堆定律、共享分量统计和样本空间缩减过程的时间模式
Heaps' law, statistics of shared components and temporal patterns from a sample-space-reducing process
摘要：
齐普夫定律是几个具有模块结构的复杂系统的标志，例如由单词组成的书籍或由基因组成的基因组。在这些组成系统中，齐普夫定律描述了组成频率的经验幂律分布。随机过程的基础上的样本空间减少（SSR）的机制，其中可访问的状态的数量随着系统的发展而减少，最近已被提出作为一个简单的解释无处不在的出现这一法律。然而，许多复杂的组件系统的特点是其他统计模式以外的齐普夫定律，如一个次线性增长的组件词汇与系统的大小，称为堆的法律，和一个特定的统计共享组件。这项工作表明，与分析计算和模拟，这些统计特性可以共同出现从SSR机制，从而使其成为一个适当的参数表示组件系统的穷人。几个替代的（同样简单的）模型，例如基于优先连接机制的模型，也可以重现希普斯和齐普夫定律，这表明应该考虑额外的统计特性来为特定系统选择最可能的生成过程。沿着这条线，我们将表明，由SSR模型预测的时间分量分布是显着不同的流行的富人越来越富的机制。与自然语言的经验数据的比较表明，SSR过程可以选择作为一个更好的候选模型的文本生成的基础上，这一统计属性。最后，SSR模型在再现文本中单词出现的经验“突发性”的局限性将被指出，从而指示了基本SSR过程的扩展的可能方向。
英文摘要：
Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component frequencies. Stochastic processes based on a sample-space-reducing (SSR) mechanism, in which the number of accessible states reduces as the system evolves, have been recently proposed as a simple explanation for the ubiquitous emergence of this law. However, many complex component systems are characterized by other statistical patterns beyond Zipf's law, such as a sublinear growth of the component vocabulary with the system size, known as Heap's law, and a specific statistics of shared components. This work shows, with analytical calculations and simulations, that these statistical properties can emerge jointly from a SSR mechanism, thus making it an appropriate parameter-poor representation for component systems. Several alternative (and equally simple) models, for example based on the preferential attachment mechanism, can also reproduce Heaps' and Zipf's laws, suggesting that additional statistical properties should be taken into account to select the most-likely generative process for a specific system. Along this line, we will show that the temporal component distribution predicted by the SSR model is markedly different from the one emerging from the popular rich-gets-richer mechanism. A comparison with empirical data from natural language indicates that the SSR process can be chosen as a better candidate model for text generation based on this statistical property. Finally, a limitation of the SSR model in reproducing the empirical "burstiness" of word appearances in texts will be pointed out, thus indicating a possible direction for extensions of the basic SSR process.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
