{"id":"https://openalex.org/W2397553202","doi":"https://doi.org/10.1007/s00454-020-00225-9","title":"Reconstruction of Convex Bodies from Moments","display_name":"Reconstruction of Convex Bodies from Moments","publication_year":2020,"publication_date":"2020-07-22","ids":{"openalex":"https://openalex.org/W2397553202","doi":"https://doi.org/10.1007/s00454-020-00225-9","mag":"2397553202"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-020-00225-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-020-00225-9","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://pure.au.dk/portal/en/publications/6ad0d31f-311c-45ee-851d-310833ea1119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076304752","display_name":"Astrid Kousholt","orcid":null},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Astrid Kousholt","raw_affiliation_strings":["Department of Mathematics, Aarhus University, Aarhus, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aarhus University, Aarhus, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112563393","display_name":"Julia Schulte","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["CH","DE"],"is_corresponding":false,"raw_author_name":"Julia Schulte","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","Department of Mathematics, Ruhr-Universit\u00e4t Bochum, Bochum, Germany"],"raw_orcid":"https://orcid.org/0000-0002-3501-7588","affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Department of Mathematics, Ruhr-Universit\u00e4t Bochum, Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076304752"],"corresponding_institution_ids":["https://openalex.org/I204337017"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.00096111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"65","issue":"1","first_page":"1","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10570","display_name":"Drug Transport and Resistance Mechanisms","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.960099995136261,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.7225962281227112},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.67218416929245},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5641786456108093},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5450215935707092},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.5446918606758118},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5219135284423828},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.5028378367424011},{"id":"https://openalex.org/keywords/velocity-moments","display_name":"Velocity Moments","score":0.47583842277526855},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46856334805488586},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4658646881580353},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4497716426849365},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4390726685523987},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.43620359897613525},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.43003910779953003},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.281959593296051},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18658262491226196},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14978346228599548},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08598175644874573},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.055339694023132324}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7225962281227112},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.67218416929245},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5641786456108093},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5450215935707092},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.5446918606758118},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5219135284423828},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5028378367424011},{"id":"https://openalex.org/C149539972","wikidata":"https://www.wikidata.org/wiki/Q7919290","display_name":"Velocity Moments","level":4,"score":0.47583842277526855},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46856334805488586},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4658646881580353},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4497716426849365},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4390726685523987},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.43620359897613525},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.43003910779953003},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.281959593296051},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18658262491226196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14978346228599548},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08598175644874573},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.055339694023132324},{"id":"https://openalex.org/C165699331","wikidata":"https://www.wikidata.org/wiki/Q461533","display_name":"Wavefront","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C92423082","wikidata":"https://www.wikidata.org/wiki/Q132146","display_name":"Zernike polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00454-020-00225-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-020-00225-9","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/6ad0d31f-311c-45ee-851d-310833ea1119","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/6ad0d31f-311c-45ee-851d-310833ea1119","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kousholt, A & Schulte, J 2021, 'Reconstruction of Convex Bodies from Moments', Discrete & Computational Geometry, vol. 65, no. 1, pp. 1-42. https://doi.org/10.1007/s00454-020-00225-9","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1605.06362","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.06362","pdf_url":"https://arxiv.org/pdf/1605.06362","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":"","raw_type":"text"},{"id":"mag:2397553202","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.06362.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1605.06362","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1605.06362","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/6ad0d31f-311c-45ee-851d-310833ea1119","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/6ad0d31f-311c-45ee-851d-310833ea1119","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kousholt, A & Schulte, J 2021, 'Reconstruction of Convex Bodies from Moments', Discrete & Computational Geometry, vol. 65, no. 1, pp. 1-42. https://doi.org/10.1007/s00454-020-00225-9","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5099999904632568}],"awards":[{"id":"https://openalex.org/G4465333562","display_name":null,"funder_award_id":"FOR 1548","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W73782397","https://openalex.org/W163224475","https://openalex.org/W581677283","https://openalex.org/W588210445","https://openalex.org/W1542343170","https://openalex.org/W1571966798","https://openalex.org/W1866311589","https://openalex.org/W1967344706","https://openalex.org/W1974818065","https://openalex.org/W1992008263","https://openalex.org/W2000380654","https://openalex.org/W2006109604","https://openalex.org/W2010029425","https://openalex.org/W2029997366","https://openalex.org/W2042920982","https://openalex.org/W2057638322","https://openalex.org/W2075322104","https://openalex.org/W2086325670","https://openalex.org/W2086588437","https://openalex.org/W2086593502","https://openalex.org/W2097883065","https://openalex.org/W2101276724","https://openalex.org/W2103717666","https://openalex.org/W2110578851","https://openalex.org/W2118203826","https://openalex.org/W2123608023","https://openalex.org/W2260608828","https://openalex.org/W2548416180","https://openalex.org/W2798707604","https://openalex.org/W2963465218","https://openalex.org/W2994178798","https://openalex.org/W4206148521","https://openalex.org/W4230552673","https://openalex.org/W4255333822","https://openalex.org/W4292025355"],"related_works":["https://openalex.org/W1970137213","https://openalex.org/W1824257344","https://openalex.org/W2469524243","https://openalex.org/W2181430840","https://openalex.org/W2126703485","https://openalex.org/W2891928587","https://openalex.org/W816501384","https://openalex.org/W3041746220","https://openalex.org/W2134926139","https://openalex.org/W151658032","https://openalex.org/W2331030174","https://openalex.org/W2068696592","https://openalex.org/W1585594744","https://openalex.org/W3100530370","https://openalex.org/W1985224403","https://openalex.org/W1548393144","https://openalex.org/W2792882578","https://openalex.org/W3135886972","https://openalex.org/W2150623833","https://openalex.org/W3105936967"],"abstract_inverted_index":{"We":[0,20,96],"investigate":[1],"how":[2],"much":[3],"information":[4],"about":[5],"a":[6,13,22,26,34,55,61,67,98,103,107],"convex":[7,27,47,71,104],"body":[8,28,105],"can":[9],"be":[10,30],"retrieved":[11],"from":[12],"finite":[14,35,56,108],"number":[15,36,57,109],"of":[16,37,58,91,110,116,132,139,150],"its":[17,38,111],"geometric":[18,39,75],"moments.":[19,76,95,113,127],"give":[21],"sufficient":[23],"condition":[24],"for":[25,70,125],"to":[29],"uniquely":[31,52],"determined":[32,53],"by":[33,54,87],"moments,":[40,92],"and":[41],"we":[42,65],"show":[43],"that":[44,80,101],"among":[45],"all":[46],"bodies,":[48],"those":[49],"which":[50],"are":[51,135],"moments":[59,134],"form":[60],"dense":[62],"set.":[63],"Further,":[64],"derive":[66],"stability":[68,82,123],"result":[69,83,124],"bodies":[72],"based":[73],"on":[74,147],"It":[77],"turns":[78],"out":[79],"the":[81,117,122,137,140,148,151],"is":[84,119,142],"improved":[85],"considerably":[86],"using":[88,106,121],"another":[89],"set":[90],"namely":[93],"Legendre":[94,112,126,133],"present":[97],"reconstruction":[99],"algorithm":[100,118,141],"approximates":[102],"The":[114],"consistency":[115,138],"established":[120,143],"When":[128],"only":[129],"noisy":[130],"measurements":[131],"available,":[136],"under":[144],"certain":[145],"assumptions":[146],"variance":[149],"noise":[152],"variables.":[153]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
