N-tuple Zipf Analysis and Modeling for Language, Computer Program and DNA

Details N-tuple Zipf Analysis and Modeling for Language, Computer Program and DNA N-tuple Zipf Analysis and Modeling for Language, Computer Program and DNA

2009-08-04

arxiv.org/abs/0908.0500v1

Physics

Data Analysis, Statistics and Probability

using RevTex4, 7 pages, 6figures, 1 supplement material

Scientific paper

n-tuple power law widely exists in language, computer program code, DNA and music. After a vast amount of Zipf analyses of n-tuple power law from empirical data, we propose a model to explain the n-tuple power law feature existed in these information translational carriers. Our model is a preferential selection approach inspired by Simon's model which explained scaling law of single symbol in a sequence Zipf analysis. The kernel mechanism is neat and simple in our model. It can be simply described as a randomly copy and paste process, that is, randomly select a random segment from current sequence and attach it to the end repeatedly. The simulation of our model shows that n-tuple power law exists in model generated data. Furthermore, two estimation equations: the Zipf exponent and the minimal length of n-tuple for power law appears all correspond to empirical data well. Our model can also reproduce the symmetry breaking process of ATGC number differences in DNA data.

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