{"id":"https://openalex.org/W3189073627","doi":"https://doi.org/10.1137/22m1528471","title":"Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams","display_name":"Signatures, Lipschitz-Free Spaces, and Paths of Persistence Diagrams","publication_year":2023,"publication_date":"2023-12-14","ids":{"openalex":"https://openalex.org/W3189073627","doi":"https://doi.org/10.1137/22m1528471","mag":"3189073627"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1528471","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"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":"http://arxiv.org/pdf/2108.02727","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067148930","display_name":"Chad Giusti","orcid":"https://orcid.org/0000-0003-2412-3622"},"institutions":[{"id":"https://openalex.org/I131249849","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60","country_code":"US","type":"education","lineage":["https://openalex.org/I131249849"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chad Giusti","raw_affiliation_strings":["Department of Mathematics, Oregon State University, Corvallis, OR 97331 USA."],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Oregon State University, Corvallis, OR 97331 USA.","institution_ids":["https://openalex.org/I131249849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010254304","display_name":"Darrick Lee","orcid":"https://orcid.org/0000-0002-1004-7908"},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB","SK"],"is_corresponding":false,"raw_author_name":"Darrick Lee","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford OX2 6GG England."],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford OX2 6GG England.","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I40120149"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.368,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.472268,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":67,"max":78},"biblio":{"volume":"7","issue":"4","first_page":"828","last_page":"866"},"is_retracted":false,"is_paratext":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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9777,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9609,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.7579356},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.46422976}],"concepts":[{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.7579356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5534009},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4996047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49633485},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.46422976},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34992355},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.24181235},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17462927},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1528471","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.02727","pdf_url":"http://arxiv.org/pdf/2108.02727","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.02727","pdf_url":"http://arxiv.org/pdf/2108.02727","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation","award_id":"NSF-1854683"},{"funder":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","award_id":"51NF40-185897"},{"funder":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada","award_id":"PGS-D3"},{"funder":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research","award_id":"N00014-16-1-2010"},{"funder":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research","award_id":"FA9550-21-1-0266"}],"datasets":[],"versions":[],"referenced_works_count":106,"referenced_works":["https://openalex.org/W100459338","https://openalex.org/W142666414","https://openalex.org/W1540155273","https://openalex.org/W1593902291","https://openalex.org/W1596721197","https://openalex.org/W1798863697","https://openalex.org/W1803377658","https://openalex.org/W1819250359","https://openalex.org/W1960384938","https://openalex.org/W1966404902","https://openalex.org/W1981276685","https://openalex.org/W1986280275","https://openalex.org/W2004095444","https://openalex.org/W2008145946","https://openalex.org/W2009940349","https://openalex.org/W2037817770","https://openalex.org/W2045044457","https://openalex.org/W2064090547","https://openalex.org/W2069314032","https://openalex.org/W2071391326","https://openalex.org/W2102368730","https://openalex.org/W2106269037","https://openalex.org/W2115445832","https://openalex.org/W2125085449","https://openalex.org/W2137226992","https://openalex.org/W2144044408","https://openalex.org/W2148561979","https://openalex.org/W2149185044","https://openalex.org/W2157942701","https://openalex.org/W2164074261","https://openalex.org/W2171910661","https://openalex.org/W2186601123","https://openalex.org/W2212660284","https://openalex.org/W2297500149","https://openalex.org/W2319717399","https://openalex.org/W2401349093","https://openalex.org/W2411877106","https://openalex.org/W2559655401","https://openalex.org/W2604272474","https://openalex.org/W2805139353","https://openalex.org/W2892787861","https://openalex.org/W2898407550","https://openalex.org/W2918723355","https://openalex.org/W2920595754","https://openalex.org/W2938995766