IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0126383.html
   My bibliography  Save this article

Topological Data Analysis of Biological Aggregation Models

Author

Listed:
  • Chad M Topaz
  • Lori Ziegelmeier
  • Tom Halverson

Abstract

We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.

Suggested Citation

  • Chad M Topaz & Lori Ziegelmeier & Tom Halverson, 2015. "Topological Data Analysis of Biological Aggregation Models," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-26, May.
    • Handle: RePEc:plo:pone00:0126383
    DOI: 10.1371/journal.pone.0126383
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0126383
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0126383&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0126383?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M Ulmer & Lori Ziegelmeier & Chad M Topaz, 2019. "A topological approach to selecting models of biological experiments," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-18, March.
    2. Kulkarni, Saumitra & Pharasi, Hirdesh K. & Vijayaraghavan, Sudharsan & Kumar, Sunil & Chakraborti, Anirban & Samal, Areejit, 2024. "Investigation of Indian stock markets using topological data analysis and geometry-inspired network measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    3. Sevvandi Kandanaarachchi & Rob J Hyndman, 2021. "Leave-one-out Kernel Density Estimates for Outlier Detection," Monash Econometrics and Business Statistics Working Papers 2/21, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0126383. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.