{"id":"https://openalex.org/W1860836677","doi":"https://doi.org/10.3233/com-14025","title":"Algorithmic Aspects of Lipschitz Functions","display_name":"Algorithmic Aspects of Lipschitz Functions","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1860836677","doi":"https://doi.org/10.3233/com-14025","mag":"1860836677"},"language":"en","primary_location":{"id":"doi:10.3233/com-14025","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-14025","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1402.2429","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Cameron Freer","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cameron Freer","raw_affiliation_strings":["Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139, USA freer@math.mit.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology, Cambridge, MA 02139, USA freer@math.mit.edu","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Bj\u00f8 rn Kjos-Hanssen","orcid":null},"institutions":[{"id":"https://openalex.org/I117965899","display_name":"University of Hawai\u02bbi at M\u0101noa","ror":"https://ror.org/01wspgy28","country_code":"US","type":"education","lineage":["https://openalex.org/I117965899"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bj\u00f8 rn Kjos-Hanssen","raw_affiliation_strings":["Department of Mathematics, University of Hawai\u0312i at M\u0101noa, 2500 Campus Rd, Honolulu, HI 96822, USA bjoern@math.hawaii.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hawai\u0312i at M\u0101noa, 2500 Campus Rd, Honolulu, HI 96822, USA bjoern@math.hawaii.edu","institution_ids":["https://openalex.org/I117965899"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Andr\u00e9 Nies","orcid":null},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Nies","raw_affiliation_strings":["Department of Computer Science, University of Auckland, Auckland 1010, New Zealandandre@cs.auckland.ac.nz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Auckland, Auckland 1010, New Zealandandre@cs.auckland.ac.nz","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":null,"display_name":"Frank Stephan","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Frank Stephan","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, 21 Lower Kent Ridge Road, Singapore 119077 fstephan@comp.nus.edu.sg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, 21 Lower Kent Ridge Road, Singapore 119077 fstephan@comp.nus.edu.sg","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4150,"currency":"USD","value_usd":4150},"apc_paid":null,"fwci":2.1409,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86524371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","issue":"1","first_page":"45","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9531999826431274,"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":0.9531999826431274,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.0142000000923872,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.010300000198185444,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.9146999716758728},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6144000291824341},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.527400016784668},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4860999882221222},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.37279999256134033},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.3070000112056732}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.9146999716758728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7736999988555908},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6144000291824341},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.527400016784668},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4860999882221222},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39879998564720154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37389999628067017},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.28529998660087585},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.2605000138282776}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/com-14025","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-14025","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1402.2429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.2429","pdf_url":"https://arxiv.org/pdf/1402.2429","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:1402.2429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.2429","pdf_url":"https://arxiv.org/pdf/1402.2429","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,9],"characterize":[1],"the":[2],"variation":[3],"functions":[4],"of":[5],"computable":[6,23],"Lipschitz":[7,24,48],"functions.":[8],"show":[10,35],"that":[11,36],"a":[12,37],"real":[13,38],"\\(<![CDATA[$z$]]\\)":[14,39],"is":[15,26,40,53],"computably":[16],"random":[17,42],"if":[18,21,43,46],"and":[19,44],"only":[20,45],"every":[22,47],"function":[25,49],"differentiable":[27,54],"at":[28,55],"\\(<![CDATA[$z$]]\\).":[29,56],"Beyond":[30],"these":[31],"principal":[32],"results,":[33],"we":[34],"Schnorr":[41],"with":[50],"\\(<![CDATA[$L_{1}$]]\\)-computable":[51],"derivative":[52]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}
