IDEAS home Printed from https://ideas.repec.org/a/wsi/acsxxx/v12y2009i02ns0219525909002155.html
   My bibliography  Save this article

A Spectral Method For Aggregating Variables In Linear Dynamical Systems With Application To Cellular Automata Renormalization

Author

Listed:
  • MARTIN NILSSON JACOBI

    (Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology, 412 96 Göteborg, Sweden)

  • OLOF GÖRNERUP

    (Complex Systems Group, Department of Energy and Environment, Chalmers University of Technology, 412 96 Göteborg, Sweden)

Abstract

We present a method for identifying coarse-grained dynamics through aggregation of variables or states in linear dynamical systems. The condition for aggregation is expressed as a permutation symmetry of a set of dual eigenvectors of the matrix that defines the dynamics. The applicability of the condition is illustrated in examples from three different generic classes of reducible Markov chains: systems consisting of independent subsystems, dynamics with symmetries, and nearly decoupled Markov chains. Furthermore we show how the method can be used to coarse-grain cellular automata.

Suggested Citation

  • Martin Nilsson Jacobi & Olof Görnerup, 2009. "A Spectral Method For Aggregating Variables In Linear Dynamical Systems With Application To Cellular Automata Renormalization," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 131-155.
    • Handle: RePEc:wsi:acsxxx:v:12:y:2009:i:02:n:s0219525909002155
    DOI: 10.1142/S0219525909002155
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219525909002155
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219525909002155?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.

    Citations

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


    Cited by:

    1. Igor Mezić & Vladimir A. Fonoberov & Maria Fonoberova & Tuhin Sahai, 2019. "Spectral Complexity of Directed Graphs and Application to Structural Decomposition," Complexity, Hindawi, vol. 2019, pages 1-18, January.

    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:wsi:acsxxx:v:12:y:2009:i:02:n:s0219525909002155. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/acs/acs.shtml .

    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.