论文标题
超图的可控性
Controllability of Hypergraphs
论文作者
论文摘要
在本文中，我们通过张量代数和多项式控制理论开发了超图的可控性概念。受统一超图的启发，我们提出了一种新的基于张量的多线性动力学系统表示，并得出了类似卡尔曼级的状态，以确定达到均匀超图的可控性所需的最小控制节点（MCN）。我们提出了一种有效的启发式方法来获得MCN。 MCN可以用作衡量鲁棒性的量度，我们表明它与模拟示例中的超图学分布有关。最后，我们使用MCN检查实际生物网络中的鲁棒性。
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.
