{"id":"https://openalex.org/W7165774235","doi":"https://doi.org/10.48550/arxiv.2606.23859","title":"Canopies: A Generalization of Vines and Vineyards for Parameterized Persistence","display_name":"Canopies: A Generalization of Vines and Vineyards for Parameterized Persistence","publication_year":2026,"publication_date":"2026-06-22","ids":{"openalex":"https://openalex.org/W7165774235","doi":"https://doi.org/10.48550/arxiv.2606.23859"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.23859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23859","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.23859","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056040649","display_name":"Barbara Giunti","orcid":"https://orcid.org/0000-0002-3500-8286"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giunti, Barbara","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043905996","display_name":"Elizabeth Munch","orcid":"https://orcid.org/0000-0002-9459-9493"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Munch, Elizabeth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9980999827384949,"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":0.9980999827384949,"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":0.0012000000569969416,"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/T10304","display_name":"Geometric and Algebraic Topology","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.7120000123977661},{"id":"https://openalex.org/keywords/monodromy","display_name":"Monodromy","score":0.6561999917030334},{"id":"https://openalex.org/keywords/persistence","display_name":"Persistence (discontinuity)","score":0.6144999861717224},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5830000042915344},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5611000061035156},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5056999921798706},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4555000066757202},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.4438999891281128},{"id":"https://openalex.org/keywords/bundle","display_name":"Bundle","score":0.4350000023841858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8080999851226807},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.7120000123977661},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.6561999917030334},{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.6144999861717224},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5611000061035156},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5056999921798706},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42590001225471497},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37119999527931213},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.3605000078678131},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3197999894618988},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30880001187324524},{"id":"https://openalex.org/C888380","wikidata":"https://www.wikidata.org/wiki/Q2427787","display_name":"Persistent data structure","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C128489963","wikidata":"https://www.wikidata.org/wiki/Q1187724","display_name":"Filtration (mathematics)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.23859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23859","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.23859","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23859","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,20,49],"paper,":[2],"we":[3,73,136],"provide":[4],"a":[5,13,52,67,89],"new":[6],"construction":[7],"for":[8],"studying":[9],"parameterized":[10],"persistence,":[11],"called":[12],"canopy.":[14,182],"We":[15,47,105],"give":[16],"two":[17],"versions":[18],"of":[19,32,42,78,80,92,103,122,129,140,153,177],"construction:":[21],"the":[22,30,33,37,40,43,58,70,94,101,110,119,138,151,170,175,181],"A-canopy,":[23],"retaining":[24],"all":[25],"information":[26,41,97],"about":[27],"points":[28,154,179],"on":[29],"diagonal":[31],"persistence":[34,45,59,71],"diagram;":[35],"and":[36,160],"D-canopy,":[38],"encoding":[39],"\"standard\"":[44],"diagram.":[46],"do":[48],"by":[50,143],"making":[51],"simple":[53],"but":[54],"major":[55],"modification":[56],"in":[57,69,132,150,169,180],"bundle":[60],"representation":[61],"information:":[62],"namely,":[63],"rather":[64,98],"than":[65,99],"tracking":[66,93],"point":[68],"diagram,":[72],"instead":[74],"track":[75],"some":[76,163],"choice":[77],"pairs":[79,130],"simplices":[81],"that":[82,126],"created":[83],"said":[84],"point.":[85],"This":[86],"viewpoint":[87],"is":[88],"combinatorial":[90],"version":[91],"chain":[95,124],"complex":[96],"just":[100],"output":[102],"persistence.":[104],"show":[106],"how":[107],"to":[108,146,157,161],"construct":[109],"canopies":[111,145],"from":[112],"any":[113],"filtered":[114,123],"filtration":[115],"function,":[116],"proving,":[117],"using":[118,144],"algebraic":[120],"structure":[121],"complexes,":[125],"different":[127],"choices":[128],"result":[131],"homeomorphic":[133],"structures.":[134],"Finally,":[135],"showcase":[137],"power":[139],"our":[141],"approach":[142],"define":[147],"vines":[148],"even":[149],"presence":[152],"with":[155,174],"multiplicity;":[156],"discuss":[158],"monodromy;":[159],"obtain":[162],"immediate":[164],"results":[165],"linking":[166],"non-trivial":[167],"monodromy":[168],"persistent":[171],"homology":[172],"transform":[173],"existence":[176],"non-Hausdorff":[178]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-25T00:00:00"}