","https://openalex.org/W2941294530","https://openalex.org/W2942078528","https://openalex.org/W2942949268","https://openalex.org/W2945456722","https://openalex.org/W2962706934","https://openalex.org/W2962818398","https://openalex.org/W2962950339","https://openalex.org/W2963276646","https://openalex.org/W2963343672","https://openalex.org/W2963611658","https://openalex.org/W2964071468","https://openalex.org/W2964143464","https://openalex.org/W2964237352","https://openalex.org/W2966039532","https://openalex.org/W2982537263","https://openalex.org/W2991612390","https://openalex.org/W2991962490","https://openalex.org/W2993904890","https://openalex.org/W2995700079","https://openalex.org/W2999905431","https://openalex.org/W3003630168","https://openalex.org/W3024956007","https://openalex.org/W3043207359","https://openalex.org/W3084776840","https://openalex.org/W3085870773","https://openalex.org/W3091823944","https://openalex.org/W3091936663","https://openalex.org/W3094622830","https://openalex.org/W3098455240","https://openalex.org/W3099100849","https://openalex.org/W3099567910","https://openalex.org/W3104309020","https://openalex.org/W3105700404","https://openalex.org/W3106027936","https://openalex.org/W3106079343","https://openalex.org/W3106391989","https://openalex.org/W3106415951","https://openalex.org/W3106515996","https://openalex.org/W3106571115","https://openalex.org/W3122545378","https://openalex.org/W3123940972","https://openalex.org/W3126104578","https://openalex.org/W3127257262","https://openalex.org/W3138784139","https://openalex.org/W3146797348","https://openalex.org/W3163616925","https://openalex.org/W3197219184","https://openalex.org/W3217443154","https://openalex.org/W378919085","https://openalex.org/W385466589","https://openalex.org/W391985582","https://openalex.org/W4206116286","https://openalex.org/W4213033583","https://openalex.org/W4233690291","https://openalex.org/W4242523994","https://openalex.org/W4249571512","https://openalex.org/W4293182332","https://openalex.org/W4308118206","https://openalex.org/W4386275867","https://openalex.org/W616109306","https://openalex.org/W617501864"],"related_works":["https://openalex.org/W4293385557","https://openalex.org/W4287172919","https://openalex.org/W3165347651","https://openalex.org/W3014335474","https://openalex.org/W2897842840","https://openalex.org/W2499849978","https://openalex.org/W2073281382","https://openalex.org/W2042906150","https://openalex.org/W2022300732","https://openalex.org/W1642415801"],"abstract_inverted_index":{".Paths":[0],"of":[1,7,12,16,31,61,66,87,117,131,154,163,216,231],"persistence":[2,53,67,88,118,192],"diagrams":[3,54,68,89],"provide":[4,56],"a":[5,13,57,95,98,103,128,135,171,175,184,203,208,223,228],"summary":[6,60],"the":[8,28,63,70,85,108,125,152,161,181,198,214],"dynamic":[9,29],"topological":[10,59],"structure":[11,75,111],"one-parameter":[14],"family":[15],"metric":[17],"spaces.":[18],"These":[19],"summaries":[20],"can":[21,55,121],"be":[22,122],"used":[23],"to":[24,112,147,222],"study":[25],"and":[26,46,73,80,142,156,186,194],"characterize":[27,149],"shape":[30],"data":[32,236],"such":[33],"as":[34],"swarming":[35,232],"behavior":[36],"in":[37,50,134,160],"multiagent":[38],"systems,":[39],"time-varying":[40],"functional":[41],"MRI":[42],"scans":[43],"from":[44,102],"neuroscience,":[45],"time-dependent":[47],"scalar":[48],"fields":[49],"hydrodynamics.":[51],"While":[52],"powerful":[58],"data,":[62],"standard":[64],"space":[65,86,100,110,153],"lacks":[69],"sufficient":[71],"algebraic":[72],"analytic":[74],"required":[76],"for":[77,190,227],"many":[78],"theoretical":[79],"computational":[81],"analyses.":[82],"We":[83,106],"enrich":[84],"by":[90,219],"isometrically":[91],"embedding":[92],"it":[93,196],"into":[94,174,207],"Lipschitz-free":[96],"space,":[97,177],"Banach":[99,109,136],"built":[101],"universal":[104,141],"construction.":[105],"utilize":[107],"define":[113],"bounded":[114],"variation":[115],"paths":[116,132,155],"diagrams,":[119,193],"which":[120,144],"studied":[123],"using":[124],"path":[126,200],"signature,":[127,201],"reparametrization-invariant":[129],"characterization":[130],"valued":[133],"space.":[137,210],"The":[138],"signature":[139],"is":[140],"characteristic,":[143],"allow":[145],"us":[146],"theoretically":[148],"measures":[150],"on":[151],"motivate":[157],"its":[158],"use":[159],"context":[162],"kernel":[164,167],"methods.":[165],"However,":[166],"methods":[168,218],"often":[169],"require":[170],"feature":[172,188,205],"map":[173,189,206],"Hilbert":[176,209],"so":[178],"we":[179,212],"introduce":[180],"moment":[182],"map,":[183],"stable":[185],"injective":[187],"static":[191],"compose":[195],"with":[197],"discrete":[199],"producing":[202],"computable":[204],"Finally,":[211],"demonstrate":[213],"efficacy":[215],"our":[217],"applying":[220],"this":[221],"parameter":[224],"estimation":[225],"problem":[226],"3-dimensional":[229],"model":[230],"behavior.Keywordspath":[233],"signaturepersistence":[234],"diagramtopological":[235],"analysiskernel":[237],"methodsMSC":[238],"codes55N3160L10":[239]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3189073627","counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-01-16T04:05:46.655072","created_date":"2021-08-16"}