{"id":"https://openalex.org/W3132778867","doi":"https://doi.org/10.1007/978-3-030-95519-9_6","title":"Nerve Theorems for Fixed Points of Neural Networks","display_name":"Nerve Theorems for Fixed Points of Neural Networks","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W3132778867","doi":"https://doi.org/10.1007/978-3-030-95519-9_6","mag":"3132778867"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-95519-9_6","doi":"https://doi.org/10.1007/978-3-030-95519-9_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-95519-9_6","pdf_url":null,"source":{"id":"https://openalex.org/S4210173241","display_name":"Association for Women in Mathematics series","issn_l":"2364-5733","issn":["2364-5733","2364-5741"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Association for Women in Mathematics Series","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4285218123","display_name":"Research in Computational Topology 2"},"type":"book-chapter","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2102.11437","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023858922","display_name":"Daniela Egas Santander","orcid":"https://orcid.org/0000-0001-9838-7992","observed_orcids":["https://orcid.org/0000-0001-9838-7992"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Daniela Egas Santander","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004640735","display_name":"Stefania Ebli","orcid":"https://orcid.org/0000-0001-9136-8924","observed_orcids":["https://orcid.org/0000-0001-9136-8924"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Stefania Ebli","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068687626","display_name":"Alice Patania","orcid":"https://orcid.org/0000-0002-3047-4376","observed_orcids":["https://orcid.org/0000-0002-3047-4376"]},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]},{"id":"https://openalex.org/I592451","display_name":"Indiana University","ror":"https://ror.org/01kg8sb98","country_code":"US","type":"education","lineage":["https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alice Patania","raw_affiliation_strings":["Indiana University Network Science Institute (IUNI), Bloomington, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indiana University Network Science Institute (IUNI), Bloomington, IN, USA","institution_ids":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055093406","display_name":"Nicole Sanderson","orcid":"https://orcid.org/0000-0002-4512-0458","observed_orcids":["https://orcid.org/0000-0002-4512-0458"]},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicole Sanderson","raw_affiliation_strings":["Lawrence Berkeley National Lab, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Lab, Berkeley, CA, USA","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038262235","display_name":"Felicia Burtscher","orcid":"https://orcid.org/0000-0001-8231-0501","observed_orcids":["https://orcid.org/0000-0001-8231-0501"]},"institutions":[{"id":"https://openalex.org/I186903577","display_name":"University of Luxembourg","ror":"https://ror.org/036x5ad56","country_code":"LU","type":"education","lineage":["https://openalex.org/I186903577"]},{"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","LU"],"is_corresponding":false,"raw_author_name":"Felicia Burtscher","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Berlin, Germany","Universit\u00e9 du Luxembourg, Belvaux, Luxembourg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Universit\u00e9 du Luxembourg, Belvaux, Luxembourg","institution_ids":["https://openalex.org/I186903577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040727760","display_name":"Katherine Mary Morrison","orcid":"https://orcid.org/0000-0002-1737-256X","observed_orcids":["https://orcid.org/0000-0002-1737-256X"]},"institutions":[{"id":"https://openalex.org/I71966907","display_name":"University of Northern Colorado","ror":"https://ror.org/016bysn57","country_code":"US","type":"education","lineage":["https://openalex.org/I71966907"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Katherine Morrison","raw_affiliation_strings":["University of Northern Colorado, Greeley, CO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Northern Colorado, Greeley, CO, USA","institution_ids":["https://openalex.org/I71966907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020021216","display_name":"Carina Curto","orcid":"https://orcid.org/0000-0001-9849-3592","observed_orcids":["https://orcid.org/0000-0001-9849-3592"]},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Carina Curto","raw_affiliation_strings":["Pennsylvania State University, University Park, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5020021216"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":1.7437,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.86747858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"129","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.5156000256538391,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10320","display_name":"Neural Networks and Applications","score":0.5156000256538391,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10581","display_name":"Neural dynamics and brain function","score":0.3774000108242035,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.0340999998152256,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/fixed-points","display_name":"fixed points","score":0.7760000228881836},{"id":"https://openalex.org/keywords/nerve-theorem","display_name":"nerve theorem","score":0.8180000185966492},{"id":"https://openalex.org/keywords/graph-covers","display_name":"graph covering","score":0.5180000066757202},{"id":"https://openalex.org/keywords/recurrent-neural-networks","display_name":"recurrent