随机布尔网络中吸引子的随机抽样与精确计数
Random sampling vs. exact enumeration of attractors in random Boolean networks
摘要：
我们澄清了不同的采样方法和加权方案的随机布尔网络（RBN）的合奏吸引子的统计效果。我们直接测量周期长度的吸引子和吸引盆地的大小在RBN使用精确枚举的状态空间。一般来说，吸引子长度的分布与随机选择初始状态并遵循动力学到达吸引子所获得的分布明显不同。我们的结果表明，前分布衰减的幂律指数为1的所有连接$K>1$在无限系统的大小限制。相反，后一种分布仅在K=2时按幂律衰减。这是因为平均盆地大小与$K>2$的吸引子周期长度呈线性增长，并且在K=2时与周期长度在统计上无关。我们还发现，盆地大小的直方图强烈的峰值为$K<3$的2的幂的整数倍。
英文摘要：
We clarify the effect different sampling methods and weighting schemes have on the statistics of attractors in ensembles of random Boolean networks (RBNs). We directly measure cycle lengths of attractors and sizes of basins of attraction in RBNs using exact enumeration of the state space. In general, the distribution of attractor lengths differs markedly from that obtained by randomly choosing an initial state and following the dynamics to reach an attractor. Our results indicate that the former distribution decays as a power-law with exponent 1 for all connectivities $K>1$ in the infinite system size limit. In contrast, the latter distribution decays as a power law only for K=2. This is because the mean basin size grows linearly with the attractor cycle length for $K>2$, and is statistically independent of the cycle length for K=2. We also find that the histograms of basin sizes are strongly peaked at integer multiples of powers of two for $K<3$.
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