This paper focuses on making up for the drawback of recent results about pinning controllability of Boolean control networks (BCNs). First of all, a sufficient criterion is derived for the controllability of BCNs. Based on this criterion, to make an arbitrary BCN be controllable, an efficient method is developed to design the feasible pinning strategy which involves identifying pinning nodes and determining control form. Comparing with the traditional pinning approach of which time complexity is $O(2^{2n})$, the time complexity of this pinning method is reduced to $O(n2^{3\kappa}+(n+m)^2)$ with the number of state variables $n$, that of input variables $m$ and the largest in-degree among all nodes $\kappa$. Since a practical genetic network is always sparsely connected, $\kappa$ is far less than $n$ despite its size being large-scale. Finally, a T-cell receptor kinetics model with $37$ state nodes and $3$ input nodes is considered to demonstrate the application of obtained theoretical results.

中文翻译：

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布尔网络的钉扎可控性：在大规模遗传网络中的应用

这篇论文的重点是弥补最近关于布尔控制网络（BCNs）的钉扎可控性的结果的缺陷。首先，推导出了 BCN 可控性的充分标准。基于该准则，为了使任意 BCN 可控，开发了一种有效的方法来设计可行的钉扎策略，包括识别钉扎节点和确定控制形式。与时间复杂度为$O(2^{2n})$的传统pinning方法相比，这种pinning方法的时间复杂度降低到$O(n2^{3\kappa}+(n+m)^2 )$ 与状态变量 $n$ 的数量，输入变量 $m$ 的数量以及所有节点中最大的入度 $\kappa$。由于实际的遗传网络总是稀疏连接的，尽管其规模很大，但 $\kappa$ 远小于 $n$。最后，