{"id":"https://openalex.org/W7160834854","doi":"https://doi.org/10.1007/978-3-032-22539-9_5","title":"Hypercomplexification of\u00a0U-Net by\u00a0Clifford Algebra Embeddings","display_name":"Hypercomplexification of\u00a0U-Net by\u00a0Clifford Algebra Embeddings","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7160834854","doi":"https://doi.org/10.1007/978-3-032-22539-9_5"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-22539-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-22539-9_5","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/A5052373363","display_name":"Roman Byrtus","orcid":"https://orcid.org/0000-0002-7452-0573"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["CZ","IT"],"is_corresponding":true,"raw_author_name":"Roman Byrtus","raw_affiliation_strings":["Department of Biomedicine, Neuroscience and Advanced Diagnostics, University of Palermo, Palermo, Italy","Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedicine, Neuroscience and Advanced Diagnostics, University of Palermo, Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]},{"raw_affiliation_string":"Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646","https://openalex.org/I4210120266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074878608","display_name":"Francesco Prinzi","orcid":"https://orcid.org/0000-0002-8152-3297"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Prinzi","raw_affiliation_strings":["Department of Biomedicine, Neuroscience and Advanced Diagnostics, University of Palermo, Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedicine, Neuroscience and Advanced Diagnostics, University of Palermo, Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000214099","display_name":"Petr Va\u0161\u00edk","orcid":"https://orcid.org/0000-0001-6725-7378"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]},{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Petr Va\u0161\u00edk","raw_affiliation_strings":["Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646","https://openalex.org/I4210120266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132713225","display_name":"Salvatore Vitabile","orcid":null},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Salvatore Vitabile","raw_affiliation_strings":["Department of Biomedicine, Neuroscience and Advanced Diagnostics, University of Palermo, Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedicine, Neuroscience and Advanced Diagnostics, University of Palermo, Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052373363"],"corresponding_institution_ids":["https://openalex.org/I4210120266","https://openalex.org/I60587646","https://openalex.org/I900890020"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.94561404,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"63","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.8790000081062317,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.8790000081062317,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.012299999594688416,"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/T11763","display_name":"Intracerebral and Subarachnoid Hemorrhage Research","score":0.0071000000461936,"subfield":{"id":"https://openalex.org/subfields/2728","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercomplex-number","display_name":"Hypercomplex number","score":0.9376999735832214},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.7639999985694885},{"id":"https://openalex.org/keywords/geometric-algebra","display_name":"Geometric algebra","score":0.6621999740600586},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6470999717712402},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5288000106811523},{"id":"https://openalex.org/keywords/multivector","display_name":"Multivector","score":0.5159000158309937},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4925999939441681},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4424999952316284}],"concepts":[{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.9376999735832214},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.7639999985694885},{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.6621999740600586},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6470999717712402},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5288000106811523},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.5159000158309937},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4959999918937683},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4424999952316284},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3677000105381012},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34459999203681946},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.33180001378059387},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.32589998841285706},{"id":"https://openalex.org/C1680195","wikidata":"https://www.wikidata.org/wiki/Q2296021","display_name":"Tensor algebra","level":5,"score":0.32420000433921814},{"id":"https://openalex.org/C32234688","wikidata":"https://www.wikidata.org/wiki/Q5133084","display_name":"Clifford bundle","level":5,"score":0.29510000348091125},{"id":"https://openalex.org/C51795389","wikidata":"https://www.wikidata.org/wiki/Q662523","display_name":"Classification of Clifford algebras","level":5,"score":0.28929999470710754},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2825999855995178},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.2662999927997589},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-22539-9_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-22539-9_5","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":11,"referenced_works":["https://openalex.org/W1901129140","https://openalex.org/W2097854005","https://openalex.org/W2141150222","https://openalex.org/W2966878259","https://openalex.org/W4249085959","https://openalex.org/W4286568264","https://openalex.org/W4289654500","https://openalex.org/W4391465849","https://openalex.org/W4408617393","https://openalex.org/W6893115455","https://openalex.org/W7133221336"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-13T06:04:23.736269","created_date":"2026-05-12T00:00:00"}
