🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001225s)

  2. Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web (2011)

    Rien Van De Weygaert, Gert Vegter, Herbert Edelsbrunner, Bernard J. T. Jones, Pratyush Pranav, Changbom Park, Wojciech A. Hellwing, Bob Eldering, Nico Kruithof, E. G. P. Bos, Johan Hidding, Job Feldbrugge, Eline Ten Have, Matti Van Engelen, Manuel Caroli, Monique Teillaud
    Abstract We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of...

  4. Topology-Driven Trajectory Synthesis With an Example on Retinal Cell Motions (2014)

    Chen Gu, Leonidas Guibas, Michael Kerber
    Abstract We design a probabilistic trajectory synthesis algorithm for generating time-varying sequences of geometric configuration data. The algorithm takes a set of observed samples (each may come from a different trajectory) and simulates the dynamic evolution of the patterns in O(n2 logn) time. To synthesize geometric configurations with indistinct identities, we use the pair correlation function to summarize point distribution, and α-shapes to maintain topological shape features based on a fast persistence matching approach. We apply our method to build a computational model for the geometric transformation of the cone mosaic in retinitis pigmentosa — an inherited and currently untreatable retinal degeneration.

  5. Euler Characteristic Surfaces: A Stable Multiscale Topological Summary of Time Series Data (2024)

    Anamika Roy, Atish J. Mitra, Tapati Dutta
    Abstract We present Euler Characteristic Surfaces as a multiscale spatiotemporal topological summary of time series data encapsulating the topology of the system at different time instants and length scales. Euler Characteristic Surfaces with an appropriate metric is used to quantify stability and locate critical changes in a dynamical system with respect to variations in a parameter, while being substantially computationally cheaper than available alternate methods such as persistent homology. The stability of the construction is demonstrated by a quantitative comparison bound with persistent homology, and a quantitative stability bound under small changes in time is established. The proposed construction is used to analyze two different kinds of simulated disordered flow situations.