{"id":"https://openalex.org/W2962844110","doi":"https://doi.org/10.1007/s00454-019-00100-2","title":"The Geometry of Synchronization Problems and Learning Group Actions","display_name":"The Geometry of Synchronization Problems and Learning Group Actions","publication_year":2019,"publication_date":"2019-05-28","ids":{"openalex":"https://openalex.org/W2962844110","doi":"https://doi.org/10.1007/s00454-019-00100-2","mag":"2962844110"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-019-00100-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-019-00100-2","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.soton.ac.uk/430926/1/Gao_Brodzki_Mukherjee_The_Geometry_of_Synchronization_Problems_and_Learning_Group_Actions.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057450352","display_name":"Tingran Gao","orcid":"https://orcid.org/0000-0002-0436-689X"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tingran Gao","raw_affiliation_strings":["Committee on Computational and Applied Mathematics, Department of Statistics, University of Chicago, Chicago, IL, 60637, USA"],"raw_orcid":"https://orcid.org/0000-0002-0436-689X","affiliations":[{"raw_affiliation_string":"Committee on Computational and Applied Mathematics, Department of Statistics, University of Chicago, Chicago, IL, 60637, USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065119311","display_name":"Jacek Brodzki","orcid":"https://orcid.org/0000-0002-4524-1081"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jacek Brodzki","raw_affiliation_strings":["Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, US","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014241799","display_name":"Sayan Mukherjee","orcid":"https://orcid.org/0000-0002-6715-3920"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sayan Mukherjee","raw_affiliation_strings":["Department of Statistical Science, Mathematics, Computer Science, and Bioinformatics & Biostatistics, Duke University, Durham, NC, 27708, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Science, Mathematics, Computer Science, and Bioinformatics & Biostatistics, Duke University, Durham, NC, 27708, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057450352"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.3996,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.89964925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"1","first_page":"150","last_page":"211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9789999723434448,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9663000106811523,"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/mathematics","display_name":"Mathematics","score":0.8202622532844543},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.41085484623908997},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36780235171318054},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32260018587112427},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3003290295600891},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19224461913108826}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8202622532844543},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.41085484623908997},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36780235171318054},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32260018587112427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3003290295600891},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19224461913108826}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-019-00100-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-019-00100-2","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:430926","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s00454-019-00100-2>).","pdf_url":"https://eprints.soton.ac.uk/430926/1/Gao_Brodzki_Mukherjee_The_Geometry_of_Synchronization_Problems_and_Learning_Group_Actions.pdf","source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":{"id":"pmh:oai:eprints.soton.ac.uk:430926","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s00454-019-00100-2>).","pdf_url":"https://eprints.soton.ac.uk/430926/1/Gao_Brodzki_Mukherjee_The_Geometry_of_Synchronization_Problems_and_Learning_Group_Actions.pdf","source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1276011550","display_name":"III: Small: Cumulon: Easy and Efficient Statistical Big-Data Analysis in the Cloud","funder_award_id":"1320357","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1355295197","display_name":null,"funder_award_id":"DMS-1418261","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1479776682","display_name":null,"funder_award_id":"1546331","funder_id":"https://openalex.org/F4320337389","funder_display_name":"Division of Information and Intelligent Systems"},{"id":"https://openalex.org/G2432954533","display_name":null,"funder_award_id":"1320357","funder_id":"https://openalex.org/F4320337389","funder_display_name":"Division of Information and Intelligent Systems"},{"id":"https://openalex.org/G2851871497","display_name":null,"funder_award_id":"1418261","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G303163932","display_name":null,"funder_award_id":"EP/N014189","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3746574654","display_name":"Coarse geometry and cohomology of large data sets","funder_award_id":"EP/I016945/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3841242684","display_name":null,"funder_award_id":"IIS-1320357","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4127705021","display_name":null,"funder_award_id":"EP/I016945/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4519643308","display_name":null,"funder_award_id":"1546331","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5228469649","display_name":"Collaborative Research: Topological Methods for Parsing  Shapes and Networks and Modeling Variation in Structure and Function","funder_award_id":"1418261","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5667765944","display_name":null,"funder_award_id":"16-13261","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G5862634707","display_name":null,"funder_award_id":"IIS 1546331","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5865894165","display_name":null,"funder_award_id":"DMS 16-13261","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6003638275","display_name":null,"funder_award_id":"DMS-1045153","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6867062684","display_name":null,"funder_award_id":"EP/N014189/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6890943872","display_name":"Joining the dots: from data to insight","funder_award_id":"EP/N014189/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8207741004","display_name":null,"funder_award_id":"400837","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G8479464286","display_name":null,"funder_award_id":"1045153","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G982519726","display_name":null,"funder_award_id":"1045153","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337389","display_name":"Division