{"id":"https://openalex.org/W4401806474","doi":"https://doi.org/10.1007/s10208-024-09679-2","title":"Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs","display_name":"Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs","publication_year":2024,"publication_date":"2024-08-23","ids":{"openalex":"https://openalex.org/W4401806474","doi":"https://doi.org/10.1007/s10208-024-09679-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-024-09679-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09679-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09679-2.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09679-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082069457","display_name":"Thomas Chaplin","orcid":"https://orcid.org/0000-0002-4395-5654"},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Thomas Chaplin","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060903723","display_name":"Heather A. Harrington","orcid":"https://orcid.org/0000-0002-1705-7869"},"institutions":[{"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"]},{"id":"https://openalex.org/I4210148197","display_name":"Center for Systems Biology Dresden","ror":"https://ror.org/05hrn3e05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I149899117","https://openalex.org/I4210111875","https://openalex.org/I4210148197","https://openalex.org/I4210159854","https://openalex.org/I78650965"]},{"id":"https://openalex.org/I4210159854","display_name":"Max Planck Institute of Molecular Cell Biology and Genetics","ror":"https://ror.org/05b8d3w18","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210159854"]},{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Heather A. Harrington","raw_affiliation_strings":["Centre for Systems Biology Dresden, Dresden, Germany","Faculty of Mathematics, Technische Universit\u00e4t Dresden, Dresden, Germany","Mathematical Institute, University of Oxford, Oxford, UK","Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Systems Biology Dresden, Dresden, Germany","institution_ids":["https://openalex.org/I4210148197"]},{"raw_affiliation_string":"Faculty of Mathematics, Technische Universit\u00e4t Dresden, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany","institution_ids":["https://openalex.org/I4210159854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071485605","display_name":"Ulrike Tillmann","orcid":"https://orcid.org/0000-0002-8076-7660"},"institutions":[{"id":"https://openalex.org/I182145113","display_name":"Isaac Newton Institute for Mathematical Sciences","ror":"https://ror.org/007vkej58","country_code":"GB","type":"facility","lineage":["https://openalex.org/I182145113"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"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"],"is_corresponding":false,"raw_author_name":"Ulrike Tillmann","raw_affiliation_strings":["Isaac Newton Institute, University of Cambridge, Cambridge, UK","Mathematical Institute, University of Oxford, Oxford, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Isaac Newton Institute, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I182145113","https://openalex.org/I241749"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5082069457"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.7691,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73907979,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"25","issue":"5","first_page":"1711","last_page":"1776"},"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":0.9488000273704529,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9279000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7624161243438721},{"id":"https://openalex.org/keywords/persistent-homology","display_name":"Persistent homology","score":0.7264007925987244},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"Topological data analysis","score":0.6253605484962463},{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.5666171908378601},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5350103974342346},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.46749579906463623},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46079665422439575},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33281803131103516},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19299393892288208},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1576330065727234},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.13318195939064026},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.10823440551757812},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.0849330723285675}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7624161243438721},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.7264007925987244},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.6253605484962463},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.5666171908378601},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5350103974342346},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.46749579906463623},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46079665422439575},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33281803131103516},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19299393892288208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1576330065727234},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.13318195939064026},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.10823440551757812},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0849330723285675},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-024-09679-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09679-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09679-2.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10208-024-09679-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-024-09679-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-024-09679-2.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1132496359","display_name":"Application driven Topological Data Analysis","funder_award_id":"EP/R018472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6066696820","display_name":null,"funder_award_id":"EP/R018472/1","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4401806474.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1983681808","https://openalex.org/W2020428772","https://openalex.org/W2122101130","https://openalex.org/W2128635744","https://openalex.org/W2133227973","https://openalex.org/W2507020368","https://openalex.org/W2569613157","https://openalex.org/W2751044447","https://openalex.org/W2950753216","https://openalex.org/W2962796441","https://openalex.org/W2963175648","https://openalex.org/W2963261462","https://openalex.org/W2964292054","https://openalex.org/W2999174208","https://openalex.org/W3037223741","https://openalex.org/W3037488155","https://openalex.org/W3098455240","https://openalex.org/W3099422512","https://openalex.org/W3118794388","https://openalex.org/W3137533807","https://openalex.org/W3163711065","https://openalex.org/W3171131780","https://openalex.org/W3201821930","https://openalex.org/W3202868818","https://openalex.org/W4210893071","https://openalex.org/W4226035642","https://openalex.org/W4237378571","https://openalex.org/W4255616439","https://openalex.org/W4281870735","https://openalex.org/W4360980502","https://openalex.org/W4367056236","https://openalex.org/W4390937024","https://openalex.org/W4395684318","https://openalex.org/W6600157417"],"related_works":["https://openalex.org/W2886923060","https://openalex.org/W2887690685","https://openalex.org/W2129730857","https://openalex.org/W4287394697","https://openalex.org/W3119689987","https://openalex.org/W3120766012","https://openalex.org/W4287826795","https://openalex.org/W3128725485","https://openalex.org/W3204835693","https://openalex.org/W4206186921"],"abstract_inverted_index":{"Abstract":[0],"Weighted":[1],"digraphs":[2],"are":[3],"used":[4],"to":[5,24,97],"model":[6],"a":[7,18,61,68],"variety":[8],"of":[9,20,56,70],"natural":[10],"systems":[11],"and":[12,26,100],"can":[13],"exhibit":[14],"interesting":[15],"structure":[16,55],"across":[17],"range":[19],"scales.":[21],"In":[22],"order":[23],"understand":[25],"compare":[27],"these":[28],"systems,":[29],"we":[30,39,88],"require":[31],"stable,":[32,93],"interpretable,":[33],"multiscale":[34],"descriptors.":[35],"To":[36],"this":[37],"end,":[38],"propose":[40],"grounded":[41],"persistent":[42],"path":[43],"homology":[44],"(":[45],"GrPPH":[46],")\u2014a":[47],"new,":[48],"functorial,":[49],"topological":[50],"descriptor":[51],"that":[52],"describes":[53],"the":[54,74,82,85,90],"an":[57],"edge-weighted":[58],"digraph":[59],"via":[60],"persistence":[62],"barcode.":[63,86],"We":[64],"show":[65,89],"there":[66],"is":[67,92],"choice":[69],"circuit":[71],"basis":[72],"for":[73,81],"graph":[75],"which":[76],"yields":[77],"geometrically":[78],"interpretable":[79],"representatives":[80],"features":[83],"in":[84,94],"Moreover,":[87],"barcode":[91],"bottleneck":[95],"distance,":[96],"both":[98],"numerical":[99],"structural":[101],"perturbations.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2024-08-24T00:00:00"}