竞争性加权演化单纯复形
Competitive and Weighted Evolving Simplicial Complexes
AI总结：
本文提出高阶网络竞争性演化模型与加权演化模型，采用差分方程和泊松过程理论推导高阶度分布等解析结果，揭示竞争因子对无标度行为的调控作用，仿真与理论一致。
摘要：
基于单纯形的网络被称为高阶网络，这类网络中的相互作用可包含两个以上的节点。许多多组分相互作用可通过单纯复形来刻画，这类结构近期已在社会、技术和生物领域得到应用。本文首先提出了一种高阶网络的竞争性演化模型。我们在高阶网络中引入差分方程分析方法，使网络分析更为严谨，避免了传统网络分析中节点度为连续变量的假设。通过运用泊松过程理论，我们得到了高阶度分布的解析表达式。研究结果表明，在d阶网络中，(d-1)维单纯形关于d阶度的无标度行为由竞争因子调控；随着竞争性增强，(d-1)维单纯形的d阶度在对数坐标下发生弯曲，而维数e<d-1的单纯形关于d阶度仍呈现无标度行为。其次，通过考虑被选中的单纯形触发的相邻单纯形权重变化，本文提出了一种新的高阶网络加权演化模型。我们利用高阶网络竞争性演化模型的结果对加权演化模型进行分析，得到了加权高阶网络的高阶度分布和高阶强度密度函数的解析表达式。仿真实验结果与理论分析一致。
英文摘要：
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently found applications in social, technological, and biological contexts. The paper first proposes a competitive evolving model of higher-order networks. We introduce the difference equation analysis approach in the high-order network to make the analysis network more rigorous. It avoids the assumption that the degrees of nodes are continuous in the traditional analysis network. We obtain an analytical expression for the distribution of higher-order degrees by employing the theory of Poisson processes. The established results indicate that in a d-order network the scale-free behavior for the (d-1)-dim simplex with respect to the d-order degree is controlled by the competitiveness factor. As the competitiveness increases, the d-order degree of the (d-1)-dim simplex is bent under the logarithmic coordinates. While the e(<d-1)-dim simplex with respect to the d-order degree exhibits scale-free behavior. Second, by considering the weight changes of the neighboring simplices, as triggered by the selected simplex, a new weighted evolving model in higher-order networks is proposed. The results of the competitive evolving model of higher-order networks are used to analyze the weighted evolving model so that obtained are the analytical expressions of the higher-order degree distribution and higher-order strength density function of weighted higher-order networks. The outcomes of the simulation experiments are consistent with the theoretical analysis.
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