基于一致性动力学的有向网络重构
Reconstruction of Directed Networks from Consensus Dynamics
摘要：
本文讨论了一个未知的，加权的，有向网络运行的共识动力学的拓扑结构识别问题。我们提出了一种方法来重建网络拓扑结构的动态响应时，系统是由未知的功率谱密度的广义平稳噪声刺激。该方法基于节点淘汰或接地过程，其中接地节点广播零而不从网络中消除。在这个方向上，我们测量接地和未接地共识的每对节点之间的输出的经验交叉功率谱密度，以重建网络的未知拓扑结构。我们还建立，在无向或纯单向网络的特殊情况下，重建不需要接地。最后，我们扩展我们的结果的情况下，一个有向网络假设的一般动力学，并证明了所开发的方法可以检测边缘和它们的方向。
英文摘要：
This paper addresses the problem of identifying the topology of an unknown, weighted, directed network running a consensus dynamics. We propose a methodology to reconstruct the network topology from the dynamic response when the system is stimulated by a wide-sense stationary noise of unknown power spectral density. The method is based on a node-knockout, or grounding, procedure wherein the grounded node broadcasts zero without being eliminated from the network. In this direction, we measure the empirical cross-power spectral densities of the outputs between every pair of nodes for both grounded and ungrounded consensus to reconstruct the unknown topology of the network. We also establish that in the special cases of undirected or purely unidirectional networks, the reconstruction does not need grounding. Finally, we extend our results to the case of a directed network assuming a general dynamics, and prove that the developed method can detect edges and their direction.
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。
