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CONVERGENCE RATE AND GLOBAL MEAN WEIGHTED FIRST-PASSAGE TIME IN A 1D CHAIN NETWORK WITH A WEIGHTED ADDING REVERSE EDGE
Fractals ( IF 4.7 ) Pub Date : 2020-03-19 , DOI: 10.1142/s0218348x20500784
TINGTING CHEN 1, 2 , MEIFENG DAI 1 , FANG HUANG 1 , SHILIN FENG 3
Affiliation  

In this paper, a 1D chain network with a reverse weighted edge is introduced. We focus on studying the relationships including the convergence rate and the length, the convergence rate and weight of adding reverse edge relationships. Laplacian characteristic determinant is calculated and subsequently, the sum of the reciprocals of all nonzero Laplacian eigenvalues is obtained. Hence, the analytic expression of global mean weighted first-passage time (GMWFPT) can be deduced. The obtained results show that there exists a linearly positive relationship between GMWFPT and the weight [Formula: see text].

中文翻译:

具有加权加法反向边的一维链网络中的收敛速度和全局平均加权首过时间

在本文中,介绍了具有反向加权边缘的一维链式网络。我们重点研究了加入反向边缘关系的收敛速度和长度、收敛速度和权重的关系。计算拉普拉斯特征行列式,然后获得所有非零拉普拉斯特征值的倒数之和。因此,可以推导出全局平均加权首过时间(GMWFPT)的解析表达式。所得结果表明GMWFPT与权重之间存在线性正相关关系[公式:见正文]。
更新日期:2020-03-19
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