遗传信息的维数

IF 0.5 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Parallel Processing Letters Pub Date : 2023-10-25 DOI:10.1142/s0129626423400121
Subhash Kak
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引用次数: 0

摘要

本文从最优表示的角度研究了遗传信息的维数。最近的研究表明,信息的最优编码是基于e的非整数维数,并且伴随着尺度不变性。既然自然是最优的,我们应该看到这个维度反映在遗传密码的组织中。在此背景下,本文探讨了密码子对氨基酸的赋值性质背后的逻辑问题,因为它们的取值范围从1到6不等。证明了这种分配的非均匀性与非整数维数是一致的,这与要求近似均匀分配的数学编码理论是相违背的。不同氨基酸的密码子分配之所以不同,是因为均匀性仅在标准向量空间中是最优性的要求,而在非整数维空间中则不是。值得注意的是,在一个e维信息空间中有20个不同的覆盖区域,这相当于氨基酸的数量。本文还讨论了在e维空间中产生但在三维向量空间中检验的数据的可视化问题。结果表明,密码子在氨基酸上的分配是分形的,可以很好地用幂律Zipf分布来模拟。值得注意的是,适用于自然语言中单词字母频率的Zipf分布也适用于氨基酸编码中三联体的排列顺序。
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The Dimensionality of Genetic Information
This paper investigates the dimensionality of genetic information from the perspective of optimal representation. Recently it has been shown that optimal coding of information is in terms of the noninteger dimension of e, which is accompanied by the property of scale invariance. Since Nature is optimal, we should see this dimension reflected in the organization of the genetic code. With this as background, this paper investigates the problem of the logic behind the nature of the assignment of codons to amino acids, for they take different values that range from 1 to 6. It is shown that the non-uniformity of this assignment, which goes against mathematical coding theory that demands a near uniform assignment, is consistent with noninteger dimensions. The reason why the codon assignment for different amino acids varies is because uniformity is a requirement for optimality only in a standard vector space, and is not so in the noninteger dimensional space. It is noteworthy that there are 20 different covering regions in an e-dimensional information space, which is equal to the number of amino acids. The problem of the visualization of data that originates in an e-dimensional space but examined in a 3-dimensional vector space is also discussed. It is shown that the assignment of the codons to the amino acids is fractal-like that is well modeled by the Zipf distribution which is a power law. It is remarkable that the Zipf distribution that holds for the letter frequencies of words in a natural language also applies to the rank order of triplets in the code for amino acids.
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来源期刊
Parallel Processing Letters
Parallel Processing Letters COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-
CiteScore
0.90
自引率
25.00%
发文量
12
期刊介绍: Parallel Processing Letters (PPL) aims to rapidly disseminate results on a worldwide basis in the field of parallel processing in the form of short papers. It fills the need for an information vehicle which can convey recent achievements and further the exchange of scientific information in the field. This journal has a wide scope and topics covered included: - design and analysis of parallel and distributed algorithms - theory of parallel computation - parallel programming languages - parallel programming environments - parallel architectures and VLSI circuits
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