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首页> 外文期刊>Automatic Control, IEEE Transactions on >Towards A Theoretical Framework for Analysis and Intervention of Random Drift on General Networks
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Towards A Theoretical Framework for Analysis and Intervention of Random Drift on General Networks

机译：寻求一种分析和干预通用网络的理论框架

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摘要

It is well known that evolution is a fundamental phenomenon driving nature. And random drift is a basic force for population evolution. This technical note aims at constructing a unified theoretical framework for analyzing and intervening in random drift of binary states on general networks. In detail, a general methodology is developed for calculating the fixation probability with different dynamics, including the Wright-Fisher (WF), birth-death (BD), and death-birth (DB) processes. In particular, we prove that the fixation probability of a mutant at node corresponds to the -th element of stationary distribution of a stochastic matrix deduced from the weight matrix of the networks. Intuitively, it provides an effective way to discover the invasion hubs of structured population and further to intervene in random drift on networks. Finally, a typical example is then given to validate the above theoretical results.
机译：众所周知，进化是驱动自然的基本现象。随机漂移是人口进化的基本动力。本技术说明旨在构建一个统一的理论框架，用于分析和干预通用网络上二进制状态的随机漂移。详细地，开发了用于计算具有不同动态的注视概率的通用方法，包括赖特-费舍（WF），出生-死亡（BD）和死亡-出生（DB）过程。特别地，我们证明了突变体在节点处的固定概率对应于从网络的权重矩阵推导的随机矩阵的平稳分布的第-个元素。直观地讲，它提供了一种有效的方法来发现结构化人口的入侵中心，并进一步干预网络上的随机漂移。最后，给出一个典型的例子来验证上述理论结果。

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