Topological self-similarity on the random binary-tree model

Ken Yamamoto, Yoshihiro Yamazaki

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.

    Original languageEnglish
    Pages (from-to)62-71
    Number of pages10
    JournalJournal of Statistical Physics
    Volume139
    Issue number1
    DOIs
    Publication statusPublished - 2010 Mar

    Fingerprint

    Random Trees
    Binary Tree
    Self-similarity
    Hierarchical Structure
    Asymptotic Analysis
    Statistical property
    Branching
    Quantify
    Branch
    Model
    Generalization

    Keywords

    • Asymptotic behavior
    • Binary tree
    • Branching pattern
    • Hierarchical structure
    • Horton-Strahler analysis
    • Topological self-similarity

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Topological self-similarity on the random binary-tree model. / Yamamoto, Ken; Yamazaki, Yoshihiro.

    In: Journal of Statistical Physics, Vol. 139, No. 1, 03.2010, p. 62-71.

    Research output: Contribution to journalArticle

    @article{16b6085da800455ea43f0e546e6b2239,
    title = "Topological self-similarity on the random binary-tree model",
    abstract = "Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.",
    keywords = "Asymptotic behavior, Binary tree, Branching pattern, Hierarchical structure, Horton-Strahler analysis, Topological self-similarity",
    author = "Ken Yamamoto and Yoshihiro Yamazaki",
    year = "2010",
    month = "3",
    doi = "10.1007/s10955-010-9928-5",
    language = "English",
    volume = "139",
    pages = "62--71",
    journal = "Journal of Statistical Physics",
    issn = "0022-4715",
    publisher = "Springer New York",
    number = "1",

    }

    TY - JOUR

    T1 - Topological self-similarity on the random binary-tree model

    AU - Yamamoto, Ken

    AU - Yamazaki, Yoshihiro

    PY - 2010/3

    Y1 - 2010/3

    N2 - Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.

    AB - Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.

    KW - Asymptotic behavior

    KW - Binary tree

    KW - Branching pattern

    KW - Hierarchical structure

    KW - Horton-Strahler analysis

    KW - Topological self-similarity

    UR - http://www.scopus.com/inward/record.url?scp=77949570160&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=77949570160&partnerID=8YFLogxK

    U2 - 10.1007/s10955-010-9928-5

    DO - 10.1007/s10955-010-9928-5

    M3 - Article

    AN - SCOPUS:77949570160

    VL - 139

    SP - 62

    EP - 71

    JO - Journal of Statistical Physics

    JF - Journal of Statistical Physics

    SN - 0022-4715

    IS - 1

    ER -