超图的可观测性
Observability of Hypergraphs
AI总结：
本文针对均匀超图提出可观测性研究框架，通过扩展动力系统引入线性输出并推导类Kalman秩条件，结合精确技术与贪心启发式方法确定局部弱可观测性及最小可观测节点集，并在多种超图拓扑和神经网络表示上验证有效性。
摘要：
本文开发了一个研究均匀超图可观测性的框架。超图作为图的扩展，允许边连接多个节点，能明确表示许多现实世界网络中普遍存在的多向关系。我们将均匀超图上的规范齐次多项式或多线性动力系统扩展以包含线性输出，并推导出一个类 Kalman 秩条件来评估局部弱可观测性。我们提出了确定局部可观测性判据的精确技术，并提出一种贪心启发式方法来确定可观测节点的最小集合。数值实验在多种超图拓扑及小鼠下丘脑内神经网络的超图表示上演示了该方法。
英文摘要：
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in many real-world networks. We extend the canonical homogeneous polynomial or multilinear dynamical system on uniform hypergraphs to include linear outputs, and we derive a Kalman-rank-like condition for assessing the local weak observability. We propose an exact techniques for determining the local observability criterion, and we propose a greedy heuristic to determine the minimum set of observable nodes. Numerical experiments demonstrate our approach on several hypergraph topologies and a hypergraph representations of neural networks within the mouse hypothalamus.
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。
