加权耦合细胞网络的交换幺半群形式和不变同步模式
Commutative Monoid Formalism for Weighted Coupled Cell Networks and Invariant Synchrony Patterns
摘要：
本文提出了一种基于幺半群矩阵的耦合细胞网络的研究框架。我们正式证明在所提出的框架内，一套结果不变的同步模式的加权网络也持有。此外，所描述的方法允许我们对任何多边和多边型网络进行推理，就好像它是单边和单边型网络一样。几个例子说明了所述的概念。此外，提出了一种改进的粗不变细化算法，以找到平衡的分区，表现出$ \mathbf{O}(\vert\mathcal{C}\vert^3) $的最坏情况下的复杂度，其中$\mathcal{C}$表示的细胞的集合。
英文摘要：
This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also holds for the weighted case. Moreover, the approach described allows us to reason about any multiedge and multiedge-type network as if it was single edge and single-edge-type. Several examples illustrate the concepts described. Additionally, an improvement of the coarsest invariant refinement algorithm to find balanced partitions is presented that exhibits a worst-case complexity of $ \mathbf{O}(\vert\mathcal{C}\vert^3) $, where $\mathcal{C}$ denotes the set of cells.
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。
