{"id":"https://openalex.org/W2965485029","doi":"https://doi.org/10.1007/s41468-022-00092-8","title":"Frontiers of sphere recognition in practice","display_name":"Frontiers of sphere recognition in practice","publication_year":2022,"publication_date":"2022-05-19","ids":{"openalex":"https://openalex.org/W2965485029","doi":"https://doi.org/10.1007/s41468-022-00092-8","mag":"2965485029"},"language":"en","primary_location":{"id":"doi:10.1007/s41468-022-00092-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-022-00092-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-022-00092-8.pdf","source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s41468-022-00092-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035639170","display_name":"Michael Joswig","orcid":"https://orcid.org/0000-0002-4974-9659"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Joswig","raw_affiliation_strings":["Institut f\u00fcr Mathematik, TU Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, 04103, Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, TU Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, 04103, Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047061541","display_name":"Davide Lofano","orcid":"https://orcid.org/0000-0002-9478-316X"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Davide Lofano","raw_affiliation_strings":["Institut f\u00fcr Mathematik, TU Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, TU Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045757470","display_name":"Frank H. Lutz","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Frank H. Lutz","raw_affiliation_strings":["Institut f\u00fcr Mathematik, TU Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, TU Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036037091","display_name":"Mimi Tsuruga","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mimi Tsuruga","raw_affiliation_strings":["Elastic, 800 W El Camino Real, Suite\u00a0350, Mountain View, CA, 94040, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Elastic, 800 W El Camino Real, Suite\u00a0350, Mountain View, CA, 94040, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.7606,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72283045,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":"4","first_page":"503","last_page":"527"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.991100013256073,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.8536217212677002},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5626153945922852},{"id":"https://openalex.org/keywords/morse-code","display_name":"Morse code","score":0.5177213549613953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45666271448135376},{"id":"https://openalex.org/keywords/discrete-morse-theory","display_name":"Discrete Morse theory","score":0.4472983181476593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4387959837913513},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42541056871414185},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3941000699996948},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37436532974243164},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34429293870925903},{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.23067837953567505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18626412749290466},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16391485929489136}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8536217212677002},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5626153945922852},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.5177213549613953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45666271448135376},{"id":"https://openalex.org/C170315498","wikidata":"https://www.wikidata.org/wiki/Q5282039","display_name":"Discrete Morse theory","level":3,"score":0.4472983181476593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4387959837913513},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42541056871414185},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3941000699996948},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37436532974243164},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34429293870925903},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.23067837953567505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18626412749290466},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16391485929489136},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s41468-022-00092-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-022-00092-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-022-00092-8.pdf","source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s41468-022-00092-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41468-022-00092-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41468-022-00092-8.pdf","source":{"id":"https://openalex.org/S4210173698","display_name":"Journal of Applied and Computational Topology","issn_l":"2367-1726","issn":["2367-1726","2367-1734"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied