{"id":"https://openalex.org/W3040264685","doi":"https://doi.org/10.1007/s00371-020-01895-5","title":"Relaxing topological surfaces in four dimensions","display_name":"Relaxing topological surfaces in four dimensions","publication_year":2020,"publication_date":"2020-07-04","ids":{"openalex":"https://openalex.org/W3040264685","doi":"https://doi.org/10.1007/s00371-020-01895-5","mag":"3040264685"},"language":"en","primary_location":{"id":"doi:10.1007/s00371-020-01895-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00371-020-01895-5","pdf_url":null,"source":{"id":"https://openalex.org/S73060445","display_name":"The Visual Computer","issn_l":"0178-2789","issn":["0178-2789","1432-2315"],"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":"The Visual Computer","raw_type":"journal-article"},"type":"article","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/A5100323369","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0001-8366-8951"},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["University of Louisville, Louisville, USA"],"raw_orcid":"https://orcid.org/0000-0001-8366-8951","affiliations":[{"raw_affiliation_string":"University of Louisville, Louisville, USA","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060280680","display_name":"Huan Liu","orcid":"https://orcid.org/0000-0002-8674-0901"},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huan Liu","raw_affiliation_strings":["University of Louisville, Louisville, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Louisville, Louisville, USA","institution_ids":["https://openalex.org/I142740786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100323369"],"corresponding_institution_ids":["https://openalex.org/I142740786"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.2562,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.9008598,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"36","issue":"10-12","first_page":"2341","last_page":"2353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6320812702178955},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.603742241859436},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.5860768556594849},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5445573329925537},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.5059439539909363},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48548415303230286},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.4397212862968445},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4390729069709778},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4344182014465332},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4296179413795471},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3875259757041931},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.29580748081207275},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2654094696044922},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22077393531799316}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6320812702178955},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.603742241859436},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.5860768556594849},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5445573329925537},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5059439539909363},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48548415303230286},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.4397212862968445},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4390729069709778},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4344182014465332},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4296179413795471},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3875259757041931},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29580748081207275},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2654094696044922},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22077393531799316},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00371-020-01895-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00371-020-01895-5","pdf_url":null,"source":{"id":"https://openalex.org/S73060445","display_name":"The Visual Computer","issn_l":"0178-2789","issn":["0178-2789","1432-2315"],"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":"The Visual Computer","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G8530901463","display_name":null,"funder_award_id":"1651581","funder_id":"https://openalex.org/F4320332169","funder_display_name":"Directorate for Computer and Information Science and Engineering"}],"funders":[{"id":"https://openalex.org/F4320332169","display_name":"Directorate for Computer and Information Science and Engineering","ror":"https://ror.org/025kzpk63"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W34897806","https://openalex.org/W92252332","https://openalex.org/W651526404","https://openalex.org/W1506123653","https://openalex.org/W1527630124","https://openalex.org/W1551417921","https://openalex.org/W1551970778","https://openalex.org/W1558400591","https://openalex.org/W1593793162","https://openalex.org/W1733346134","https://openalex.org/W1847044884","https://openalex.org/W1867324358","https://openalex.org/W1967368660","https://openalex.org/W1973766890","https://openalex.org/W1975118850","https://openalex.org/W1983195839","https://openalex.org/W1987654363","https://openalex.org/W1992709202","https://openalex.org/W1993550984","https://openalex.org/W2002713832","https://openalex.org/W2004312117","https://openalex.org/W2020327719","https://openalex.org/W2048373891","https://openalex.org/W2060747124","https://openalex.org/W2068497209","https://openalex.org/W2137148860","https://openalex.org/W2137745368","https://openalex.org/W2145728221","https://openalex.org/W2147545324","https://openalex.org/W2167482691","https://openalex.org/W3037054873","https://openalex.org/W4210844569","https://openalex.org/W4253777962","https://openalex.org/W4301204685","https://openalex.org/W4302570923","https://openalex.org/W6638094454"],"related_works":["https://openalex.org/W2068608913","https://openalex.org/W3124914020","https://openalex.org/W2141033859","https://openalex.org/W2077542787","https://openalex.org/W2071701083","https://openalex.org/W2383687187","https://openalex.org/W2156434174","https://openalex.org/W2121496884","https://openalex.org/W1980956817","https://openalex.org/W2221819563"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
