遗传密码的简并性与Hadamard矩阵

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摘要翻译：
遗传密码表示的矩阵形式被描述为分析遗传密码结构的认知形式。在信号处理理论中也采用了类似的矩阵形式。研究了基于遗传矩阵[C A；U G]的Kronecker族遗传矩阵，其中C,A,U,G是遗传字母表的字母。第三次Kronecker幂中的这个矩阵是(8*8)-矩阵，它包含64个三元组。脊椎动物线粒体遗传密码退化的特点反映在该遗传(8*8)矩阵的对称黑白镶嵌中。这种马赛克矩阵在算法上与信号处理、谱分析、量子力学和量子计算机中著名的Hadamard矩阵不期而遇地联系在一起。数值遗传矩阵的一种特殊分解揭示了它们与一族8维超复数（而不是Cayley的八倍数）的密切关系。在这些现象学事实的基础上，提出了一些假设和思想。
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英文标题：
《The degeneracy of the genetic code and Hadamard matrices》
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作者：
Sergey V. Petoukhov
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最新提交年份：
2010
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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：
  The matrix form of the presentation of the genetic code is described as the cognitive form to analyze structures of the genetic code. A similar matrix form is utilized in the theory of signal processing. The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. This matrix in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. Peculiarities of the degeneracy of the vertebrate mitochondria genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard matrices unexpectedly, which are famous in the theory of signal processing, spectral analysis, quantum mechanics and quantum computers. A special decomposition of numeric genetic matrices reveals their close relations with a family of 8-dimensional hypercomplex numbers (not Cayley's octonions). Some hypothesis and thoughts are formulated on the basis of these phenomenological facts.
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PDF链接：
https://arxiv.org/pdf/0802.3366

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