{"id":"https://openalex.org/W3097718334","doi":"https://doi.org/10.1090/mcom/3740","title":"Computing equilibrium measures with power law kernels","display_name":"Computing equilibrium measures with power law kernels","publication_year":2022,"publication_date":"2022-04-20","ids":{"openalex":"https://openalex.org/W3097718334","doi":"https://doi.org/10.1090/mcom/3740","mag":"3097718334"},"language":"lv","primary_location":{"id":"doi:10.1090/mcom/3740","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3740","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.00045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064837586","display_name":"Timon S. Gutleb","orcid":"https://orcid.org/0000-0002-8239-2372"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Timon Gutleb","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022412709","display_name":"Jos\u00e9 A. Carrillo","orcid":"https://orcid.org/0000-0001-8819-4660"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Carrillo","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010027385","display_name":"Sheehan Olver","orcid":"https://orcid.org/0000-0001-6920-0826"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Sheehan Olver","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5134,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.79255986,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"91","issue":"337","first_page":"2247","last_page":"2281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9975000023841858,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/algorithm","display_name":"Algorithm","score":0.4433833956718445},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32648324966430664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2259305715560913}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4433833956718445},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32648324966430664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2259305715560913}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3740","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3740","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.00045","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.00045","pdf_url":"https://arxiv.org/pdf/2011.00045","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"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/88648","is_oa":true,"landing_page_url":"http://hdl.handle.net/10044/1/88648","pdf_url":"http://hdl.handle.net/10044/1/88648","source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Working Paper"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:7fc4ddcd-2581-42d5-b5c4-69fbc917e28a","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:7fc4ddcd-2581-42d5-b5c4-69fbc917e28a","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"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":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/95127","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/95127","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2281","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.00045","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.00045","pdf_url":"https://arxiv.org/pdf/2011.00045","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8100000023841858}],"awards":[{"id":"https://openalex.org/G1119130631","display_name":"Spectral element methods for fractional differential equations, with applications in applied analysis and medical imaging","funder_award_id":"EP/T022132/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1257672279","display_name":null,"funder_award_id":"EP/T022132/1","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G2708424170","display_name":null,"funder_award_id":"883363","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G5079537571","display_name":null,"funder_award_id":"RPG-2019-144","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5634516057","display_name":null,"funder_award_id":"883363","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G5894658213","display_name":null,"funder_award_id":"RPG-2019-144","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G6700243956","display_name":null,"funder_award_id":"883363","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7050360088","display_name":null,"funder_award_id":"RPG-2019-144","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G7742257476","display_name":null,"funder_award_id":"EP/T022132/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8153339990","display_name":null,"funder_award_id":"EP/T022132/1","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W588998842","https://openalex.org/W1482888786","https://openalex.org/W1522727408","https://openalex.org/W1523113578","https://openalex.org/W1553338987","https://openalex.org/W1563853427","https://openalex.org/W1585160083","https://openalex.org/W1591074427","https://openalex.org/W1593505867","https://openalex.org/W1601581883","https://openalex.org/W1602827292","https://openalex.org/W1678272269","https://openalex.org/W1898203370","https://openalex.org/W1975529482","https://openalex.org/W2001354695","https://openalex.org/W2005140191","https