超图的可控性
Controllability of Hypergraphs
摘要：
本文利用张量代数和多项式控制理论给出了超图的可控性概念。受均匀超图的启发，提出了一种新的基于张量的多线性动力系统表示，并推导了一个类卡尔曼秩条件，用以确定均匀超图达到可控性所需的最小控制节点数.我们提出了一个有效的启发式获得MCN。MCN可以作为一个衡量的鲁棒性，我们表明，它是有关的超图度分布在模拟的例子。最后，我们使用MCN来检验真实生物网络的鲁棒性。
英文摘要：
In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a Kalman-rank-like condition to determine the minimum number of control nodes (MCN) needed to achieve controllability of even uniform hypergraphs. We present an efficient heuristic to obtain the MCN. MCN can be used as a measure of robustness, and we show that it is related to the hypergraph degree distribution in simulated examples. Finally, we use MCN to examine robustness in real biological networks.
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。
