随机布尔网络中外部调节和异步动力学的传播
Propagation of external regulation and asynchronous dynamics in random Boolean networks
摘要：
布尔网络及其动力学在从生物学到计算机科学的各个学科中作为抽象建模方案引起了极大的兴趣。虽然并行更新方案已被广泛研究，在过去的几年中，异步更新方案的理解水平仍然很差。本文研究了由调节输入变量给出的外部信息在随机布尔网络中的传播。我们计算分析和数值的时间演化和渐近行为的传播外部监管（PER）。特别是，这使我们能够识别完全由外部信息决定的变量。网络中所有不直接由PER固定的变量形成一个核心，其中特别包含所有非平凡的反馈回路。我们设计了一个消息传递的方法，允许这些核心的统计特性的布尔网络和外部条件的依赖。最后，我们建立了PER动态和布尔网络的完全随机异步动态之间的联系。
英文摘要：
Boolean Networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level of understanding of asynchronous updates schemes is still very poor. In this paper we study the propagation of external information given by regulatory input variables into a random Boolean network. We compute both analytically and numerically the time evolution and the asymptotic behavior of this propagation of external regulation (PER). In particular, this allows us to identify variables which are completely determined by this external information. All those variables in the network which are not directly fixed by PER form a core which contains in particular all non-trivial feedback loops. We design a message-passing approach allowing to characterize the statistical properties of these cores in dependence of the Boolean network and the external condition. At the end we establish a link between PER dynamics and the full random asynchronous dynamics of a Boolean network.
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