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
SN - 0022-4715
VL - 139
SP - 62
EP - 71
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 1
ER -