论文标题
随机重置为多个节点的网络上随机步行
Random walks on networks with stochastic reset to multiple nodes
论文作者
论文摘要
在上一章中，我们探讨了重置对一个和两个节点的网络的影响。在本章中，我们将描述随机步行的概括，并重置为任意数量的节点$ \ MATHCAL {M} $。为了使方程式清晰易懂，有必要引入更紧凑的符号。一旦理论得到了充分的解释和实施，我们将将此概括应用于比简单环，尤其是对开莉树，连续空间中点的随机分布以及相互作用的周期的更复杂的结构。对于最后类型的网络，我们将动态重置为所有节点的Google搜索策略。 我们介绍了总重置概率$β$和全局平均第一通道时间$ \ mathcal {t} $，这是所有目标和源节点上MFPT的平均值，因此其值不取决于随机Walker的初始条件。主要目的是展示参数$β$如何影响$ \ Mathcal {t} $，并在某些情况下对其进行优化。
In the previous chapters, we explored the effects of resetting on networks considering one and two nodes. In this chapter, we will describe a generalization of random walks with resetting to an arbitrary number of nodes $\mathcal{M}$. In order to make the equations clear and understandable, it is necessary to introduce a more compact notation. Once the theory is fully explained and implemented, we will apply this generalization to more complex structures than the simple ring, particularly to Cayley trees, random distribution of points in a continuous space, and interacting cycles. For this last type of networks, we apply the Google search strategy where the dynamics resets to all nodes. We introduce the total resetting probability $β$ and the global mean first passage time $\mathcal{T}$, which is the average of the MFPT over all the target and source nodes, consequently its value does not depend on the initial condition of the random walker. The main objective is to show how the parameter $β$ affects $\mathcal{T}$ and in some cases optimizes it.
