前馈网络的拓扑可逆性和因果性
Topological reversibility and causality in feed-forward networks
摘要：
从进化树到河流流域或交通网络，其组织显示因果不对称约束的系统通常可以用离散状态空间上的有向路径（因果流）来描述。这样的一组路径定义了前馈、非循环网络。与这些系统相关的一个关键问题涉及表征其内在的路径可逆性程度：给定图中的一个结束节点，向后恢复过程直到原点的不确定性是什么？在这里，我们提出了一个新的概念，\textit{topological reversibility}，它严格加权的路径依赖量化的最小信息量所需的成功恢复因果path.Within建议的框架，我们还分析了拓扑可逆和最大熵结构的极限情况下的不确定性。这些措施的背景下，进化动力学的相关性突出。
英文摘要：
Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths defines a feed-forward, acyclic network. A key problem associated with these systems involves characterizing their intrinsic degree of path reversibility: given an end node in the graph, what is the uncertainty of recovering the process backwards until the origin? Here we propose a novel concept, \textit{topological reversibility}, which rigorously weigths such uncertainty in path dependency quantified as the minimum amount of information required to successfully revert a causal path. Within the proposed framework we also analytically characterize limit cases for both topologically reversible and maximally entropic structures. The relevance of these measures within the context of evolutionary dynamics is highlighted.
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