Inference of the gene regulation mechanism from gene expression patterns becomes increasingly popular, in recent years with the advent of microarray technology. Obtaining the states of genes and their regulatory relationships would greatly enable the scientists to investigate and understand the diseases mechanisms. However, it is still a big challenge to determine relationships from several thousands of genes still remains as a chanllege. Here, we simplify the above complex gene states determination problem as an inference of the distribution of the ensemble Boolean Networks (BNs). In order to investigate and calculate the distribution of the BNs’ states, we first compute the probabilities of the different BNs’ states and obtain the number of states Ω. Then, we find the maximum possible distribution of the number of the BNs’ staes and calculate the fluctuation of the distribution. Finally, two reprentative experiments are conducted and the efficiency of the obtained results are verified. The proposed algorithm is conceptually concise and easily applicable to many other realistic models; furthermore, it is highly extensible for various situations.

中文翻译：

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确定布尔网络集成分布的最大状态

近年来，随着微阵列技术的出现，从基因表达模式推断基因调控机制变得越来越流行。获得基因状态及其调控关系将极大地帮助科学家研究和理解疾病机制。然而，仍然要从数千个基因中确定关系仍然是一个巨大的挑战。在这里，我们将上述复杂的基因状态确定问题简化为对集成布尔网络 (BN) 分布的推断。为了研究和计算 BN 状态的分布，我们首先计算不同 BN 状态的概率并获得状态数Ω。然后，我们找到 BN 状态数的最大可能分布并计算分布的波动。最后，进行了两次具有代表性的实验，并验证了所得结果的有效性。所提出的算法在概念上简洁且易于适用于许多其他现实模型；此外，它对于各种情况都具有高度的可扩展性。