Rules of Stochastics of Genomic DNAs, Biological Dualism "Stochastics-Determinism",and Tensor-Unitary Transformations

Abstract

The article is devoted to algebraic modeling of universal rules of stochastic organization of genomic DNA of higher and lower organisms, previously published by the author. The proposed algebraic apparatus, which uses formalisms of quantum mechanics and quantum informatics and which is based on the so-called tensor-unitary transformations of vectors that generate families of interrelated stochastic-deterministic vectors of increased dimensions. The features of the vectors' interconnections in these families model the stochastic-deterministic properties of the named phenomenological rules. There are new approaches to modeling of developing multi-parameter biosystems, whose number of parameters increases in the course of step-by-step development. In the light of the presented materials, the issues of fractal-like organization in genetically inherited biosystems are considered. The development of the theory of stochastic determinism as an antipode of deterministic chaos is discussed.

Доктрина Энергоинформационной Эволюции На Основе Био-Антенных Решеток И Алгебраическая Биология

“…В этой двойственной связи заключается важное отличие систем био-антенных решеток от инженерных Интеллектуальных Антенн. Для алгебраического моделирования квантово-подобных особенностей в системах вероятностей геномных ДНК автором введено понятие тензор-унитарных преобразований как операторов, сохраняющих длины векторов при их тензорном преобразовании в векторы пространства повышенной размерности [Petoukhov, 2022c;Petoukhov, He, 2023]. Они являются операторами расширения стохастико-детерминистской памяти с сохранением всей предыдущей памяти.…”

“…For algebraic modeling of quantum-like features in probability systems of genomic DNA, the author introduced the concept of tensor-unitary transformations as operators that preserve the lengths of vectors during their tensor transformation into space vectors of increased dimensionality [Petoukhov, 2022c;Petoukhov, He, 2023]. They are operators for expanding stochastic-deterministic memory while preserving all previous memory.…”

“…This phenomenological connection leads to the existence of a fractal dichotomous tree of percentages (Fig. 8), in which each node is the beginning of its own fractal dichotomous tree [Petoukhov, 2022;Petoukhov, 2023a,b].…”