{"id":"https://openalex.org/W1978305449","doi":"https://doi.org/10.1080/10586458.2003.10504499","title":"Can Computers Discover Ideal Knots?","display_name":"Can Computers Discover Ideal Knots?","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1978305449","doi":"https://doi.org/10.1080/10586458.2003.10504499","mag":"1978305449"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2003.10504499","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2003.10504499","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5075733920","display_name":"Eric J. Rawdon","orcid":"https://orcid.org/0000-0002-7190-8193"},"institutions":[{"id":"https://openalex.org/I165102784","display_name":"Duquesne University","ror":"https://ror.org/02336z538","country_code":"US","type":"education","lineage":["https://openalex.org/I165102784"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eric J. Rawdon","raw_affiliation_strings":["Duquesne University, Department of Mathematics and Computer Science , Pittsburgh , PA , 15282 E-mail: rawdon@mathcs.duq.edu"],"affiliations":[{"raw_affiliation_string":"Duquesne University, Department of Mathematics and Computer Science , Pittsburgh , PA , 15282 E-mail: rawdon@mathcs.duq.edu","institution_ids":["https://openalex.org/I165102784"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075733920"],"corresponding_institution_ids":["https://openalex.org/I165102784"],"apc_list":null,"apc_paid":null,"fwci":3.8964,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.9348903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"3","first_page":"287","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9988999962806702,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9368000030517578,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10126","display_name":"Logic, programming, and type systems","score":0.9146000146865845,"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/knot","display_name":"Knot (papermaking)","score":0.8128859996795654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7920200228691101},{"id":"https://openalex.org/keywords/inscribed-figure","display_name":"Inscribed figure","score":0.5910835266113281},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5125157833099365},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.44242265820503235},{"id":"https://openalex.org/keywords/knot-theory","display_name":"Knot theory","score":0.4288632869720459},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.27595216035842896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1977342963218689}],"concepts":[{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.8128859996795654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7920200228691101},{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.5910835266113281},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5125157833099365},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.44242265820503235},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.4288632869720459},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27595216035842896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1977342963218689},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2003.10504499","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2003.10504499","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ir.stthomas.edu:cas_mathpub-1049","is_oa":false,"landing_page_url":"https://ir.stthomas.edu/cas_mathpub/50","pdf_url":null,"source":{"id":"https://openalex.org/S4377196573","display_name":"UST Research Online (University of St. Thomas - Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161515732","host_organization_name":"University of St. Thomas - Minnesota","host_organization_lineage":["https://openalex.org/I161515732"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications &amp; Data","raw_type":"text"},{"id":"pmh:oai:CULeuclid:euclid.em/1087329232","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1087329232","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W84591330","https://openalex.org/W131438526","https://openalex.org/W612603251","https://openalex.org/W1602661116","https://openalex.org/W1610621306","https://openalex.org/W1616784375","https://openalex.org/W1630072945","https://openalex.org/W1649495583","https://openalex.org/W1964381670","https://openalex.org/W1966394703","https://openalex.org/W1984189140","https://openalex.org/W1984441614","https://openalex.org/W1993874841","https://openalex.org/W2000214520","https://openalex.org/W2000815453","https://openalex.org/W2022182754","https://openalex.org/W2024006365","https://openalex.org/W2026930233","https://openalex.org/W2046501806","https://openalex.org/W2052631562","https://openalex.org/W2068960528","https://openalex.org/W2071034769","https://openalex.org/W2075461230","https://openalex.org/W2082938731","https://openalex.org/W2087704519","https://openalex.org/W2092538847","https://openalex.org/W2103282036","https://openalex.org/W2132373652","https://openalex.org/W2150812234","https://openalex.org/W2153292122","https://openalex.org/W2158251088","https://openalex.org/W2325575424","https://openalex.org/W2478127955","https://openalex.org/W2498660707","https://openalex.org/W4251482051"],"related_works":["https://openalex.org/W3207350140","https://openalex.org/W2964242695","https://openalex.org/W2793606861","https://openalex.org/W2311482425","https://openalex.org/W2753977118","https://openalex.org/W2950745323","https://openalex.org/W2101575898","https://openalex.org/W2032825982","https://openalex.org/W2954666679","https://openalex.org/W2951467187"],"abstract_inverted_index":{"We":[0,15],"discuss":[1],"the":[2,33,52,58,62],"relationship":[3],"between":[4],"polygonal":[5,26,46,54,82],"knot":[6,10,20,27,41,64],"energies":[7],"and":[8,50],"smooth":[9,19,63,74,91],"energies,":[11],"concentrating":[12],"on":[13,81],"ropelength.":[14],"show":[16,44],"that":[17,32,45,51],"a":[18,25,30,39,73],"can":[21],"be":[22],"inscribed":[23],"in":[24,28,85],"such":[29],"way":[31],"ropelength":[34,47,60,75,78,88],"values":[35],"are":[36],"close.":[37],"For":[38],"given":[40],"type,":[42],"we":[43],"minima":[48],"exist":[49],"minimal":[53,59],"ropelengths":[55],"converge":[56],"to":[57,72],"of":[61,68],"type.":[65],"A":[66],"subsequence":[67],"these":[69],"polygons":[70],"converges":[71],"minimum.":[76],"Thus,":[77],"minimizations":[79,89],"performed":[80],"knots":[83],"do,":[84],"fact,":[86],"approximate":[87],"for":[90],"knots.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
