标题： 活动传播与赫布学习 显示英文标题

标题： Activity propagation with Hebbian learning

摘要： 我们研究赫布学习对接触过程的影响，这是一个典型的感染传播模型，也被提出作为捕捉区域间脑活动传播以及种群扩散动态的简单模型。 每个这些情境都需要对接触过程进行局部学习的扩展。 我们引入赫布学习作为在每次成功激活事件后对一对站点之间的激活率的正向或负向强化。 学习可以在两个方向发生，这是由社交距离驱动的（互惠学习模型），或者只在一个方向发生，这是由大脑和种群动力学驱动的（源学习或目标学习模型）。 赫布学习导致了一类丰富的涌现行为，其中局部激励可能导致相反的全局效应。 一般来说，正向强化（增加激活率）会导致活跃相的丧失，而负向强化（降低激活率）可以将不活跃相转变为全局活跃相。 在二维及以上维度，负向强化的效果是双重的：它促进活动的传播，但同时也会产生有效免疫区域，导致出现两个不同的临界点。 正向强化可以通过活动环的形成导致格里菲斯效应，这是一种“蚂蚁迷宫”现象的表现，具有非普遍的幂律标度。 显示英文摘要

摘要： We investigate the impact of Hebbian learning on the contact process, a paradigmatic model for infection spreading, which has been also proposed as a simple model to capture the dynamics of inter-regional brain activity propagation as well as population spreading. Each of these contexts calls for an extension of the contact process with local learning. We introduce Hebbian learning as a positive or negative reinforcement of the activation rate between a pair of sites after each successful activation event. Learning can happen either in both directions motivated by social distancing (mutual learning model), or in only one of the directions motivated by brain and population dynamics (source or target learning models). Hebbian learning leads to a rich class of emergent behavior, where local incentives can lead to the opposite global effects. In general, positive reinforcement (increasing activation rates) leads to a loss of the active phase, while negative reinforcement (reducing activation rates) can turn the inactive phase into a globally active phase. In two dimensions and above, the effect of negative reinforcement is twofold: it promotes the spreading of activity, but at the same time gives rise to the appearance of effectively immune regions, entailing the emergence of two distinct critical points. Positive reinforcement can lead to Griffiths effects with non-universal power-law scaling, through the formation of random loops of activity, a manifestation of the ``ant mill" phenomenon.