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摘要翻译：
两个元素的时间序列中包含的相互信息量给出了它们的活动协调程度的度量。在一个由相互作用的元素组成的大型复杂网络中，如细胞内的遗传调节网络，所有对的互信息的平均值<I>是系统协调其内部动力学的全局度量。假设网络中的链路是随机放置的，我们研究了随机布尔网络中的平均成对互信息作为每个元素上实现的布尔规则分布的函数。计算<i>的有效数值方法表明，当网络节点数N接近无穷大时，网络节点数N<i>在与临界RBN相对应的参数值处表现出不连续性。对于有限系统，它在临界值附近达到峰值，但对于典型的参数变化，它在无序区域略有变化。N<i>高值的来源是来自不同长链的元素对之间具有共同起点的间接关联。对于临界网络，直接连接的对的贡献接近于零，在无序状态的深处达到峰值。
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英文标题：
《Mutual information in random Boolean models of regulatory networks》
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作者：
Andre S. Ribeiro, Stuart A. Kauffman, Jason Lloyd-Price, Bj\"orn
Samuelsson and Joshua E. S. Socolar
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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一级分类：Quantitative Biology 数量生物学
二级分类：Quantitative Methods 定量方法
分类描述：All experimental, numerical, statistical and mathematical contributions of value to biology
对生物学价值的所有实验、数值、统计和数学贡献
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英文摘要：
The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs <I> is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating <I> show that as the number of network nodes N approaches infinity, the quantity N<I> exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N<I> is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.
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PDF链接：
https://arxiv.org/pdf/0707.3642
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