IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v336y2018icp162-175.html
   My bibliography  Save this article

Strongly maximal intersection-complete neural codes on grids are convex

Author

Listed:
  • Williams, Robert

Abstract

The brain encodes spatial structure through a combinatorial code of neural activity. Experiments suggest such codes correspond to convex areas of the subject’s environment. We present an intrinsic condition that implies a neural code may correspond to a collection of convex sets and give a bound on the minimal dimension underlying such a realization.

Suggested Citation

  • Williams, Robert, 2018. "Strongly maximal intersection-complete neural codes on grids are convex," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 162-175.
  • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:162-175
    DOI: 10.1016/j.amc.2018.04.064
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318303904
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.04.064?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Carina Curto & Vladimir Itskov, 2008. "Cell Groups Reveal Structure of Stimulus Space," PLOS Computational Biology, Public Library of Science, vol. 4(10), pages 1-13, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sudhamayee, K. & Krishna, M. Gopal & Manimaran, P., 2023. "Simplicial network analysis on EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Samir Chowdhury & Bowen Dai & Facundo Mémoli, 2018. "The importance of forgetting: Limiting memory improves recovery of topological characteristics from neural data," PLOS ONE, Public Library of Science, vol. 13(9), pages 1-20, September.
    3. Y Dabaghian & F Mémoli & L Frank & G Carlsson, 2012. "A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology," PLOS Computational Biology, Public Library of Science, vol. 8(8), pages 1-14, August.
    4. Mamiko Arai & Vicky Brandt & Yuri Dabaghian, 2014. "The Effects of Theta Precession on Spatial Learning and Simplicial Complex Dynamics in a Topological Model of the Hippocampal Spatial Map," PLOS Computational Biology, Public Library of Science, vol. 10(6), pages 1-14, June.

    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:eee:apmaco:v:336:y:2018:i:c:p:162-175. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.