{"id":"https://openalex.org/W2806484334","doi":"https://doi.org/10.1137/18m1205509","title":"Morphisms of Neural Codes","display_name":"Morphisms of Neural Codes","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2806484334","doi":"https://doi.org/10.1137/18m1205509","mag":"2806484334"},"language":"en","primary_location":{"id":"doi:10.1137/18m1205509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1205509","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.02014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073562767","display_name":"R. Amzi Jeffs","orcid":"https://orcid.org/0000-0003-2653-2286"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Amzi Jeffs","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073562767"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9081,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.71036443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"4","issue":"1","first_page":"99","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10448","display_name":"Memory and Neural Mechanisms","score":0.9969000220298767,"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":0.9969000220298767,"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/T11266","display_name":"Neuroinflammation and Neurodegeneration Mechanisms","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"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":0.9923999905586243,"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/morphism","display_name":"Morphism","score":0.7871299982070923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6993722915649414},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5924464464187622},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5839366316795349},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5613380670547485},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5219385027885437},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5089530944824219},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.44171369075775146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38550522923469543},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3286544382572174},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22343069314956665},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08706465363502502}],"concepts":[{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.7871299982070923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6993722915649414},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5924464464187622},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5839366316795349},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5613380670547485},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5219385027885437},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5089530944824219},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.44171369075775146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38550522923469543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3286544382572174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22343069314956665},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08706465363502502},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1205509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1205509","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1806.02014","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.02014","pdf_url":"https://arxiv.org/pdf/1806.02014","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.02014","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.02014","pdf_url":"https://arxiv.org/pdf/1806.02014","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1849417957","display_name":null,"funder_award_id":"DGE-1761124","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1977368668","https://openalex.org/W2052515926","https://openalex.org/W2067016370","https://openalex.org/W2104874563","https://openalex.org/W2239693057","https://openalex.org/W2254969213","https://openalex.org/W2522272220","https://openalex.org/W2563233401","https://openalex.org/W2621129596","https://openalex.org/W2963005544","https://openalex.org/W2963014315","https://openalex.org/W2963292637","https://openalex.org/W2964231066","https://openalex.org/W2970101799","https://openalex.org/W3103819555","https://openalex.org/W3104100870","https://openalex.org/W4287869597","https://openalex.org/W4297299157","https://openalex.org/W4300147872","https://openalex.org/W4302338846"],"related_works":["https://openalex.org/W2366107444","https://openalex.org/W1964872188","https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W2949367465","https://openalex.org/W2587048717","https://openalex.org/W4388145910","https://openalex.org/W4235203617","https://openalex.org/W2006359264","https://openalex.org/W3029201158"],"abstract_inverted_index":{"We":[0,20,39,62,105],"define":[1,45],"a":[2,17,32,46,60,97],"notion":[3],"of":[4,12,56,71,80,112],"morphism":[5],"between":[6],"combinatorial":[7,14],"codes,":[8,74],"making":[9],"the":[10,41,54,69,78],"class":[11,55],"all":[13,50],"codes":[15,51,58,94],"into":[16],"category":[18],"Code.":[19],"show":[21,86],"that":[22,35,87],"morphisms":[23,36],"can":[24],"be":[25],"used":[26],"to":[27,44,66],"remove":[28],"redundant":[29],"information":[30],"from":[31],"code":[33,100],"and":[34,95],"preserve":[37],"convexity.":[38],"use":[40],"latter":[42],"fact":[43],"partial":[47],"order":[48],"on":[49,77],"in":[52,68],"which":[53,75],"convex":[57],"forms":[59],"down-set.":[61,82],"investigate":[63],"minimal":[64],"obstructions":[65],"convexity":[67],"form":[70],"\"minimally":[72],"nonconvex\"":[73],"lie":[76],"boundary":[79],"this":[81],"In":[83],"particular,":[84],"we":[85],"there":[88],"are":[89],"infinitely":[90],"many":[91],"minimally":[92,98],"nonconvex":[93,99],"construct":[96],"with":[101],"no":[102],"local":[103],"obstructions.":[104],"conclude":[106],"by":[107],"giving":[108],"an":[109],"algebraic":[110],"formulation":[111],"our":[113],"results.":[114]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}