论文标题
点构型，系统发育树和差异向量
Point configurations, phylogenetic trees, and dissimilarity vectors
论文作者
论文摘要
2004年，Pachter和Speyer引入了系统发育树的较高差异图，并询问了有关它们与热带草个植物关系的两个重要问题。使用独立方法的多个作者回答了这些问题中的第一个，表明差异向量位于热带格拉斯曼尼亚语上，但第二个问题是，差异矢量的集合是否形成了热带的亚变量，仍被打开。我们通过表明热带平衡状况失败来解决这个问题。但是，通过用加权变体代替差异图的定义，我们表明，加权差异矢量形成了热带grassmannian的热带亚种，正是帕克特（Pachter）所设想的方式。此外，我们根据有效的正常曲线的点配置提供了几何解释，并构建了有限的热带基础，该基础具有加权差异向量的明确表征。
In 2004 Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter--Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.
