Abstract The rate of successfully acquiring knowledge depends on whether the individual has previously held that knowledge. In an earlier work, we represented this phenomenon by dividing the dynamical process of knowledge transmission into initial and retransmission stages, and applied mean field theory to identify an approximate condition for knowledge survival on homogeneous networks. In this work we move beyond our earlier, approximate results for homogeneous networks to provide rigorous results applicable to complex networks of arbitrary topology - including heterogeneous real world social networks. Specifically, we extend the Intertwined Continuous Markov Chain (ICMC) and Probabilistic Discrete Markov Chain (PDMC) models to address the Naive-Evangelical-Agnostic-Evangelical (VEAE) knowledge transmission process in complex networks. We identify the corresponding basic reproduction number R0, the quantity which dictates whether or not knowledge survives, and deduce simple upper and lower bounds for this measure. Moreover, simulations are performed to verify both the theoretical results, and the mutual consistency of the ICMC, PDMC and Monte Carlo methods. The simulations demonstrate that the initial transmission process directly affects the initial rate of change of the number of evangelical individuals, but has no effect on evangelical density in the steady state. However, the retransmission process has a direct effect on the steady state density of evangelical individuals.

中文翻译：

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复杂网络中初始传输和重传在知识持久性中的不同作用

摘要 成功获取知识的速度取决于个人以前是否拥有该知识。在早期的工作中，我们通过将知识传输的动态过程分为初始和重新传输阶段来表示这种现象，并应用平均场理论来确定同构网络上知识生存的近似条件。在这项工作中，我们超越了我们早期的同类网络的近似结果，以提供适用于任意拓扑复杂网络的严格结果 - 包括异构现实世界社交网络。具体来说，我们扩展了交织连续马尔可夫链 (ICMC) 和概率离散马尔可夫链 (PDMC) 模型，以解决复杂网络中的天真-福音-不可知-福音 (VEAE) 知识传输过程。我们确定相应的基本再生数 R0，即决定知识是否存在的数量，并推导出该度量的简单上限和下限。此外，还进行了模拟以验证理论结果以及 ICMC、PDMC 和蒙特卡罗方法的相互一致性。模拟表明，初始传播过程直接影响福音派人数的初始变化率，但对稳定状态下的福音派密度没有影响。然而，重传过程对福音派个体的稳态密度有直接影响。进行模拟以验证理论结果以及 ICMC、PDMC 和蒙特卡罗方法的相互一致性。模拟表明，初始传播过程直接影响福音派人数的初始变化率，但对稳定状态下的福音派密度没有影响。然而，重传过程对福音派个体的稳态密度有直接影响。进行模拟以验证理论结果以及 ICMC、PDMC 和蒙特卡罗方法的相互一致性。模拟表明，初始传播过程直接影响福音派人数的初始变化率，但对稳定状态下的福音派密度没有影响。然而，重传过程对福音派个体的稳态密度有直接影响。