A growth model that generates an n-tuple Zipf law

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• 作者：Xiaocong Gan^a ; ^{sliant@mail.bnu.edu.cn} ; Dahui Wang^a ; ^{wangdh@bnu.edu.cn} ; Zhangang Han ; ^a ; ^{zhan@bnu.edu.cn}
• 关键词：Zipf law ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVG-51JF84G-2&_mathId=mml65&_user=10&_cdi=5534&_pii=S0378437110009489&_rdoc=4&_issn=03784371&_acct=C000052141&_version=1&_userid=
• 刊名：Physica A
• 出版年：2011
• 出版时间：1 March 2011
• 年：2011
• 卷：390
• 期：5
• 页码：792-800
• 全文大小：525 K

文摘

The n-tuple Zipf law widely exists in real symbol sequences such as DNA and language. Based on the n-tuple Zipf analysis on a vast amount of empirical data, we propose a model that can generate sequences with n-tuple Zipf features. In simple words, it is an iterative copy and paste process: repeatedly select a random subsequence from the current sequence and attach it to the end. Numerical results of our model show that the n-tuple Zipf law exists in our model generated data. We give detailed analytical derivations of our model, and get two estimation equations: the Zipf exponent and the minimal length of n-tuple for Zipf law to appear. Our model can also reproduce the symmetry breaking process of ATGC number differences in DNA data.