and Computational Topology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1326879771","display_name":null,"funder_award_id":"TRR 195","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2466786576","display_name":null,"funder_award_id":"EXC 2046","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5489237795","display_name":null,"funder_award_id":"GRK 2434","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G588593503","display_name":null,"funder_award_id":"SFB-TRR 195","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G8548417885","display_name":null,"funder_award_id":"SFB-TRR 195","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/F4320316912","display_name":"Berlin Mathematical School","ror":"https://ror.org/03zekj455"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320943","display_name":"Danmarks Grundforskningsfond","ror":"https://ror.org/00znyv691"},{"id":"https://openalex.org/F4320323688","display_name":"Einstein Stiftung Berlin","ror":"https://ror.org/03s0fv852"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2965485029.pdf","grobid_xml":"https://content.openalex.org/works/W2965485029.grobid-xml"},"referenced_works_count":77,"referenced_works":["https://openalex.org/W206167714","https://openalex.org/W346770570","https://openalex.org/W1482922445","https://openalex.org/W1486393174","https://openalex.org/W1496383623","https://openalex.org/W1497485110","https://openalex.org/W1504831268","https://openalex.org/W1509420953","https://openalex.org/W1556556489","https://openalex.org/W1617730875","https://openalex.org/W1625293856","https://openalex.org/W1970564715","https://openalex.org/W1974720683","https://openalex.org/W1976521022","https://openalex.org/W1977010014","https://openalex.org/W1977436094","https://openalex.org/W1980124684","https://openalex.org/W1987227236","https://openalex.org/W1992051521","https://openalex.org/W1996989230","https://openalex.org/W2002165972","https://openalex.org/W2006339185","https://openalex.org/W2015161630","https://openalex.org/W2015894047","https://openalex.org/W2017741614","https://openalex.org/W2024312634","https://openalex.org/W2032980094","https://openalex.org/W2034142621","https://openalex.org/W2042992603","https://openalex.org/W2045097502","https://openalex.org/W2050735826","https://openalex.org/W2050736535","https://openalex.org/W2064020260","https://openalex.org/W2069366912","https://openalex.org/W2069732768","https://openalex.org/W2071132581","https://openalex.org/W2075891690","https://openalex.org/W2081349787","https://openalex.org/W2086825813","https://openalex.org/W2101570837","https://openalex.org/W2101918237","https://openalex.org/W2110221038","https://openalex.org/W2119035647","https://openalex.org/W2126757328","https://openalex.org/W2128282971","https://openalex.org/W2134383282","https://openalex.org/W2141950593","https://openalex.org/W2157891871","https://openalex.org/W2233474732","https://openalex.org/W2254123846","https://openalex.org/W2282388032","https://openalex.org/W2288437196","https://openalex.org/W2298471787","https://openalex.org/W2316016684","https://openalex.org/W2333586270","https://openalex.org/W2504355181","https://openalex.org/W2564133731","https://openalex.org/W2752853835","https://openalex.org/W2785155418","https://openalex.org/W2885117406","https://openalex.org/W2949332555","https://openalex.org/W2963260537","https://openalex.org/W2963397105","https://openalex.org/W2963905120","https://openalex.org/W2963969495","https://openalex.org/W2964028703","https://openalex.org/W3004768961","https://openalex.org/W3043764587","https://openalex.org/W3098571429","https://openalex.org/W3104286808","https://openalex.org/W3123529907","https://openalex.org/W3172337659","https://openalex.org/W3194441333","https://openalex.org/W4210651336","https://openalex.org/W4249696562","https://openalex.org/W6632518436","https://openalex.org/W6757062490"],"related_works":["https://openalex.org/W4389768470","https://openalex.org/W2037435271","https://openalex.org/W2185671344","https://openalex.org/W1539643790","https://openalex.org/W4298393012","https://openalex.org/W2106662121","https://openalex.org/W1595332435","https://openalex.org/W4308897745","https://openalex.org/W2162558730","https://openalex.org/W4281700539"],"abstract_inverted_index":{"Abstract":[0],"Sphere":[1],"recognition":[2,43],"is":[3,18],"known":[4,19],"to":[5,37],"be":[6],"undecidable":[7],"in":[8,20],"dimensions":[9,21],"five":[10],"and":[11,13,23,30],"beyond,":[12],"no":[14],"polynomial":[15],"time":[16],"method":[17],"three":[22],"four.":[24],"Here":[25],"we":[26],"report":[27],"on":[28],"positive":[29],"negative":[31],"computational":[32],"results":[33],"with":[34],"the":[35,39],"goal":[36],"explore":[38],"limits":[40],"of":[41,48],"sphere":[42],"from":[44],"a":[45],"practical":[46],"point":[47],"view.":[49],"An":[50],"important":[51],"ingredient":[52],"are":[53],"randomly":[54],"constructed":[55],"discrete":[56],"Morse":[57],"functions.":[58]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
