Zipf's law from a communicative phase transition
Zipf's law from a communicative phase transition
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DOI：
10.1140/epjb/e2005-00340-y
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发表时间：
2005-10-01
影响因子：
1.6
通讯作者：
Cancho, RFI
中科院分区：
文献类型：
--
作者：
Cancho, RFI
本文提出了一个新的人类词频齐夫定律模型。该模型利用信息论定义了沟通的目标和成本。该模型显示了从无通信到完美通信的连续相变。在两相边界处发现了符合齐夫定律的标度。指数与最小化词的熵一致。该模型不同于以前的模型[Ferrer i Cancho， Sole, Proc. Natl]。学会科学。美国100,788-791(2003)]在两个方面。首先，它假设体验某种刺激的概率是由交流系统的内部结构控制的，而不是由在“外部”世界体验到这种刺激的概率控制的，这使得它特别适合精神分裂症患者的语言。其次，预测频率与等级分布的指数α在α > 1的范围内，这可以解释一些精神分裂症患者和一些儿童的α =1.5-1.6。在齐夫定律的众多模型中，没有一个能解释该特定指数范围的齐夫定律。特别是，两个过于简单的模型无法解释这一特定指数范围：间歇性沉默和西蒙的模型。我们支持Zipf定律在通信系统中可以在约束条件下实现信息传输的最大化。
Here we present a new model for Zipf's law in human word frequencies. The model defines the goal and the cost of communication using information theory. The model shows a continuous phase transition from a no communication to a perfect communication phase. Scaling consistent with Zipf's law is found in the boundary between phases. The exponents are consistent with minimizing the entropy of words. The model differs from a previous model [Ferrer i Cancho, Sole, Proc. Natl. Acad. Sci. USA 100, 788-791 (2003)] in two aspects. First, it assumes that the probability of experiencing a certain stimulus is controlled by the internal structure of the communication system rather than by the probability of experiencing it in the `outside' world, which makes it specially suitable for the speech of schizophrenics. Second, the exponent alpha predicted for the frequency versus rank distribution is in a range where alpha > 1, which may explain that of some schizophrenics and some children, with alpha=1.5-1.6. Among the many models for Zipf's law, none explains Zipf's law for that particular range of exponents. In particular, two simplistic models fail to explain that particular range of exponents: intermittent silence and Simon's model. We support that Zipf's law in a communication system may maximize the information transfer under constraints.