广义排斥过程的定态分布
Steady state distributions in generalized exclusion processes
摘要：
不对称简单排阻过程（ASEP）是一种用于研究生物过程（如mRNA翻译）的粒子转运模型。2014年，Zhao和Krishnan介绍了一种使用概率布尔网络（PBN）分析ASEP的新方法。在本文中，我们重新审视并进一步探讨PBN方法，重点是计算稳态分布。给出了几种常见跃迁的结构矩阵的显式表达式。此外，还导出了布尔函数结构矩阵的简化计算方法和布尔函数的一般写法。这些方法也被推广到多值逻辑网络的多物种排斥过程中的应用。
英文摘要：
The asymmetric simple exclusion process (ASEP) is a model of particle transport used in the study of biological processes such as mRNA translation. In 2014, Zhao and Krishnan introduced a new approach for analyzing the ASEP using probabilistic Boolean networks (PBN). In this paper, we revisit and further explore the PBN approach, with focus on computing steady state distributions. Explicit forms of the structure matrices of some common transitions are obtained. In addition, we derive a simplified method for computing the structure matrices of Boolean functions and a general method for writing the Boolean functions. These methods are also extended to multi-valued logic networks for application in multi-species exclusion processes.
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