标题： 临界Kauffman模型中的吸引子数量是指数级的 显示英文标题

标题： Number of attractors in the critical Kauffman model is exponential

摘要： Kauffman模型是遗传计算的典型模型。 它突出了临界性的重要性，许多生物系统似乎都处于这种状态。 在一系列进展中，研究人员专注于临界区域中吸引子数量如何随网络大小增长。 但一个明确的答案一直难以确定。 我们证明，在连接度为一的临界Kauffman模型中，吸引子的数量至少和最多都按照 $(2/\!\sqrt{e})^N$ 增长。 这是第一个证明临界Kauffman模型中的吸引子数量呈指数增长的结论。 显示英文摘要

摘要： The Kauffman model is the archetypal model of genetic computation. It highlights the importance of criticality, at which many biological systems seem poised. In a series of advances, researchers have honed in on how the number of attractors in the critical regime grows with network size. But a definitive answer has proved elusive. We prove that, for the critical Kauffman model with connectivity one, the number of attractors grows at least, and at most, as $(2/\!\sqrt{e})^N$. This is the first proof that the number of attractors in a critical Kauffman model grows exponentially.