当相关性很重要时-动态网络对小扰动的响应
When correlations matter - response of dynamical networks to small perturbations
摘要：
我们系统地研究和比较小的外部扰动（损伤）下的随机布尔和阈值网络的损伤传播，这是一个问题，这是许多生物网络。我们确定了一个新的特征连通性$K_s$，在该连通性下，经过大量的动态更新后，受损节点的平均数量与节点总数$N$无关。我们估计的临界连接有限$N$，并表明它系统地偏离退火近似。扩展在以前的研究中遵循的方法，我们提出了新的结果表明，内部动态相关性往往不仅增加小的概率，而且对于非常大的损坏事件，导致广泛的，厚尾分布的损坏大小。这些发现表明，有限规模网络的平均序参量的描述和预测价值是有限的--即使对于生物高度相关的规模高达几千个节点--也是如此。
英文摘要：
We systematically study and compare damage spreading for random Boolean and threshold networks under small external perturbations (damage), a problem which is relevant to many biological networks. We identify a new characteristic connectivity $K_s$, at which the average number of damaged nodes after a large number of dynamical updates is independent of the total number of nodes $N$. We estimate the critical connectivity for finite $N$ and show that it systematically deviates from the annealed approximation. Extending the approach followed in a previous study, we present new results indicating that internal dynamical correlations tend to increase not only the probability for small, but also for very large damage events, leading to a broad, fat-tailed distribution of damage sizes. These findings indicate that the descriptive and predictive value of averaged order parameters for finite size networks - even for biologically highly relevant sizes up to several thousand nodes - is limited.
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