{"id":"https://openalex.org/W2999174208","doi":"https://doi.org/10.3390/a13010019","title":"Computing Persistent Homology of Directed Flag Complexes","display_name":"Computing Persistent Homology of Directed Flag Complexes","publication_year":2020,"publication_date":"2020-01-07","ids":{"openalex":"https://openalex.org/W2999174208","doi":"https://doi.org/10.3390/a13010019","mag":"2999174208"},"language":"en","primary_location":{"id":"doi:10.3390/a13010019","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13010019","pdf_url":"https://www.mdpi.com/1999-4893/13/1/19/pdf?version=1579147057","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/13/1/19/pdf?version=1579147057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020090635","display_name":"Daniel L\u00fctgehetmann","orcid":null},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Daniel L\u00fctgehetmann","raw_affiliation_strings":["Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK","institution_ids":["https://openalex.org/I195460627"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072228660","display_name":"Dejan Govc","orcid":"https://orcid.org/0000-0002-7156-7966"},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dejan Govc","raw_affiliation_strings":["Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK","institution_ids":["https://openalex.org/I195460627"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073806578","display_name":"Jason P. Smith","orcid":"https://orcid.org/0000-0002-4209-1604"},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jason P. Smith","raw_affiliation_strings":["Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK","institution_ids":["https://openalex.org/I195460627"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065001653","display_name":"Ran Levi","orcid":"https://orcid.org/0000-0001-5297-8295"},"institutions":[{"id":"https://openalex.org/I195460627","display_name":"University of Aberdeen","ror":"https://ror.org/016476m91","country_code":"GB","type":"education","lineage":["https://openalex.org/I195460627"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Ran Levi","raw_affiliation_strings":["Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3FX, UK","institution_ids":["https://openalex.org/I195460627"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065001653"],"corresponding_institution_ids":["https://openalex.org/I195460627"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.179,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.93231383,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"13","issue":"1","first_page":"19","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.991599977016449,"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"}},{"id":"https://openalex.org/T11266","display_name":"Neuroinflammation and Neurodegeneration Mechanisms","score":0.9648000001907349,"subfield":{"id":"https://openalex.org/subfields/2808","display_name":"Neurology"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7728718519210815},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.674458920955658},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6074942350387573},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.5249583721160889},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.5229954719543457},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.5202368497848511},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4805060625076294},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37724265456199646},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35408884286880493},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2993941903114319},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2898433804512024},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20535627007484436},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.19633910059928894},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11499530076980591},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06849858164787292}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7728718519210815},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.674458920955658},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6074942350387573},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5249583721160889},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.5229954719543457},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.5202368497848511},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4805060625076294},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37724265456199646},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35408884286880493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2993941903114319},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2898433804512024},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20535627007484436},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.19633910059928894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11499530076980591},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06849858164787292},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a13010019","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13010019","pdf_url":"https://www.mdpi.com/1999-4893/13/1/19/pdf?version=1579147057","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:irep.ntu.ac.uk:42749","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400559","display_name":"Nottingham Trent University's Institutional Repository (Nottingham Trent Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I52590639","host_organization_name":"Nottingham Trent University","host_organization_lineage":["https://openalex.org/I52590639"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:1dbc71d8d1904d90a5f91d52831b9df1","is_oa":true,"landing_page_url":"https://doaj.org/article/1dbc71d8d1904d90a5f91d52831b9df1","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 13, Iss 1, p 19 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/13/1/19/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/a13010019","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a13010019","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13010019","pdf_url":"https://www.mdpi.com/1999-4893/13/1/19/pdf?version=1579147057","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4227803659","display_name":null,"funder_award_id":"EP/P025072/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7508466219","display_name":"Topological Analysis of Neural Systems","funder_award_id":"EP/P025072/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999174208.pdf","grobid_xml":"https://content.openalex.org/works/W2999174208.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W28435248","https://openalex.org/W131619556","https://openalex.org/W1899982405","https://openalex.org/W1972488821","https://openalex.org/W1979273469","https://openalex.org/W1992454573","https://openalex.org/W2027566319","https://openalex.org/W2040092971","https://openalex.org/W2064020260","https://openalex.org/W2231970151","https://openalex.org/W2333586270","https://openalex.org/W2962807402","https://openalex.org/W3040586665","https://openalex.org/W3104997105","https://openalex.org/W3175762873","https://openalex.org/W4233690291","https://openalex.org/W6815424340"],"related_works":["https://openalex.org/W3162517897","https://openalex.org/W4360887047","https://openalex.org/W2958601279","https://openalex.org/W4206186921","https://openalex.org/W3143913977","https://openalex.org/W2770791287","https://openalex.org/W4386755584","https://openalex.org/W3005059017","https://openalex.org/W2102692026","https://openalex.org/W2745914844"],"abstract_inverted_index":{"We":[0,102],"present":[1],"a":[2,15,67,143],"new":[3],"computing":[4],"package":[5],"Flagser,":[6],"designed":[7],"to":[8,111,152],"construct":[9],"the":[10,28,31,44,60,80,104,112,115,126,160,164,166,171],"directed":[11,17,61,116],"flag":[12,62,117],"complex":[13,63,118],"of":[14,39,59,82,106,114,119,122,140,168],"finite":[16],"graph,":[18],"and":[19,30,130,170],"compute":[20,97,172],"persistent":[21,35],"homology":[22,36,88],"for":[23,54],"flexibly":[24],"defined":[25],"filtrations":[26],"on":[27,43],"graph":[29],"resulting":[32],"complex.":[33],"The":[34,57],"computation":[37,139],"part":[38],"Flagser":[40,77,90,107,151],"is":[41,51,64],"based":[42],"program":[45],"Ripser":[46],"by":[47,73,108,125],"U.":[48],"Bauer,":[49],"but":[50],"optimised":[52],"specifically":[53],"large":[55],"computations.":[56],"construction":[58,113],"done":[65],"in":[66,163],"way":[68],"that":[69],"allows":[70],"easy":[71],"parallelisation":[72],"arbitrarily":[74],"many":[75],"cores.":[76],"also":[78,149],"has":[79,91],"option":[81],"working":[83],"with":[84,99],"undirected":[85],"graphs.":[86],"For":[87,142],"computations":[89],"an":[92],"approximate":[93],"option,":[94],"which":[95],"shortens":[96],"time":[98,173],"remarkable":[100],"accuracy.":[101],"demonstrate":[103],"power":[105],"applying":[109],"it":[110],"digital":[120],"reconstructions":[121],"brain":[123],"microcircuitry":[124],"Blue":[127],"Brain":[128],"Project":[129],"several":[131],"other":[132,154],"examples.":[133],"In":[134,157],"some":[135,153],"instances":[136],"we":[137,148],"perform":[138],"homology.":[141],"more":[144],"complete":[145],"performance":[146],"analysis,":[147],"apply":[150],"data":[155],"collections.":[156],"all":[158],"cases":[159],"hardware":[161],"used":[162],"computation,":[165],"use":[167],"memory":[169],"are":[174],"recorded.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2020-01-23T00:00:00"}
