{"id":"https://openalex.org/W7167795418","doi":"https://doi.org/10.48550/arxiv.2607.06696","title":"Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds","display_name":"Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds","publication_year":2026,"publication_date":"2026-07-07","ids":{"openalex":"https://openalex.org/W7167795418","doi":"https://doi.org/10.48550/arxiv.2607.06696"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.06696","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.06696","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.06696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140364138","display_name":"Kisung You","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"You, Kisung","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035523112","display_name":"Boram Cho","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cho, Boram","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.3091000020503998,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.3091000020503998,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.2831999957561493,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.08529999852180481,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5512999892234802},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5501000285148621},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.47909998893737793},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.40880000591278076},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.3962000012397766},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.39100000262260437},{"id":"https://openalex.org/keywords/heat-flow","display_name":"Heat flow","score":0.36890000104904175},{"id":"https://openalex.org/keywords/geometric-mean","display_name":"Geometric mean","score":0.35280001163482666}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.715499997138977},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5512999892234802},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5501000285148621},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.47909998893737793},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C2985596519","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat flow","level":3,"score":0.36890000104904175},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3508000075817108},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.34130001068115234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3377000093460083},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32170000672340393},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C187530423","wikidata":"https://www.wikidata.org/wiki/Q7140503","display_name":"Particle size","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C66696666","wikidata":"https://www.wikidata.org/wiki/Q17105612","display_name":"Sample entropy","level":3,"score":0.28870001435279846},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2759000062942505},{"id":"https://openalex.org/C3020318244","wikidata":"https://www.wikidata.org/wiki/Q4812187","display_name":"Large sample","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.06696","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.06696","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.06696","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.06696","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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":{"Weighted":[0],"empirical":[1],"measures":[2],"on":[3],"compact":[4,87],"manifolds":[5],"appear":[6],"in":[7],"importance":[8,105],"sampling,":[9],"particle":[10],"approximations,":[11],"posterior":[12],"summaries,":[13],"quadrature,":[14],"and":[15,22,59,99,122,128,137,142],"representation":[16],"learning.":[17],"Ordinary":[18],"effective":[19,62,66,77],"sample":[20,63,67,78],"size":[21,68,79],"related":[23],"weight":[24],"summaries":[25,144],"ignore":[26],"the":[27,30,109],"geometry":[28],"of":[29,46],"support.":[31],"We":[32],"introduce":[33],"heat-kernel":[34,53],"entropy":[35],"profiles":[36],"to":[37],"measure":[38],"nonuniformity":[39],"after":[40],"intrinsic":[41],"diffusion":[42],"at":[43],"a":[44,60,100],"range":[45],"scales.":[47],"For":[48],"order-two":[49],"R\u00e9nyi":[50],"entropy,":[51],"pairwise":[52],"overlaps":[54,81],"give":[55,126],"an":[56],"exact":[57],"profile":[58,92,111],"geometric":[61],"size.":[64],"This":[65],"discounts":[69],"nearby":[70],"or":[71],"duplicate":[72],"particles.":[73],"It":[74],"approaches":[75],"ordinary":[76],"as":[80],"between":[82],"distinct":[83],"particles":[84],"vanish.":[85],"On":[86,107],"boundaryless":[88],"manifolds,":[89],"we":[90],"establish":[91],"monotonicity,":[93],"gESS":[94],"scale":[95],"limits,":[96],"deterministic-weight":[97],"consistency,":[98],"bounded-ratio":[101],"result":[102],"for":[103],"self-normalized":[104],"sampling.":[106],"spheres,":[108],"unlogged":[110],"decomposes":[112],"into":[113],"spherical-harmonic":[114],"energies.":[115],"The":[116],"first":[117],"terms":[118],"are":[119],"squared":[120],"mean-resultant":[121],"traceless-second-moment":[123],"energies,":[124],"which":[125],"vMF-":[127],"Bingham-type":[129],"scalar":[130],"summaries.":[131],"Experiments":[132],"identify":[133],"antipodal,":[134],"girdle,":[135],"multimodal,":[136],"duplicate-particle":[138],"structures":[139],"that":[140],"weight-only":[141],"first-moment":[143],"miss.":[145]},"counts_by_year":[],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2026-07-10T00:00:00"}