标题： 在线参与对线下抗议的溢出效应建模：网络上的随机动力学和平均场近似 显示英文标题

标题： Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks

摘要： 社交媒体正在改变线下生活的各个方面，从日常决策如用餐选择到冲突的发展进程。 在本研究中，我们提出了一种耦合建模框架，包含一个在线社交网络层，以分析特定主题上的参与如何溢出到线下抗议活动。 我们开发了一个随机模型，并推导了几种不同复杂度的平均场模型。 这些模型使我们能够估计繁殖数并预测活动激增可能发生的时间。 一个关键因素是在线和线下领域之间的传播率；为了出现线下爆发，这一比率必须处于一个临界范围内，既不太低也不太高。 此外，利用合成网络，我们研究了网络结构如何影响这些近似值的准确性。 我们的研究结果表明，低密度网络需要更复杂的近似，而简单的模型可以有效地表示高密度网络。 然而，在两个现实世界的网络上进行测试时，增加复杂度并未提高准确性。 显示英文摘要

摘要： Social media is transforming various aspects of offline life, from everyday decisions such as dining choices to the progression of conflicts. In this study, we propose a coupled modelling framework with an online social network layer to analyse how engagement on a specific topic spills over into offline protest activities. We develop a stochastic model and derive several mean-field models of varying complexity. These models allow us to estimate the reproductive number and anticipate when surges in activity are likely to occur. A key factor is the transmission rate between the online and offline domains; for offline outbursts to emerge, this rate must fall within a critical range, neither too low nor too high. Additionally, using synthetic networks, we examine how network structure influences the accuracy of these approximations. Our findings indicate that low-density networks need more complex approximations, whereas simpler models can effectively represent higher-density networks. When tested on two real-world networks, however, increased complexity did not enhance accuracy.