Van Pelt J, Uylings H B, Verwer R W, Pentney R J, Woldenberg M J
Netherlands Institute for Brain Research, Amsterdam.
Bull Math Biol. 1992 Sep;54(5):759-84. doi: 10.1007/BF02459929.
The topological structure of a binary tree is characterized by a measure called tree asymmetry, defined as the mean value of the asymmetry of its partitions. The statistical properties of this tree-asymmetry measure have been studied using a growth model for binary trees. The tree-asymmetry measure appears to be sensitive for topological differences and the tree-asymmetry expectation for the growth model that we used appears to be almost independent of the size of the trees. These properties and the simple definition make the measure suitable for practical use, for instance for characterizing, comparing and interpreting sets of branching patterns. Examples are given of the analysis of three sets of neuronal branching patterns. It is shown that the variance in tree-asymmetry values for these observed branching patterns corresponds perfectly with the variance predicted by the used growth model.
二叉树的拓扑结构由一种称为树不对称性的度量来表征，该度量定义为其分区不对称性的平均值。已使用二叉树生长模型研究了这种树不对称性度量的统计特性。树不对称性度量似乎对拓扑差异敏感，并且我们使用的生长模型的树不对称性期望似乎几乎与树的大小无关。这些特性和简单的定义使得该度量适用于实际应用，例如用于表征、比较和解释分支模式集。给出了对三组神经元分支模式进行分析的示例。结果表明，这些观察到的分支模式的树不对称性值的方差与所用生长模型预测的方差完美对应。
