DNA序列的Poincaré递归
Poincaré recurrences of DNA sequence
摘要：
我们分析了从Ensembl基因组数据库中获取的人类、哺乳动物和其他DNA序列的庞加莱递归的统计特性，这些序列具有高达150亿个碱基对。我们表明，庞加莱递归的概率以代数的方式与庞加莱指数$β\approx 4$衰减，即使振荡的依赖性很明显。递归衰减与一个指数$ν\approx 0.6$，导致一个异常的超扩散行走。然而，对于智人序列，具有最大的可用统计量，扩散系数在大于百万个碱基对的距离上收敛到有限值。我们认为，基于Poncaré递归的方法确定了不同物种之间的新的邻近特征，并揭示了它们的进化历史。
英文摘要：
We analyze the statistical properties of Poincaré recurrences of Homo sapiens, mammalian and other DNA sequences taken from Ensembl Genome data base with up to fifteen billions base pairs. We show that the probability of Poincaré recurrences decays in an algebraic way with the Poincaré exponent $β\approx 4$ even if oscillatory dependence is well pronounced. The correlations between recurrences decay with an exponent $ν\approx 0.6$ that leads to an anomalous super-diffusive walk. However, for Homo sapiens sequences, with the largest available statistics, the diffusion coefficient converges to a finite value on distances larger than million base pairs. We argue that the approach based on Poncaré recurrences determines new proximity features between different species and shed a new light on their evolution history.
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