex.org/W2162488560","https://openalex.org/W4378833818","https://openalex.org/W1577244276"],"abstract_inverted_index":{"Rodents":[0],"use":[1],"two":[2,221],"distinct":[3,209],"neuronal":[4,86],"coordinate":[5],"systems":[6],"to":[7,41,52,111,180],"estimate":[8],"their":[9],"position:":[10],"place":[11,24,55,298],"fields":[12,18],"in":[13,19,143,147,175],"the":[14,20,42,60,76,81,85,122,129,136,140,145,149,183,201,205,217,240,252,261,270,278,285,288,295,301],"hippocampus":[15],"and":[16,56,155,168,269],"grid":[17,33,57,97,117,177,185,222,241,253,289],"entorhinal":[21],"cortex.":[22],"Whereas":[23],"cells":[25,34,118],"spike":[26,158],"at":[27,36],"only":[28],"one":[29,199],"particular":[30],"spatial":[31,69,93,123,166,188,197,206,210,218,271],"location,":[32],"fire":[35],"multiple":[37],"sites":[38],"that":[39,212,225,251,293],"correspond":[40],"points":[43],"of":[44,63,72,132,173,192,260,281,287,294,304],"an":[45],"imaginary":[46],"hexagonal":[47],"lattice.":[48],"We":[49,138],"study":[50],"how":[51],"best":[53,184,296],"construct":[54],"codes,":[58],"taking":[59],"probabilistic":[61],"nature":[62],"neural":[64],"spiking":[65],"into":[66],"account.":[67],"Which":[68],"encoding":[70],"properties":[71,224],"individual":[73],"neurons":[74],"confer":[75],"highest":[77],"resolution":[78,124,167,189,219,286],"when":[79],"decoding":[80],"animal's":[82],"position":[83,94,146],"from":[84,95],"population":[87],"response?":[88],"A":[89],"priori,":[90],"estimating":[91,144],"a":[92,96,170,176,181,257],"code":[98,178,186,242,290,299],"could":[99],"be":[100,244],"ambiguous,":[101],"as":[102],"regular":[103],"periodic":[104],"lattices":[105,115],"possess":[106],"translational":[107],"symmetry.":[108],"The":[109],"solution":[110],"this":[112],"problem":[113],"requires":[114,208],"for":[116,156,187,274],"with":[119,195,300],"different":[120,196,247],"spacings;":[121],"crucially":[125],"depends":[126],"on":[127],"choosing":[128],"right":[130],"ratios":[131],"these":[133,265],"spacings":[134,233],"across":[135,246],"population.":[137],"compute":[139],"expected":[141],"error":[142],"both":[148],"asymptotic":[150],"limit,":[151],"using":[152,160],"Fisher":[153],"information,":[154],"low":[157],"counts,":[159],"maximum":[161],"likelihood":[162],"estimation.":[163],"Achieving":[164],"high":[165],"covering":[169],"large":[171],"range":[172,207,280],"space":[174],"leads":[179],"trade-off:":[182],"is":[190],"built":[191],"nested":[193],"modules":[194],"periods,":[198],"inside":[200],"other,":[202],"whereas":[203],"maximizing":[204],"periods":[211],"are":[213,267],"pairwisely":[214],"incommensurate.":[215],"Optimizing":[216],"predicts":[220],"cell":[223],"have":[226],"been":[227],"experimentally":[228],"observed.":[229],"First,":[230],"short":[231],"lattice":[232,237,248,262],"should":[234,243],"outnumber":[235],"long":[236],"spacings.":[238],"Second,":[239],"self-similar":[245],"spacings,":[249],"so":[250],"field":[254],"always":[255],"covers":[256],"fixed":[258],"fraction":[259],"period.":[263],"If":[264],"conditions":[266],"satisfied":[268],"\"tuning":[272],"curves\"":[273],"each":[275],"neuron":[276],"span":[277],"same":[279,302],"firing":[282],"rates,":[283],"then":[284],"easily":[291],"exceeds":[292],"possible":[297],"number":[303],"neurons.":[305]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}