://openalex.org/W2012405657","https://openalex.org/W2016518303","https://openalex.org/W2018529115","https://openalex.org/W2035608633","https://openalex.org/W2037054313","https://openalex.org/W2040416019","https://openalex.org/W2042564923","https://openalex.org/W2062391453","https://openalex.org/W2063723224","https://openalex.org/W2067711323","https://openalex.org/W2069175799","https://openalex.org/W2072076940","https://openalex.org/W2093141193","https://openalex.org/W2119323323","https://openalex.org/W2119414533","https://openalex.org/W2120575449","https://openalex.org/W2151793824","https://openalex.org/W2157942701","https://openalex.org/W2162452471","https://openalex.org/W2171692351","https://openalex.org/W2282345054","https://openalex.org/W2323056003","https://openalex.org/W2345531252","https://openalex.org/W2406592375","https://openalex.org/W2469638860","https://openalex.org/W2518263702","https://openalex.org/W2616864018","https://openalex.org/W2625804581","https://openalex.org/W2768435914","https://openalex.org/W2774131624","https://openalex.org/W2775596627","https://openalex.org/W2790765814","https://openalex.org/W2796079430","https://openalex.org/W2898551752","https://openalex.org/W2948936768","https://openalex.org/W2962716964","https://openalex.org/W2962792386","https://openalex.org/W2962910852","https://openalex.org/W2963172715","https://openalex.org/W2964132515","https://openalex.org/W3040590284","https://openalex.org/W3100014801","https://openalex.org/W3102224879","https://openalex.org/W3103271357","https://openalex.org/W3105163269","https://openalex.org/W3109089832","https://openalex.org/W3178771730","https://openalex.org/W3200698245","https://openalex.org/W4212793308","https://openalex.org/W6705060144"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"We":[0,209],"introduce":[1],"a":[2,162,169,173,218],"method":[3,157,216],"to":[4,164,172,225,246],"numerically":[5,240],"compute":[6],"equilibrium":[7,187,251,273],"measures":[8,252],"for":[9,264],"problems":[10],"with":[11,228,244],"attractive-repulsive":[12],"power":[13,265],"law":[14,266],"kernels":[15],"of":[16,185,195,214,250,262,271],"the":[17,183,186,196,205,215,269,272],"form":[18],"<inline-formula":[19],"content-type=\"math/mathml\">":[20],"<mml:math":[21],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[22],"alttext=\"upper":[23],"K":[24],"left-parenthesis":[25],"x":[26,33,46],"minus":[27,34,43,47],"y":[28,35,48],"right-parenthesis":[29],"equals":[30],"StartFraction":[31,44],"StartAbsoluteValue":[32,45],"EndAbsoluteValue":[36,49],"Superscript":[37,50],"alpha":[38,41],"Baseline":[39,52],"Over":[40,53],"EndFraction":[42],"beta":[51,54],"EndFraction\">":[55],"<mml:semantics>":[56],"<mml:mrow>":[57,70,100],"<mml:mi>K</mml:mi>":[58],"<mml:mo":[59,66,73,84,103,114],"stretchy=\"false\">(</mml:mo>":[60],"<mml:mi>x</mml:mi>":[61,76,106],"<mml:mo>":[62,77,96,107],"\u2212":[63,78,97,108],"</mml:mo>":[64,79,98,109],"<mml:mi>y</mml:mi>":[65,80,110],"stretchy=\"false\">)</mml:mo>":[67],"<mml:mo>=</mml:mo>":[68],"<mml:mfrac>":[69,99],"<mml:mrow":[71,82,101,112],"class=\"MJX-TeXAtom-ORD\">":[72,83,102,113],"stretchy=\"false\">|</mml:mo>":[74,85,104,115],"</mml:mrow>":[75,86,91,105,116,121,126],"<mml:msup>":[81,111],"<mml:mi>":[87,92,117,122],"\u03b1":[88,93],"</mml:mi>":[89,94,119,124],"</mml:msup>":[90,120],"</mml:mfrac>":[95,125],"\u03b2":[118,123],"<mml:annotation":[127],"encoding=\"application/x-tex\">K(x-y)":[128],"=":[129],"\\frac":[130],"{|x-y|^\\alpha":[131],"}{\\alpha":[132],"}-\\frac":[133],"{|x-y|^\\beta":[134],"}{\\beta":[135],"}</mml:annotation>":[136],"</mml:semantics>":[137],"</mml:math>":[138],"</inline-formula>":[139],"using":[140],"recursively":[141],"generated":[142],"banded":[143,146],"and":[144,191,212,221,248],"approximately":[145],"operators":[147,198],"acting":[148],"on":[149],"expansions":[150],"in":[151,200,204,259],"ultraspherical":[152],"polynomial":[153],"bases.":[154],"The":[155,189],"proposed":[156],"reduces":[158],"what":[159],"is":[160],"na\u00efvely":[161],"difficult":[163],"approach":[165],"optimization":[166,175,207],"problem":[167,176],"over":[168,177],"measure":[170,274],"space":[171],"straightforward":[174],"one":[178],"or":[179],"two":[180,277],"variables":[181],"fixing":[182],"support":[184,270],"measure.":[188],"structure":[190],"rapid":[192],"convergence":[193,213],"properties":[194],"obtained":[197],"result":[199],"high":[201],"computational":[202],"efficiency":[203],"individual":[206],"steps.":[208],"discuss":[210],"stability":[211],"under":[217],"Tikhonov":[219],"regularization":[220],"use":[222],"an":[223],"implementation":[224],"showcase":[226],"comparisons":[227],"analytically":[229],"known":[230],"solutions":[231],"as":[232,234,253,255],"well":[233,254],"discrete":[235],"particle":[236],"simulations.":[237],"Finally,":[238],"we":[239],"explore":[241],"open":[242],"questions":[243],"respect":[245],"existence":[247],"uniqueness":[249],"gap":[256],"forming":[257],"behaviour":[258],"parameter":[260],"ranges":[261],"interest":[263],"kernels,":[267],"where":[268],"splits":[275],"into":[276],"intervals.":[278]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}