neural networks","score":0.8450000286102295},{"id":"https://openalex.org/keywords/directed-graphs","display_name":"directed graphs","score":0.7089999914169312},{"id":"https://openalex.org/keywords/transient-dynamics","display_name":"transient dynamics","score":0.7160000205039978},{"id":"https://openalex.org/keywords/asymptotic-dynamics","display_name":"asymptotic dynamics","score":0.9639999866485596},{"id":"https://openalex.org/keywords/nonlinear-network-dynamics","display_name":"nonlinear network dynamics","score":0.6439999938011169}],"concepts":[{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6212339401245117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5452336668968201},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47538721561431885},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4659603238105774},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.4354987144470215},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.4258174002170563},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4171741008758545},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.41101112961769104},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4065135717391968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33156493306159973},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16204214096069336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0726298987865448},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-030-95519-9_6","doi":"https://doi.org/10.1007/978-3-030-95519-9_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-95519-9_6","pdf_url":null,"source":{"id":"https://openalex.org/S4210173241","display_name":"Association for Women in Mathematics series","issn_l":"2364-5733","issn":["2364-5733","2364-5741"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Association for Women in Mathematics Series","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:2102.11437","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.11437","pdf_url":"https://arxiv.org/pdf/2102.11437","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2102.11437","doi":"https://doi.org/10.48550/arxiv.2102.11437","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2102.11437","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2102.11437","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.11437","pdf_url":"https://arxiv.org/pdf/2102.11437","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1235099019","display_name":null,"funder_award_id":"R01 EB022862","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G164894665","display_name":"Emergent dynamics from network connectivity: a minimal model","funder_award_id":"R01EB022862","funder_id":"https://openalex.org/F4320337363","funder_display_name":"National Institute of Biomedical Imaging and Bioengineering"},{"id":"https://openalex.org/G305516501","display_name":"Second Workshop for Women in Computational Topology (WinCompTop 2)","funder_award_id":"1841455","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3304432272","display_name":"Collaborative Research: Emergent Sequences in Inhibition-Dominated Recurrent Networks","funder_award_id":"1951599","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4161841536","display_name":null,"funder_award_id":"DMS-1951165","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4264324352","display_name":null,"funder_award_id":"DMS-1951599","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4373504808","display_name":"Collaborative Research: Emergent Sequences in Inhibition-Dominated Recurrent Networks","funder_award_id":"1951165","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7960031013","display_name":"CRCNS: Circuit dynamics in zebrafish larvae: mechanisms, modulation, and mathematical modeling of network topology and attractor dynamics","funder_award_id":"R01NS120581","funder_id":"https://openalex.org/F4320337359","funder_display_name":"National Institute of Neurological Disorders and Stroke"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308488","display_name":"Association for Women in Mathematics","ror":"https://ror.org/04172mv97"},{"id":"https://openalex.org/F4320323570","display_name":"Australian Mathematical Sciences Institute","ror":"https://ror.org/00yn60108"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337359","display_name":"National Institute of Neurological Disorders and Stroke","ror":"https://ror.org/01s5ya894"},{"id":"https://openalex.org/F4320337363","display_name":"National Institute of Biomedical Imaging and Bioengineering","ror":"https://ror.org/00372qc85"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W749223900","https://openalex.org/W1494334782","https://openalex.org/W1572063013","https://openalex.org/W1995363724","https://openalex.org/W2032458141","https://openalex.org/W2108902061","https://openalex.org/W2115761837","https://openalex.org/W2147103442","https://openalex.org/W2182625954","https://openalex.org/W2402319927","https://openalex.org/W2499653599","https://openalex.org/W2795469741","https://openalex.org/W2971423343","https://openalex.org/W3093197877","https://openalex.org/W3173593323","https://openalex.org/W3198788718","https://openalex.org/W4239497995"],"related_works":["https://openalex.org/W2795469741","https://openalex.org/W2795723626","https://openalex.org/W3046571286","https://openalex.org/W2971423343","https://openalex.org/W2003636219","https://openalex.org/W2109320703","https://openalex.org/W3198788718","https://openalex.org/W3183775718","https://openalex.org/W4323667259","https://openalex.org/W2076760379"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2021-03-01T00:00:00"}
