{"id":"https://openalex.org/W1549842019","doi":"https://doi.org/10.1007/978-3-540-72823-8_51","title":"Riemannian Curvature-Driven Flows for Tensor-Valued Data","display_name":"Riemannian Curvature-Driven Flows for Tensor-Valued Data","publication_year":2007,"publication_date":"2007-07-22","ids":{"openalex":"https://openalex.org/W1549842019","doi":"https://doi.org/10.1007/978-3-540-72823-8_51","mag":"1549842019"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-72823-8_51","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72823-8_51","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/A5060645648","display_name":"Mourad Z\u00e9ra\u00ef","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131288","display_name":"National Engineering School of Tunis","ror":"https://ror.org/03b1zjt31","country_code":"TN","type":"education","lineage":["https://openalex.org/I4210131288","https://openalex.org/I63596082"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"Mourad Z\u00e9ra\u00ef","raw_affiliation_strings":["Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis Belv\u00e9d\u00e8re, Tunisia","Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT, LAMSIN, Tunis Belv\u00e9d\u00e8re, Tunisia#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis Belv\u00e9d\u00e8re, Tunisia","institution_ids":["https://openalex.org/I4210131288"]},{"raw_affiliation_string":"Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT, LAMSIN, Tunis Belv\u00e9d\u00e8re, Tunisia#TAB#","institution_ids":["https://openalex.org/I4210131288"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049541486","display_name":"Maher Moakher","orcid":"https://orcid.org/0000-0002-9432-0456"},"institutions":[{"id":"https://openalex.org/I4210131288","display_name":"National Engineering School of Tunis","ror":"https://ror.org/03b1zjt31","country_code":"TN","type":"education","lineage":["https://openalex.org/I4210131288","https://openalex.org/I63596082"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Maher Moakher","raw_affiliation_strings":["Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis Belv\u00e9d\u00e8re, Tunisia","Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT, LAMSIN, Tunis Belv\u00e9d\u00e8re, Tunisia#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis Belv\u00e9d\u00e8re, Tunisia","institution_ids":["https://openalex.org/I4210131288"]},{"raw_affiliation_string":"Laboratory for Mathematical and Numerical Modeling in Engineering Science, National Engineering School at Tunis, ENIT, LAMSIN, Tunis Belv\u00e9d\u00e8re, Tunisia#TAB#","institution_ids":["https://openalex.org/I4210131288"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060645648"],"corresponding_institution_ids":["https://openalex.org/I4210131288"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":8.3008,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.97960754,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"592","last_page":"602"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9631999731063843,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9623000025749207,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/covariant-derivative","display_name":"Covariant derivative","score":0.7392987012863159},{"id":"https://openalex.org/keywords/positive-definiteness","display_name":"Positive definiteness","score":0.7320398092269897},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.728010892868042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6231141686439514},{"id":"https://openalex.org/keywords/covariant-transformation","display_name":"Covariant transformation","score":0.6131795644760132},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.609872043132782},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.6081089377403259},{"id":"https://openalex.org/keywords/covariance-and-contravariance-of-vectors","display_name":"Covariance and contravariance of vectors","score":0.5851710438728333},{"id":"https://openalex.org/keywords/riemann-curvature-tensor","display_name":"Riemann curvature tensor","score":0.5684452652931213},{"id":"https://openalex.org/keywords/curvature-of-riemannian-manifolds","display_name":"Curvature of Riemannian manifolds","score":0.5560643672943115},{"id":"https://openalex.org/keywords/geometric-flow","display_name":"Geometric flow","score":0.508018970489502},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5054388046264648},{"id":"https://openalex.org/keywords/metric-tensor","display_name":"Metric tensor","score":0.49695995450019836},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.48879215121269226},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4840054214000702},{"id":"https://openalex.org/keywords/christoffel-symbols","display_name":"Christoffel symbols","score":0.483650803565979},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.48229148983955383},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.45946502685546875},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.45898330211639404},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3661697506904602},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24897420406341553},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.21940934658050537},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1923922896385193},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.19004106521606445},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14959239959716797}],"concepts":[{"id":"https://openalex.org/C19492387","wikidata":"https://www.wikidata.org/wiki/Q2287715","display_name":"Covariant derivative","level":2,"score":0.7392987012863159},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.7320398092269897},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.728010892868042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6231141686439514},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.6131795644760132},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.609872043132782},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.6081089377403259},{"id":"https://openalex.org/C206236147","wikidata":"https://www.wikidata.org/wiki/Q3555165","display_name":"Covariance and contravariance of vectors","level":2,"score":0.5851710438728333},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.5684452652931213},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.5560643672943115},{"id":"https://openalex.org/C32209215","wikidata":"https://www.wikidata.org/wiki/Q5535483","display_name":"Geometric flow","level":3,"score":0.508018970489502},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5054388046264648},{"id":"https://openalex.org/C8466233","wikidata":"https://www.wikidata.org/wiki/Q757269","display_name":"Metric tensor","level":3,"score":0.49695995450019836},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.48879215121269226},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4840054214000702},{"id":"https://openalex.org/C77850982","wikidata":"https://www.wikidata.org/wiki/Q847816","display_name":"Christoffel symbols","level":2,"score":0.483650803565979},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.48229148983955383},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.45946502685546875},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.45898330211639404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3661697506904602},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24897420406341553},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.21940934658050537},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1923922896385193},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.19004106521606445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14959239959716797},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-72823-8_51","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72823-8_51","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W92310073","https://openalex.org/W572198187","https://openalex.org/W1516517100","https://openalex.org/W1525296983","https://openalex.org/W1571699948","https://openalex.org/W1572793615","https://openalex.org/W1598557217","https://openalex.org/W1667854146","https://openalex.org/W1964802316","https://openalex.org/W1982446433","https://openalex.org/W1983496390","https://openalex.org/W1989893875","https://openalex.org/W2027401313","https://openalex.org/W2044981864","https://openalex.org/W2057220024","https://openalex.org/W2103559027","https://openalex.org/W2104404402","https://openalex.org/W2106401644","https://openalex.org/W2112473379","https://openalex.org/W2121494337","https://openalex.org/W2122752532","https://openalex.org/W2146052399","https://openalex.org/W2154865683","https://openalex.org/W2164350703","https://openalex.org/W2164355691","https://openalex.org/W2168501356","https://openalex.org/W2274528885","https://openalex.org/W2410358037","https://openalex.org/W2502277634","https://openalex.org/W2561675875","https://openalex.org/W2914396913","https://openalex.org/W3142006300","https://openalex.org/W4206868379","https://openalex.org/W6737448088"],"related_works":["https://openalex.org/W2617689998","https://openalex.org/W2036579864","https://openalex.org/W3113913322","https://openalex.org/W16976967","https://openalex.org/W3015220556","https://openalex.org/W3006823253","https://openalex.org/W2282826665","https://openalex.org/W4235702818","https://openalex.org/W1549842019","https://openalex.org/W1626238372"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
