IDEAS home Printed from https://ideas.repec.org/a/sae/envira/v21y1989i11p1541-1546.html
   My bibliography  Save this article

Maximum-Entropy Representations in Convex Polytopes: Applications to Spatial Interaction

Author

Listed:
  • P B Slater

    (Community and Organization Research Institute, University of California, Santa Barbara, CA 93106, USA)

Abstract

Of all representations of a given point situated in a convex polytope, as a convex combination of extreme points, there exists one for which the probability or weighting distribution has maximum entropy. The determination of this multiplicative or exponential distribution can be accomplished by inverting a certain bijection—developed by Rothaus and by Bregman—of convex polytopes into themselves. An iterative algorithm is available for this procedure. The doubly stochastic matrix with a given set of transversals (generalized diagonal products) can be found by means of this method. Applications are discussed of the Rothaus -Bregman map to a proof of Birkhoff's theorem and to the calculation of trajectories of points leading to stationary or equilibrium values of the generalized permanent, in particular in spatial interaction modeling.

Suggested Citation

  • P B Slater, 1989. "Maximum-Entropy Representations in Convex Polytopes: Applications to Spatial Interaction," Environment and Planning A, , vol. 21(11), pages 1541-1546, November.
    • Handle: RePEc:sae:envira:v:21:y:1989:i:11:p:1541-1546
    DOI: 10.1068/a211541
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/a211541
    Download Restriction: no
    File URL: https://libkey.io/10.1068/a211541?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
    ---><---

    References listed on IDEAS

    as
    1. Paul Slater, 1981. "Combinatorial procedures for structuring internal migration and other transaction flows," Quality & Quantity: International Journal of Methodology, Springer, vol. 15(2), pages 179-202, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Slater, Paul B., 1992. "Minimum relative entropies of low-dimensional spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 145-154.

    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. P B Slater & Referee C Wymer, 1987. "Algorithm 13: Strong Component Hierarchical Clustering," Environment and Planning A, , vol. 19(1), pages 117-125, January.
    2. P B Slater, 1982. "Hierarchical Elimination and Regionalization in Spatial Choice," Environment and Planning A, , vol. 14(1), pages 127-130, January.
    3. P B Slater, 1984. "A Partial Hierarchical Regionalization of 3140 US Counties on the Basis of 1965–1970 Intercounty Migration," Environment and Planning A, , vol. 16(4), pages 545-550, April.
    4. P B Slater, 1985. "Point-to-Point Migration Functions and Gravity Model Renormalization: Approaches to Aggregation in Spatial Interaction Modeling," Environment and Planning A, , vol. 17(8), pages 1025-1044, August.
    5. G L Clark, 1982. "Volatility in the Geographical Structure of Short-Run US Interstate Migration," Environment and Planning A, , vol. 14(2), pages 145-167, February.

    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:sae:envira:v:21:y:1989:i:11:p:1541-1546. 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: SAGE Publications (email available below). General contact details of provider: .

    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.