Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2114613785', 'doi': 'https://doi.org/10.1007/s11464-012-0262-x', 'title': 'Best rank one approximation of real symmetric tensors can be chosen symmetric', 'display_name': 'Best rank one approximation of real symmetric tensors can be chosen symmetric', 'publication_year': 2012, 'publication_date': '2012-12-06', 'ids': {'openalex': 'https://openalex.org/W2114613785', 'doi': 'https://doi.org/10.1007/s11464-012-0262-x', 'mag': '2114613785'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s11464-012-0262-x', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S87035759', 'display_name': 'Frontiers of Mathematics in China', 'issn_l': '1673-3452', 'issn': ['1673-3452', '1673-3576'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311889', 'host_organization_name': 'Higher Education Press', 'host_organization_lineage': ['https://openalex.org/P4310311889'], 'host_organization_lineage_names': ['Higher Education Press'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://figshare.com/articles/journal_contribution/Best_rank_one_approximation_of_real_symmetric_tensors_can_be_chosen_symmetric/10771475/1/files/19284125.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5002855648', 'display_name': 'Shmuel Friedland', 'orcid': 'https://orcid.org/0000-0002-0423-5005'}, 'institutions': [{'id': 'https://openalex.org/I39422238', 'display_name': 'University of Illinois at Chicago', 'ror': 'https://ror.org/02mpq6x41', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I39422238']}], 'countries': ['US'], 'is_corresponding': True, 'raw_author_name': 'Shmuel Friedland', 'raw_affiliation_strings': ['Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, USA'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, USA', 'institution_ids': ['https://openalex.org/I39422238']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5002855648'], 'corresponding_institution_ids': ['https://openalex.org/I39422238'], 'apc_list': None, 'apc_paid': None, 'fwci': 1.907, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 63, 'citation_normalized_percentile': {'value': 0.98773, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 96, 'max': 97}, 'biblio': {'volume': '8', 'issue': '1', 'first_page': '19', 'last_page': '40'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12303', 'display_name': 'Tensor Decompositions and Applications in Multilinear Algebra', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2605', 'display_name': 'Computational 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/T12303', 'display_name': 'Tensor Decompositions and Applications in Multilinear Algebra', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2605', 'display_name': 'Computational 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/T10792', 'display_name': 'Matrix Algorithms and Iterative Methods', 'score': 0.9931, '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/T11366', 'display_name': 'Biomechanical Modeling of Arterial Tissues', 'score': 0.9837, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/rank', 'display_name': 'Rank (graph theory)', 'score': 0.76273525}, {'id': 'https://openalex.org/keywords/triple-system', 'display_name': 'Triple system', 'score': 0.6574504}, {'id': 'https://openalex.org/keywords/symmetric-closure', 'display_name': 'Symmetric closure', 'score': 0.64960724}, {'id': 'https://openalex.org/keywords/stanley-symmetric-function', 'display_name': 'Stanley symmetric function', 'score': 0.5211851}, {'id': 'https://openalex.org/keywords/higher-order-tensors', 'display_name': 'Higher-Order Tensors', 'score': 0.486681}, {'id': 'https://openalex.org/keywords/cartesian-tensor', 'display_name': 'Cartesian tensor', 'score': 0.46149835}], 'concepts': [{'id': 'https://openalex.org/C20178491', 'wikidata': 'https://www.wikidata.org/wiki/Q2204117', 'display_name': 'Symmetric tensor', 'level': 3, 'score': 0.89836013}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8409068}, {'id': 'https://openalex.org/C164226766', 'wikidata': 'https://www.wikidata.org/wiki/Q7293202', 'display_name': 'Rank (graph theory)', 'level': 2, 'score': 0.76273525}, {'id': 'https://openalex.org/C155281189', 'wikidata': 'https://www.wikidata.org/wiki/Q3518150', 'display_name': 'Tensor (intrinsic definition)', 'level': 2, 'score': 0.6639139}, {'id': 'https://openalex.org/C109385661', 'wikidata': 'https://www.wikidata.org/wiki/Q11358307', 'display_name': 'Triple system', 'level': 2, 'score': 0.6574504}, {'id': 'https://openalex.org/C167552581', 'wikidata': 'https://www.wikidata.org/wiki/Q194221', 'display_name': 'Symmetric closure', 'level': 5, 'score': 0.64960724}, {'id': 'https://openalex.org/C136197465', 'wikidata': 'https://www.wikidata.org/wiki/Q1729295', 'display_name': 'Variety (cybernetics)', 'level': 2, 'score': 0.5819726}, {'id': 'https://openalex.org/C78136718', 'wikidata': 'https://www.wikidata.org/wiki/Q7600073', 'display_name': 'Stanley symmetric function', 'level': 5, 'score': 0.5211851}, {'id': 'https://openalex.org/C64338288', 'wikidata': 'https://www.wikidata.org/wiki/Q2235316', 'display_name': 'Elementary symmetric polynomial', 'level': 4, 'score': 0.51509064}, {'id': 'https://openalex.org/C156903151', 'wikidata': 'https://www.wikidata.org/wiki/Q17102788', 'display_name': 'Ring of symmetric functions', 'level': 4, 'score': 0.5141416}, {'id': 'https://openalex.org/C93776189', 'wikidata': 'https://www.wikidata.org/wiki/Q1404488', 'display_name': 'Tensor product of Hilbert spaces', 'level': 4, 'score': 0.48927853}, {'id': 'https://openalex.org/C64835786', 'wikidata': 'https://www.wikidata.org/wiki/Q17004583', 'display_name': 'Cartesian tensor', 'level': 5, 'score': 0.46149835}, {'id': 'https://openalex.org/C171436396', 'wikidata': 