系统发生网络之间的CSD同态
CSD Homomorphisms Between Phylogenetic Networks
摘要：
自达尔文以来，物种树一直被用来作为关系的简化描述，总结了现实的复杂网络$N$。然而，最近的杂交和横向基因转移的证据表明，有些情况下树木是不够的。因此，重要的是确定表征与$N$密切相关的网络的性质，并且可能比树更复杂，但缺乏$N$的全部复杂性。连通满射有向图映射（CSD）是从一个网络$N$到另一个网络$M$的映射$f$，使得每个弧或者折叠成单个顶点或者取为弧，使得$f$是满射的，并且使得顶点的逆像总是连通的。CSD地图表现良好的组合下。证明了如果存在从$N$到$M$的CSD映射，则存在将$M$的无向版本提升到$N$的方法，通常具有增加的分辨率。从$N$到$M$的CSD映射对$N$施加了强约束。一般来说，研究网络的类别可能是有用的，使得对于任何$N$，存在从$N$到该类别的某个标准成员的CSD映射。
英文摘要：
Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate. Consequently it is important to determine properties that characterize networks closely related to $N$ and possibly more complicated than trees but lacking the full complexity of $N$. A connected surjective digraph map (CSD) is a map $f$ from one network $N$ to another network $M$ such that every arc is either collapsed to a single vertex or is taken to an arc, such that $f$ is surjective, and such that the inverse image of a vertex is always connected. CSD maps are shown to behave well under composition. It is proved that if there is a CSD map from $N$ to $M$, then there is a way to lift an undirected version of $M$ into $N$, often with added resolution. A CSD map from $N$ to $M$ puts strong constraints on $N$. In general, it may be useful to study classes of networks such that, for any $N$, there exists a CSD map from $N$ to some standard member of that class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
