布尔网络中的局部负回路与不动点
Local negative circuits and fixed points in Boolean networks
摘要：
对于从{0，1}^n到自身的每个布尔函数F和{0，1}^n中的每个点x，我们将包含正（或正）的n阶有符号有向图G_F（x）关联起来。负的）弧从j到i，如果f_i关于x_j的偏导数是正的（相应地，负的）在点X处。然后我们集中讨论了下面的公开问题：G_F（x）中对{0，1}^n中的所有x不存在负回路是否是F至少有一个不动点的充分条件？作为主要结果，我们在对{0，1}^n中的所有x，G_F（x）的每个顶点的出度至多为1的附加条件下解决了这个问题。
英文摘要：
To each Boolean function F from {0,1}^n to itself and each point x in {0,1}^n, we associate the signed directed graph G_F(x) of order n that contains a positive (resp. negative) arc from j to i if the partial derivative of f_i with respect of x_j is positive (resp. negative) at point x. We then focus on the following open problem: Is the absence of a negative circuit in G_F(x) for all x in {0,1}^n a sufficient condition for F to have at least one fixed point? As main result, we settle this problem under the additional condition that, for all x in {0,1}^n, the out-degree of each vertex of G_F(x) is at most one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
