{"id":"https://openalex.org/W2097261271","doi":"https://doi.org/10.1007/3-540-45435-7_2","title":"Entropy, Combinatorial Dimensions and Random Averages","display_name":"Entropy, Combinatorial Dimensions and Random Averages","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2097261271","doi":"https://doi.org/10.1007/3-540-45435-7_2","mag":"2097261271"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45435-7_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45435-7_2","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5053455526","display_name":"Shahar Mendelson","orcid":"https://orcid.org/0000-0002-5673-7576"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Shahar Mendelson","raw_affiliation_strings":["RSISE, The Australian National University, Canberra, ACT, 0200, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RSISE, The Australian National University, Canberra, ACT, 0200, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070281692","display_name":"Roman Vershynin","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Roman Vershynin","raw_affiliation_strings":["Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.2832,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.58733502,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"14","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9957000017166138,"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"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9897000193595886,"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/T10136","display_name":"Statistical Methods and Inference","score":0.984000027179718,"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/unit-cube","display_name":"Unit cube","score":0.7498158812522888},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6655956506729126},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.65538489818573},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5684176683425903},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5216639041900635},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4844382107257843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40173181891441345},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3722016513347626},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0948631763458252}],"concepts":[{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.7498158812522888},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6655956506729126},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.65538489818573},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5684176683425903},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5216639041900635},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4844382107257843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40173181891441345},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3722016513347626},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0948631763458252},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/3-540-45435-7_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45435-7_2","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.110.762","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.762","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucdavis.edu/~vershynin/papers/colt.pdf","raw_type":"text"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/73501","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/73501","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Learning Theory","raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W188867022","https://openalex.org/W1507545330","https://openalex.org/W1519789693","https://openalex.org/W1526777878","https://openalex.org/W1537193711","https://openalex.org/W1542886316","https://openalex.org/W1572043320","https://openalex.org/W1981601376","https://openalex.org/W1990064648","https://openalex.org/W2010353172","https://openalex.org/W2017753243","https://openalex.org/W2042024619","https://openalex.org/W2055262205","https://openalex.org/W2058239479","https://openalex.org/W2071570468","https://openalex.org/W2100116519","https://openalex.org/W2103012681","https://openalex.org/W2112528242","https://openalex.org/W4238472918","https://openalex.org/W4249716558","https://openalex.org/W4301425558"],"related_works":["https://openalex.org/W2904804828","https://openalex.org/W4246372503","https://openalex.org/W2031281829","https://openalex.org/W2073870969","https://openalex.org/W2480729894","https://openalex.org/W3088374900","https://openalex.org/W2009482999","https://openalex.org/W2122070455","https://openalex.org/W2754017260","https://openalex.org/W1987895267"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}