{"id":"https://openalex.org/W2934250468","doi":"https://doi.org/10.1162/neco_a_01231","title":"On Functions Computed on Trees","display_name":"On Functions Computed on Trees","publication_year":2019,"publication_date":"2019-09-16","ids":{"openalex":"https://openalex.org/W2934250468","doi":"https://doi.org/10.1162/neco_a_01231","mag":"2934250468","pmid":"https://pubmed.ncbi.nlm.nih.gov/31525312"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01231","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01231","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":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1904.02309","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Roozbeh Farhoodi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roozbeh Farhoodi","raw_affiliation_strings":["Departments of Bioengineering and Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, U.S.A"],"affiliations":[{"raw_affiliation_string":"Departments of Bioengineering and Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, U.S.A","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Khashayar Filom","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Khashayar Filom","raw_affiliation_strings":["Department of Mathematics, Northwestern University, Evanston, IL 60208, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northwestern University, Evanston, IL 60208, U.S.A","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ilenna Simone Jones","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ilenna Simone Jones","raw_affiliation_strings":["Departments of Bioengineering and Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, U.S.A"],"affiliations":[{"raw_affiliation_string":"Departments of Bioengineering and Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Konrad Paul Kording","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konrad Paul Kording","raw_affiliation_strings":["Departments of Bioengineering and Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, U.S.A"],"affiliations":[{"raw_affiliation_string":"Departments of Bioengineering and Neuroscience, University of Pennsylvania, Philadelphia, PA 19104, U.S.A","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1996,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51805705,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"31","issue":"11","first_page":"2075","last_page":"2137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.2093999981880188,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.2093999981880188,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.2004999965429306,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.06960000097751617,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6553000211715698},{"id":"https://openalex.org/keywords/models-of-neural-computation","display_name":"Models of neural computation","score":0.5343999862670898},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5162000060081482},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4986000061035156},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4828999936580658},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46230000257492065},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.461899995803833},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4320000112056732},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.41449999809265137},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.40059998631477356}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6553000211715698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5837000012397766},{"id":"https://openalex.org/C3832189","wikidata":"https://www.wikidata.org/wiki/Q8588916","display_name":"Models of neural computation","level":3,"score":0.5343999862670898},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5162000060081482},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4986000061035156},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47690001130104065},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46230000257492065},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.461899995803833},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3977000117301941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3695000112056732},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.33379998803138733},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C167528306","wikidata":"https://www.wikidata.org/wiki/Q5508776","display_name":"Function representation","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.2906000018119812},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.2870999872684479},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C140528856","wikidata":"https://www.wikidata.org/wiki/Q191884","display_name":"Inverse function","level":3,"score":0.26589998602867126},{"id":"https://openalex.org/C153576954","wikidata":"https://www.wikidata.org/wiki/Q594452","display_name":"Functional equation","level":3,"score":0.258899986743927}],"mesh":[{"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":"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/neco_a_01231","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01231","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":"pmh:oai:arXiv.org:1904.02309","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.02309","pdf_url":"https://arxiv.org/pdf/1904.02309","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmid:31525312","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31525312","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":{"id":"pmh:oai:arXiv.org:1904.02309","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.02309","pdf_url":"https://arxiv.org/pdf/1904.02309","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W312350839","https://openalex.org/W913685725","https://openalex.org/W1481803585","https://openalex.org/W1814698663","https://openalex.org/W1978611788","https://openalex.org/W1997112349","https://openalex.org/W1997935387","https://openalex.org/W1998255116","https://openalex.org/W2026208997","https://openalex.org/W2057426891","https://openalex.org/W2061186544","https://openalex.org/W2089947415","https://openalex.org/W2097886040","https://openalex.org/W2107998050","https://openalex.org/W2108671543","https://openalex.org/W2113314179","https://openalex.org/W2117120818","https://openalex.org/W2125988384","https://openalex.org/W2126685080","https://openalex.org/W2155020618","https://openalex.org/W2164649534","https://openalex.org/W2481190328","https://openalex.org/W2511261638","https://openalex.org/W2550848904","https://openalex.org/W2605622124","https://openalex.org/W2612252966","https://openalex.org/W2751947065","https://openalex.org/W2797443475","https://openalex.org/W2963095610","https://openalex.org/W4235630307","https://openalex.org/W4237970627","https://openalex.org/W4248269519","https://openalex.org/W4255885670","https://openalex.org/W4298227433","https://openalex.org/W4301460572"],"related_works":[],"abstract_inverted_index":{"Any":[0],"function":[1,33,143],"can":[2,16,66,157],"be":[3,17,67,94],"constructed":[4],"using":[5],"a":[6,14,20,32,70,76,85],"hierarchy":[7,15],"of":[8,26,53,78,84,87,106,129,150],"simpler":[9],"functions":[10,50,65,119,155],"through":[11],"compositions.":[12],"Such":[13],"characterized":[18],"by":[19],"binary":[21],"rooted":[22],"tree.":[23,72],"Each":[24],"node":[25],"this":[27],"tree":[28],"is":[29,56],"associated":[30],"with":[31,153],"that":[34,92,99,122],"takes":[35],"as":[36],"inputs":[37],"two":[38],"numbers":[39],"from":[40],"its":[41],"children":[42],"and":[43,108,120,159,165],"produces":[44],"one":[45],"output.":[46],"Since":[47],"thinking":[48],"about":[49],"in":[51,81,104,139],"terms":[52],"computation":[54,151],"graphs":[55,152],"becoming":[57],"popular,":[58],"we":[59,74,97,115],"may":[60],"want":[61],"to":[62,133,141,163],"know":[63],"which":[64],"implemented":[68],"on":[69],"given":[71],"Here,":[73],"describe":[75],"set":[77],"necessary":[79],"constraints":[80],"the":[82,112,148,154],"form":[83],"system":[86],"nonlinear":[88],"partial":[89],"differential":[90],"equations":[91],"must":[93],"satisfied.":[95],"Moreover,":[96],"prove":[98],"these":[100],"conditions":[101],"are":[102,124],"sufficient":[103],"contexts":[105],"analytic":[107],"bit-valued":[109],"functions.":[110],"In":[111],"latter":[113],"case,":[114],"explicitly":[116],"enumerate":[117],"discrete":[118],"observe":[121],"there":[123],"relatively":[125],"few.":[126],"Our":[127,145],"point":[128],"view":[130],"allows":[131],"us":[132],"compare":[134],"different":[135],"neural":[136],"network":[137],"architectures":[138],"regard":[140],"their":[142],"spaces.":[144],"work":[146],"connects":[147],"structure":[149],"they":[156],"implement":[158],"has":[160],"potential":[161],"applications":[162],"neuroscience":[164],"computer":[166],"science.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-04-11T00:00:00"}
