{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/wasserstein-distance-as-a-new-tool-for","title":"Wasserstein distance as a new tool for discriminating cosmologies through the topology of large scale structure","arxiv_id":"2301.09411","date":"2023-01-23","proceeding":null,"authors":["Maksym Tsizh","Vitalii Tymchyshyn","Franco Vazza"],"abstract":"In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\\sigma_8$ cosmological parameter (present root-mean-square matter fluctuation averaged over a sphere of radius 8 Mpc comoving). The Wasserstein distance (a.k.a. the pair-matching distance) was proposed to measure the difference between two networks in terms of persistent homology. The advantage of this approach consists in its non-parametric way of probing the topology of the Cosmic web, in contrast to graph-theoretical approach depending on linking length. By treating the halos of the Cosmic Web as points in a point cloud we calculate persistent homologies, build persistence (birth-death) diagrams and evaluate Wasserstein distance between them. The latter showed itself as a convenient tool to compare simulated Cosmic webs. We show that one can discern two Cosmic webs (simulated or real) with different $\\sigma_8$ parameter. It turns out that Wasserstein distance's discrimination ability depends on redshift $z$, as well as on the dimensionality of considered homology features. We find that the highest discriminating power this tool obtains at $z=2$ snapshots, among the considered $z=2$, $1$, and $0.1$ ones.","url_abs":"https://arxiv.org/abs/2301.09411v2","url_pdf":"https://arxiv.org/pdf/2301.09411v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"wasserstein-distance-as-a-new-tool-for","repo_url":"https://github.com/mtsizh/bottleneck-distance-for-sigma8","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}