'https://www.wikidata.org/wiki/Q5156499', 'display_name': 'Complete homogeneous symmetric polynomial', 'level': 5, 'score': 0.44172335}, {'id': 'https://openalex.org/C129010115', 'wikidata': 'https://www.wikidata.org/wiki/Q1298683', 'display_name': 'Power sum symmetric polynomial', 'level': 5, 'score': 0.43272883}, {'id': 'https://openalex.org/C148125525', 'wikidata': 'https://www.wikidata.org/wiki/Q904927', 'display_name': 'Tensor density', 'level': 4, 'score': 0.42713886}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.42077276}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.41827592}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.31943834}, {'id': 'https://openalex.org/C166077713', 'wikidata': 'https://www.wikidata.org/wiki/Q1758924', 'display_name': 'Tensor field', 'level': 3, 'score': 0.30512196}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.28267515}, {'id': 'https://openalex.org/C520416788', 'wikidata': 'https://www.wikidata.org/wiki/Q5419229', 'display_name': 'Exact solutions in general relativity', 'level': 2, 'score': 0.13193417}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.05182776}, {'id': 'https://openalex.org/C43176163', 'wikidata': 'https://www.wikidata.org/wiki/Q8023263', 'display_name': 'Wilson polynomials', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C10628310', 'wikidata': 'https://www.wikidata.org/wiki/Q619458', 'display_name': 'Orthogonal polynomials', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C52537462', 'wikidata': 'https://www.wikidata.org/wiki/Q5282055', 'display_name': 'Discrete orthogonal polynomials', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C86607863', 'wikidata': 'https://www.wikidata.org/wiki/Q5275279', 'display_name': 'Difference polynomials', 'level': 3, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s11464-012-0262-x', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S87035759', 'display_name': 'Frontiers of Mathematics in China', 'issn_l': '1673-3452', 'issn': ['1673-3452', '1673-3576'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311889', 'host_organization_name': 'Higher Education Press', 'host_organization_lineage': ['https://openalex.org/P4310311889'], 'host_organization_lineage_names': ['Higher Education Press'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://figshare.com/articles/journal_contribution/Best_rank_one_approximation_of_real_symmetric_tensors_can_be_chosen_symmetric/10771475', 'pdf_url': 'https://figshare.com/articles/journal_contribution/Best_rank_one_approximation_of_real_symmetric_tensors_can_be_chosen_symmetric/10771475/1/files/19284125.pdf', 'source': {'id': 'https://openalex.org/S4306402621', 'display_name': 'INDIGO (University of Illinois at Chicago)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I39422238', 'host_organization_name': 'University of Illinois at Chicago', 'host_organization_lineage': ['https://openalex.org/I39422238'], 'host_organization_lineage_names': ['University of Illinois at Chicago'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1110.5689', 'pdf_url': 'https://arxiv.org/pdf/1110.5689', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://figshare.com/articles/journal_contribution/Best_rank_one_approximation_of_real_symmetric_tensors_can_be_chosen_symmetric/10771475', 'pdf_url': 'https://figshare.com/articles/journal_contribution/Best_rank_one_approximation_of_real_symmetric_tensors_can_be_chosen_symmetric/10771475/1/files/19284125.pdf', 'source': {'id': 'https://openalex.org/S4306402621', 'display_name': 'INDIGO (University of Illinois at Chicago)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I39422238', 'host_organization_name': 'University of Illinois at Chicago', 'host_organization_lineage': ['https://openalex.org/I39422238'], 'host_organization_lineage_names': ['University of Illinois at Chicago'], 'type': 'repository'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 7, 'referenced_works': ['https://openalex.org/W1509568713', 'https://openalex.org/W2040091574', 'https://openalex.org/W2059343728', 'https://openalex.org/W2066624117', 'https://openalex.org/W2113722075', 'https://openalex.org/W2126381689', 'https://openalex.org/W2798909945'], 'related_works': ['https://openalex.org/W4211222368', 'https://openalex.org/W3045701420', 'https://openalex.org/W2964348582', 'https://openalex.org/W2962861350', 'https://openalex.org/W2949691349', 'https://openalex.org/W2949072321', 'https://openalex.org/W2901510162', 'https://openalex.org/W2028338466', 'https://openalex.org/W2009793866', 'https://openalex.org/W188141326'], 'abstract_inverted_index': {'We': [0], 'show': [1], 'that': [2], 'a': [3, 9, 24, 31, 43], 'best': [4, 26], 'rank': [5, 27], 'one': [6, 28], 'approximation': [7, 29], 'to': [8, 30], 'real': [10, 45], 'symmetric': [11, 25, 32], 'tensor,': [12], 'which': [13], 'in': [14], 'principle': [15], 'can': [16, 19], 'be': [17, 20], 'nonsymmetric,': [18], 'chosen': [21], 'symmetric.': [22], 'Furthermore,': [23], 'tensor': [33, 38], 'is': [34], 'unique': [35], 'if': [36], 'the': [37], 'does': [39], 'not': [40], 'lie': [41], 'on': [42], 'certain': [44], 'algebraic': [46], 'variety.': [47]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2114613785', 'counts_by_year': [{'year': 2024, 'cited_by_count': 3}, {'year': 2023, 'cited_by_count': 3}, {'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 4}, {'year': 2020, 'cited_by_count': 7}, {'year': 2019, 'cited_by_count': 6}, {'year': 2018, 'cited_by_count': 6}, {'year': 2017, 'cited_by_count': 7}, {'year': 2016, 'cited_by_count': 7}, {'year': 2015, 'cited_by_count': 5}, {'year': 2014, 'cited_by_count': 8}, {'year': 2013, 'cited_by_count': 4}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-09-10T01:00:04.735967', 'created_date': '2016-06-24'}