论文标题
网络结构化的社交互动模型
Network structured kinetic models of social interactions
论文作者
论文摘要
本文的目的是研究在社会过程中出现的相互作用的适当中间和宏观模型的推导。模型有两个主要特征，即相互作用的网络结构，我们通过适当的介绍描述来对待，以及相互作用剂的不同作用。后者与在经典统计力学中处理的相互作用不同，因为代理没有对称角色，但有一个相当活跃的被动剂。我们将展示如何获得某种形式的动力学方程，以描述介观级别的这种相互作用，此外，还从这些方程式中获取了这些相互作用的宏观模型。 该派生自然会导致非局部反应扩散方程（或在其适当的极限局部版本中）的系统，这可以解释从微观相互作用中发现的空间相分离现象。我们将在三个例子中强调这种方法，即人类语言中方言的演变，社会规范的构建以及流行病的传播。
The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of interactions, which we treat by an appropriate mesoscopic description, and a different role of interacting agents. The latter differs from interactions treated in classical statistical mechanics in the sense that the agents do not have symmetric roles, but there is rather an active and a passive agent. We will demonstrate how a certain form of kinetic equations can be obtained to describe such interactions at a mesoscopic level and moreover obtain macroscopic models from monokinetics solutions of those. The derivation naturally leads to systems of nonlocal reaction-diffusion equations (or in a suitable limit local versions thereof), which can explain spatial phase separation phenomena found to emerge from the microscopic interactions. We will highlight the approach in three examples, namely the evolution and coarsening of dialects in human language, the construction of social norms, and the spread of an epidemic.
