{"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/euclidean-mirrors-and-first-order","title":"Euclidean mirrors and first-order changepoints in network time series","arxiv_id":"2405.11111","date":"2024-05-17","proceeding":null,"authors":["Tianyi Chen","Zachary Lubberts","Avanti Athreya","Youngser Park","Carey E. Priebe"],"abstract":"We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution.","url_abs":"https://arxiv.org/abs/2405.11111v3","url_pdf":"https://arxiv.org/pdf/2405.11111v3.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":"euclidean-mirrors-and-first-order","repo_url":"https://github.com/TianyiChen97/Euclidean-mirrors-and-first-order-changepoints-in-network-time-series","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}