DNA编码与G“odel编号

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摘要翻译：
进化由不同的阶段组成：宇宙学阶段、生物阶段、语言阶段。由于生物学是自然科学和语言学的边缘，我们期望它从这两种知识形式中共享结构和特征。事实上，在DNA中我们遇到了生物“原子”，即四个核苷酸分子。同时，这四个核苷酸可以被认为是字母表中的“字母”。这四个“字母”，通过一个遗传密码，生成生物“词”、“短语”、“句子”（氨基酸、蛋白质、细胞、生命体）。本着这种精神，我们可以同样地把DNA链看作是一种数学陈述。受Kurt G\“Odel工作的启发，我们在每条DNA链上附加一个G\”Odel数，一个质数的乘积，提高到适当的幂。每个DNA链对应一个G\“Odel的数字$G$，相反地，给定一个G\”Odel的数字$G$，我们可以指定它所代表的DNA链。接下来，考虑由$N$碱基组成的单链，我们研究了$G$的统计分布，即$G$的对数。我们的假设是，第m个项的选择是随机的，对于四种可能的结果具有相等的概率。“实验”，在某种程度上，似乎是扔$N乘以一个四面模具。通过矩母函数，我们得到了$G$的离散分布和连续分布。在我们的形式主义和模拟数据之间有一个极好的一致性。最后，我们将我们的形式与实际数据进行比较，以说明非随机动力学痕迹的存在。
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英文标题：
《DNA coding and G\"odel numbering》
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作者：
Argyris Nicolaidis, Fotis Psomopoulos
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最新提交年份：
2019
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  Evolution consists of distinct stages: cosmological, biological, linguistic. Since biology verges on natural sciences and linguistics, we expect that it shares structures and features from both forms of knowledge. Indeed, in DNA we encounter the biological "atoms", the four nucleotide molecules. At the same time these four nucleotides may be considered as the "letters" of an alphabet. These four "letters", through a genetic code, generate biological "words", "phrases", "sentences" (aminoacids, proteins, cells, living organisms). In this spirit we may consider equally well a DNA strand as a mathematical statement. Inspired by the work of Kurt G\"odel, we attach to each DNA strand a G\"odel's number, a product of prime numbers raised to appropriate powers. To each DNA chain corresponds a single G\"odel's number $G$, and inversely given a G\"odel's number $G$, we can specify the DNA chain it stands for. Next, considering a single DNA strand composed of $N$ bases, we study the statistical distribution of $g$, the logarithm of $G$. Our assumption is that the choice of the $m$-th term is random and with equal probability for the four possible outcomes. The "experiment", to some extent, appears as throwing $N$ times a four-faces die. Through the moment generating function we obtain the discrete and then the continuum distribution of $g$. There is an excellent agreement between our formalism and simulated data. At the end we compare our formalism to actual data, to specify the presence of traces of non-random dynamics.
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PDF链接：
https://arxiv.org/pdf/1909.13574

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关键词：del DNA ODE Quantitative distribution random formalism 模具 Odel strand