论文标题
陷入困境：关于空间嵌入网络对的拓扑连接
Ensnarled: On the topological linkage of spatially embedded network pairs
论文作者
论文摘要
生物学，聚合物物理和生物系统中类似网状网络网络的观察，设计和分析提出了广泛的令人着迷的结构的目录，其中一个子组共享一个特定但非常严重的属性：被嵌入太空中的属性，使得它们无法将其拉开，而无需将其拆除，而没有Edges的先进来源，我们将在这里呼吁我们在这里呼吁，我们将在这里呼吁我们，我们在这里呼吁，我们可以将其置于一个我们的状态。在这项研究中，我们详细阐述了一种理论方法，以根据HOPF-LINK识别分析2组分网的滞留有限。这样做，我们能够构建一个边缘优先运算符，这些操作员从空间图的循环基础的链接数中得出，该循环基础突出显示了关键边缘。在它的基础上，我们开发了一种贪婪的算法，该算法确定了最佳的边缘去除以实现未链接，从而可以建立一个新的拓扑度量，该拓扑表征了陷入的网络对状态。
The observation, design and analysis of mesh-like networks in bionics, polymer physics and biological systems has brought forward an extensive catalog of fascinating structures of which a subgroup share a particular, yet critically under appreciated attribute: being embedded in space such that one wouldn't be able to pull them apart without prior removal of a subset of edges, a state which we here call ensnarled. In this study we elaborate on a graph theoretical method to analyze ensnarled finite, 2-component nets on the basis of Hopf-link identification. Doing so we are able to construct an edge priority operator, derived from the linking numbers of the spatial graphs' cycle bases, which highlights critical edges. On its basis we developed a greedy algorithm which identifies optimal edge removals to achieve unlinking, allowing for the establishment of a new topological metric characterizing the state of ensnarled network pairs.
