AI 中文总结
研究无根系统发育网络中根放置问题，建立鲁棒可定向网络结构条件，证明2级及以下或基于树的无根网络是鲁棒可定向的，还给出鲁棒类$\mathcal C$等相关结论，揭示网络与树在鲁棒性上的关系。
AI 中文摘要
标准的系统发育重建技术通常会产生无根系统发育网络，随后将其生根以推断进化历史。此过程中的一个常见问题是确定所得网络所属的结构类。本文研究了无根网络，其中任何根的选择都会产生有效的有根系统发育网络，我们将此属性定义为“鲁棒可定向”。然后我们为此类建立了严格的结构条件，即无根网络当且仅当它不包含汇组件时才是鲁棒可定向的。我们还表明，如果无根网络是2级或更低级别，或者它是基于树的，那么它就是鲁棒可定向的。此外，我们定义一个无根网络如果任何根的选择都会产生属于类$\mathcal C$的网络，则为“鲁棒类$\mathcal C$”。我们证明，无根网络当且仅当它是1级或更低级别时才是鲁棒树子或鲁棒无栈的。最后，我们表明系统发育网络当且仅当它是系统发育树时才是鲁棒正规的。
英文摘要
Standard phylogenetic reconstruction techniques often yield unrooted phylogenetic networks; these are subsequently rooted to infer evolutionary history. A common problem in this process is to determine the structural classes to which the resulting network will belong. In this paper, we investigate unrooted networks in which the choice of any root results in a valid rooted phylogenetic network, a property we define as {\em robustly orientable}. We then establish a strict structural condition for this class, specifically, that an unrooted network is robustly orientable if and only if it contains no sink components. We also show that if an unrooted network is level-$2$ or less, or if it is tree-based, then it is robustly orientable. Furthermore, we define an unrooted network to be {\em robustly class $\mathcal C$} if the choice of any root results in a network belonging to class $\mathcal C$. We demonstrate that an unrooted network is robustly tree-child or robustly stack-free if and only if it is level-$1$ or less. Finally, we show that a phylogenetic network is robustly normal if and only if it is a phylogenetic tree.
Comments16 pages, 4 figures
