热带线段上的树拓扑
Tree Topologies along a Tropical Line Segment
摘要：
具有极大代数的热带几何已被应用于树空间上的统计学习模型，因为具有树空间上的热带度量的几何具有一些很好的性质，例如热带度量的凸性。热带几何在树空间中的应用面临的挑战之一是难以用热带度量解释统计模型的结果。本文研究了树空间上两棵系统树之间沿一条具有热带度量的内禀测地线--热带线段的树拓扑的组合学，并给出了两棵树之间热带线段的一些性质.具体来说，我们表明，概率热带线段的两个随机选择的树木通过原点如果叶数大于4，则（星型树）为零，并且我们还表明，如果两棵给定的树仅相差一个最近邻交换（NNI）移动，则它们之间的热带线段中的树的树拓扑是具有可能的零分支长度的这两个给定树之一的相同树拓扑。
英文摘要：
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical metric over tree spaces has some nice properties such as convexity in terms of the tropical metric. One of the challenges in applications of tropical geometry to tree spaces is the difficulty interpreting outcomes of statistical models with the tropical metric. This paper focuses on combinatorics of tree topologies along a tropical line segment, an intrinsic geodesic with the tropical metric, between two phylogenetic trees over the tree space and we show some properties of a tropical line segment between two trees. Specifically we show that a probability of a tropical line segment of two randomly chosen trees going through the origin (the star tree) is zero if the number of leave is greater than four, and we also show that if two given trees differ only one nearest neighbor interchange (NNI) move, then the tree topology of a tree in the tropical line segment between them is the same tree topology of one of these given two trees with possible zero branch lengths.
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