{"paper":{"title":"Density Sensitive Bifiltered Dowker Complexes via Total Weight","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jan Spali\\'nski, Niklas Hellmer","submitted_at":"2024-05-24T14:24:49Z","abstract_excerpt":"In this paper, we introduce new density-sensitive bifiltrations for data using the framework of Dowker complexes.\n  Previously, Dowker complexes were studied to address directional or bivariate data whereas density-sensitive bifiltrations on \\v{C}ech and Vietoris--Rips complexes were suggested to make them more robust, while increasing computational complexity.\n  We combine these two lines of research, noting that the superlevels of the total weight function of a Dowker complex can be identified as an instance of Sheehy's multicover filtration.\n  We prove a version of Dowker duality that is co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15592","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.15592/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}