两社区网络中基于Agent的中立竞争
Agent-based neutral competition in two-community networks
摘要：
替代状态之间的竞争是社会和生物网络中的一个重要过程。中性竞争可以由无偏随机漂移过程表示，其中顶点的状态（例如，观点、基因型或物种）通过重复选择两个连接的顶点来更新。其中一个顶点复制选定邻居的状态。重复这样的更新，直到所有顶点都处于相同的“一致”状态。选择要更新的顶点对没有唯一的规则。现实世界的过程包括三个限制因素，可以影响所选的边和传播方向：（1）顶点向其邻居发送状态的速率，（2）邻居接收状态的速率，以及（3）状态可以通过连接边交换的速率。我们研究了这三个限制如何影响网络中的中性竞争与两个社区产生的随机块模型。通过蒙特卡罗模拟，我们展示了社区结构和更新规则如何决定状态的成功概率和达成共识的时间。我们提出了一个与蒙特卡罗模拟相一致的非均匀平均场论.非均匀平均场论的有效性意味着即使经验数据（例如，从生态实地考察或社会互动的观察）不允许网络中所有边的完全重建。
英文摘要：
Competition between alternative states is an essential process in social and biological networks. Neutral competition can be represented by an unbiased random drift process in which the states of vertices (e.g., opinions, genotypes, or species) in a network are updated by repeatedly selecting two connected vertices. One of these vertices copies the state of the selected neighbor. Such updates are repeated until all vertices are in the same "consensus" state. There is no unique rule for selecting the vertex pair to be updated. Real-world processes comprise three limiting factors that can influence the selected edge and the direction of spread: (1) the rate at which a vertex sends a state to its neighbors, (2) the rate at which a state is received by a neighbor, and (3) the rate at which a state can be exchanged through a connecting edge. We investigate how these three limitations influence neutral competition in networks with two communities generated by a stochastic block model. By using Monte Carlo simulations, we show how the community structure and update rule determine the states' success probabilities and the time until a consensus is reached. We present a heterogeneous mean-field theory that agrees well with the Monte Carlo simulations. The effectiveness of the heterogeneous mean-field theory implies that quantitative predictions about the consensus are possible even if empirical data (e.g., from ecological fieldwork or observations of social interactions) do not allow a complete reconstruction of all edges in the network.
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