2010/01/01 by Robert J. Adler, Omer Bobrowski, Matthew Strom Borman +3 · 1 citation
Computer Science · Engineering · Mathematics · #Algebraic number #Algebraic structure #Algebraic topology #Algorithm #Amino acid #Artificial intelligence #Biology #Combinatorics #Computational topology #Computer science #Engineering #Excursion #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Persistent homology #Point cloud #Pure mathematics #Random field #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AT #math.PR #msc:55N35 #msc:60G15 #msc:60G55 #msc:62H35
paper · pdf · doi:10.1214/10-imscoll609
published as Borrowing Strength: Theory Powering Applications, A Festschrift for Lawrence D. Brown, IMS Collections 6, 124-143, 2010
openalex publication_date 2010/01/01 · arxiv created 2010/03/26 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
<!-- *** Custom HTML *** --> We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices and, in most detail, the algebraic topology of the excursion sets of random fields.