网络上的Logistic增长：SI模型的精确解
Logistic growth on networks: exact solutions for the SI model
摘要：
SI模型是所有用于描述信息在总体中传播的房室模型中最基本的。尽管它表面上很简单，但这个模型在网络上的解析解仍然缺乏。我们在这里解决这个问题，使用一个新的配方的灵感来自多体量子系统的数学处理。这使我们能够根据网络子图的贡献来组织单个节点状态的时间依赖期望值。我们系统地计算这些贡献，并找到一组不同拓扑的子图之间的对称关系。我们使用我们的新方法来计算三个不同样本网络上的信息传播。精确解与蒙特卡罗模拟相匹配，明显偏离平均场结果。
英文摘要：
The SI model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here, using a novel formulation inspired by the mathematical treatment of many-body quantum systems. This allows us to organize the time-dependent expectation values for the state of individual nodes in terms of contributions from subgraphs of the network. We compute these contributions systematically and find a set of symmetry relations among subgraphs of differing topologies. We use our novel approach to compute the spreading of information on three different sample networks. The exact solution, which matches with Monte-Carlo simulations, visibly departs from the mean-field results.
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。