of Information and Intelligent Systems","ror":"https://ror.org/053a2cp42"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962844110.pdf","grobid_xml":"https://content.openalex.org/works/W2962844110.grobid-xml"},"referenced_works_count":178,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W101115925","https://openalex.org/W323935674","https://openalex.org/W385466589","https://openalex.org/W603006721","https://openalex.org/W614472450","https://openalex.org/W642236699","https://openalex.org/W863038102","https://openalex.org/W1509036934","https://openalex.org/W1511378139","https://openalex.org/W1521419904","https://openalex.org/W1524047195","https://openalex.org/W1540596182","https://openalex.org/W1547877468","https://openalex.org/W1555017801","https://openalex.org/W1557324374","https://openalex.org/W1571072992","https://openalex.org/W1578099820","https://openalex.org/W1578848569","https://openalex.org/W1585160083","https://openalex.org/W1586275925","https://openalex.org/W1589741152","https://openalex.org/W1590776313","https://openalex.org/W1593631596","https://openalex.org/W1599815147","https://openalex.org/W1660371282","https://openalex.org/W1675187506","https://openalex.org/W1750017912","https://openalex.org/W1804414602","https://openalex.org/W1866515447","https://openalex.org/W1951611851","https://openalex.org/W1966949944","https://openalex.org/W1973836644","https://openalex.org/W1974956622","https://openalex.org/W1977220192","https://openalex.org/W1977257583","https://openalex.org/W1978479505","https://openalex.org/W1981859328","https://openalex.org/W1982015992","https://openalex.org/W1983033166","https://openalex.org/W1986853035","https://openalex.org/W1987297766","https://openalex.org/W1988254157","https://openalex.org/W1993747418","https://openalex.org/W1994911252","https://openalex.org/W2001141328","https://openalex.org/W2005358863","https://openalex.org/W2006554089","https://openalex.org/W2007206727","https://openalex.org/W2008590575","https://openalex.org/W2009918127","https://openalex.org/W2010134232","https://openalex.org/W2011828424","https://openalex.org/W2023155126","https://openalex.org/W2029171346","https://openalex.org/W2032618685","https://openalex.org/W2040957249","https://openalex.org/W2046644584","https://openalex.org/W2050991582","https://openalex.org/W2051327384","https://openalex.org/W2053186076","https://openalex.org/W2057101663","https://openalex.org/W2057125755","https://openalex.org/W2059917035","https://openalex.org/W2060663265","https://openalex.org/W2063079497","https://openalex.org/W2065140986","https://openalex.org/W2068565459","https://openalex.org/W2072011469","https://openalex.org/W2073027160","https://openalex.org/W2074551095","https://openalex.org/W2079746361","https://openalex.org/W2083563151","https://openalex.org/W2084840427","https://openalex.org/W2086326407","https://openalex.org/W2086886817","https://openalex.org/W2087841994","https://openalex.org/W2091000302","https://openalex.org/W2091791686","https://openalex.org/W2094732964","https://openalex.org/W2097308346","https://openalex.org/W2100657858","https://openalex.org/W2100685794","https://openalex.org/W2101657948","https://openalex.org/W2112997637","https://openalex.org/W2118405557","https://openalex.org/W2118557299","https://openalex.org/W2121947440","https://openalex.org/W2124123435","https://openalex.org/W2130406232","https://openalex.org/W2132914434","https://openalex.org/W2133368951","https://openalex.org/W2134753888","https://openalex.org/W2135175318","https://openalex.org/W2135915144","https://openalex.org/W2136226659","https://openalex.org/W2137964266","https://openalex.org/W2138486270","https://openalex.org/W2143113961","https://openalex.org/W2143133882","https://openalex.org/W2143703915","https://openalex.org/W2143796943","https://openalex.org/W2144012927","https://openalex.org/W2146932984","https://openalex.org/W2147554450","https://openalex.org/W2151870994","https://openalex.org/W2153399947","https://openalex.org/W2156838815","https://openalex.org/W2156855194","https://openalex.org/W2161654109","https://openalex.org/W2164435545","https://openalex.org/W2171176228","https://openalex.org/W2171244244","https://openalex.org/W2184495546","https://openalex.org/W2187089797","https://openalex.org/W2230284341","https://openalex.org/W2230899220","https://openalex.org/W2248896003","https://openalex.org/W2258798086","https://openalex.org/W2272677673","https://openalex.org/W2285077570","https://openalex.org/W2293497821","https://openalex.org/W2295766446","https://openalex.org/W2312140512","https://openalex.org/W2337089604","https://openalex.org/W2471188671","https://openalex.org/W2472414548","https://openalex.org/W2525125412","https://openalex.org/W2529985811","https://openalex.org/W2565756275","https://openalex.org/W2595798497","https://openalex.org/W2605552558","https://openalex.org/W2621081915","https://openalex.org/W2734469280","https://openalex.org/W2734727858","https://openalex.org/W2747134202","https://openalex.org/W2804286000","https://openalex.org/W2886307152","https://openalex.org/W2952488104","https://openalex.org/W2962936676","https://openalex.org/W2963122501","https://openalex.org/W2963183404","https://openalex.org/W2963381078","https://openalex.org/W2963537367","https://openalex.org/W2963986398","https://openalex.org/W2964243522","https://openalex.org/W2964258018","https://openalex.org/W2967026314","https://openalex.org/W3084957446","https://openalex.org/W3097988337","https://openalex.org/W3100905299","https://openalex.org/W3101492630","https://openalex.org/W3103496808","https://openalex.org/W3105794348","https://openalex.org/W3140579943","https://openalex.org/W4213367101","https://openalex.org/W4230962939","https://openalex.org/W4234333941","https://openalex.org/W4236305466","https://openalex.org/W4236942578","https://openalex.org/W4241492945","https://openalex.org/W4243293508","https://openalex.org/W4244766844","https://openalex.org/W4246446534","https://openalex.org/W4247496922","https://openalex.org/W4248532778","https://openalex.org/W4248598408","https://openalex.org/W4255783720","https://openalex.org/W4293203252","https://openalex.org/W4300651159","https://openalex.org/W4301388364","https://openalex.org/W6603538048","https://openalex.org/W6604267941","https://openalex.org/W6609553175","https://openalex.org/W6610310711","https://openalex.org/W6630691879","https://openalex.org/W6744473170","https://openalex.org/W6814234141"],"related_works":["https://openalex.org/W3106133691","https://openalex.org/W4249580765","https://openalex.org/W2096753949","https://openalex.org/W1985218657","https://openalex.org/W1557945163","https://openalex.org/W2742285599","https://openalex.org/W2064847051","https://openalex.org/W3103780039","https://openalex.org/W2963341196","https://openalex.org/W2023661790"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}