具有嵌套渠化函数的随机布尔网络的phase diagram
The phase diagram of random Boolean networks with nested canalizing functions
摘要：
我们得到了具有嵌套渠化函数的随机布尔网络的相图。使用退火近似，我们得到的演变的节点数$b_t$的值为1，和网络的灵敏度$λ$，我们比较淬火网络的数值模拟。我们发现，与Kauffman等人[Proc. Natl. Acad. Sci. 2004 101 49 17102-7]，这些网络具有丰富的相图，其中存在“混沌”和冻结相，以及$b_t$值的振荡状态。我们认为，在考夫曼等人的工作中，只有冻结相的存在仅仅是由于所使用的特定参数化，而不是这类函数的固有特征。然而，这些网络比允许所有可能的布尔函数的变体更稳定。
英文摘要：
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $λ$, and we compare with numerical simulations of quenched networks. We find that, contrary to what was reported by Kauffman et al. [Proc. Natl. Acad. Sci. 2004 101 49 17102-7], these networks have a rich phase diagram, were both the "chaotic" and frozen phases are present, as well as an oscillatory regime of the value of $b_t$. We argue that the presence of only the frozen phase in the work of Kauffman et al. was due simply to the specific parametrization used, and is not an inherent feature of this class of functions. However, these networks are significantly more stable than the variants where all possible Boolean functions are allowed.
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