论文标题
系统发育网络及其多型的GALOIS连接
Galois connections for phylogenetic networks and their polytopes
论文作者
论文摘要
我们描述了两种组合结构之间出现的galois连接，这两种结构都以标记的叶子概括了树，然后将这些连接应用于多面体家族。 我们研究的图可以充满度量特性或与向量相关联。著名的例子是系统发育树的Billera-Holmes-Vogtmann公制空间，以及Eickmeyer，Huggins，Pachter和Yoshida所描述的系统发育树的平衡最小进化多型。最近，Devadoss和Petti已将树木的空间扩展到分裂网络，而系统发育多型的定义已被杜雷尔（Durell and Force）概括为包含1个纽约系统发育网络。我们描述的第一个Galois连接是（未加权）圆形拆分网络和1个循环系统发育网络之间的反映。这些结构的某些度量版本之间存在另一个Galois连接。在几何情况下，纯粹的组合poset之间的反射变成了核心荧光。 除了发现Galois连接之外，我们的主要贡献是：使用PC-Trees和网络之间的方法翻译，一种查看网络上的权重的新方法，以及对系统发育多层的面孔的更全面表征。
We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labelled leaves, and then apply those connections to a family of polytopes. The graphs we study can be imbued with metric properties or associated to vectors. Famous examples are the Billera-Holmes-Vogtmann metric space of phylogenetic trees, and the Balanced Minimal Evolution polytopes of phylogenetic trees described by Eickmeyer, Huggins, Pachter and Yoshida. Recently the space of trees has been expanded to split networks by Devadoss and Petti, while the definition of phylogenetic polytopes has been generalized to encompass 1-nested phylogenetic networks, by Durell and Forcey. The first Galois connection we describe is a reflection between the (unweighted) circular split networks and the 1-nested phylogenetic networks. Another Galois connection exists between certain metric versions of these structures. Reflection between the purely combinatorial posets becomes a coreflection in the geometric case. Our chief contributions here, beyond the discovery of the Galois connections, are: a translation between approaches using PC-trees and networks, a new way to look at weightings on networks, and a fuller characterization of faces of the phylogenetic polytopes.
