AI 中文总结
本文通过mu向量刻画树-子系统发育网络，提出有序树路径分解及纯向量条件，给出可行性判据，为重建和算法应用提供基础。
AI 中文摘要
我们根据mu表示来刻画树-子系统发育网络。首先，我们通过有序树路径分解给出了树-子网络的结构刻画。然后，我们将这种分解转化为对N^n中有限子集M的一组纯向量条件。我们证明，这样的集合M是树-子系统发育网络的mu表示，当且仅当它是树-子mu兼容的。这为树-子mu表示提供了一个可行性判据，可作为重建和进一步算法应用的基础。注意，本文呈现了正在进行中的树-子网络研究的结果，这些结果将在后续版本中进一步发展和置于适当背景中。
英文摘要
We characterize tree-child phylogenetic networks in terms of their mu-representations. First, we give a structural characterization of tree-child networks by means of ordered tree-path decompositions. We then translate this decomposition into a set of purely vectorial conditions on finite subsets M in N^n. We prove that such a set M is the mu-representation of a tree-child phylogenetic network if and only if it is tree-child mu-compatible. This provides a feasibility criterion for tree-child mu-representations which can be used as a basis for reconstruction and further algorithmic applications. Note that this paper presents results arising from ongoing research on tree-child networks and that the results will be further developed and placed into proper context in subsequent versions.
Comments12 pages, 2 figures
