摘要翻译：
本文致力于应用投影算子模拟分子遗传密码系统的唯象性质。斜投影算子被考虑，它与以Rademacher和Hadamard矩阵形式表示的遗传编码系统的矩阵有关。结果表明，这种投影的和可以充分模拟遗传生物现象的集合，包括生物周期的集合、叶序模式的形态发生集合、镜像对称模式等。为此，作者提出了多维向量空间，其子空间在遗传投影的基础上通过一组矩阵算子进行选择性控制（或编码）。讨论了遗传生物力学的发展。在研究遗传系统和遗传矩阵时，作者提出并描述了特殊的多维数系，命名为联合超复数。在提出等效寡核苷酸四基团概念的基础上，描述了长核苷酸序列的新规则。所述结果可用于发展代数生物学、生物技术应用以及其他一些科学和技术领域。
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英文标题：
《The genetic code, algebra of projection operators and problems of
  inherited biological ensembles》
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作者：
Sergey Petoukhov
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最新提交年份：
2017
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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：
  This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system. Oblique projection operators are under consideration, which are connected with matrix representations of the genetic coding system in forms of the Rademacher and Hadamard matrices. Evidences are shown that sums of such projectors give abilities for adequate simulations of ensembles of inherited biological phenomena including ensembles of biological cycles, morphogenetic ensembles of phyllotaxis patterns, mirror-symmetric patterns, etc. For such modeling, the author proposes multidimensional vector spaces, whose subspaces are under a selective control (or coding) by means of a set of matrix operators on base of genetic projectors. Development of genetic biomechanics is discussed. The author proposes and describes special systems of multidimensional numbers under names united-hypercomplex numbers, which attracted his attention when he studied genetic systems and genetic matrices. New rules of long nucleotide sequences are described on the base of the proposed notion of tetra-groups of equivalent oligonucleotides. Described results can be used for developing algebraic biology, bio-technical applications and some other fields of science and technology.
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PDF链接：
https://arxiv.org/pdf/1307.7882