标题： 竞争布尔节点高度连接网络临界状态中的渠道化 显示英文标题

标题： Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes

摘要： canalization 是发育生物学中的一个经典概念，被认为是有进化系统的重要的特征。 在布尔网络中，它是一种网络鲁棒性形式，其中输入信号的一个子集无论其余输入如何都控制节点的行为。 已经证明， 如果布尔网络通过节点之间的挫败竞争进行进化，它们可以变得具有 canalization。 这一点已经在每个节点有 K=3 个输入的大规模网络中得到证实。 这些网络进化到两种动态行为相位边界处的临界稳态。 此外，这些网络的进化已被证明与进化的动态对称性有关。 我们将这些结果扩展到连接度更高的 K>3 的情况，并表明类似的具有相同相关动态对称性的 canalized 临界稳态出现，但仅当进化动力学偏向于同质布尔函数时才如此。 显示英文摘要

摘要： Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior of a node regardless of the remaining input. It has been shown that Boolean networks can become canalized if they evolve through a frustrated competition between nodes. This was demonstrated for large networks in which each node had K=3 inputs. Those networks evolve to a critical steady-state at the boarder of two phases of dynamical behavior. Moreover, the evolution of these networks was shown to be associated with the symmetry of the evolutionary dynamics. We extend these results to the more highly connected K>3 cases and show that similar canalized critical steady states emerge with the same associated dynamical symmetry, but only if the evolutionary dynamics is biased toward homogeneous Boolean functions.