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Sergey V. Petoukhov

Publications and source records attributed to Sergey V. Petoukhov.

10 recordsLinked to original sources

Towards a Better Model with Dual Transformer for Drug Response Prediction

GNN-based methods have achieved excellent results as a mainstream task in drug response prediction tasks in recent years. Traditional GNN methods use only the atoms in a drug molecule as nodes to obtain the representation of the molecular graph through node information passing, whereas the method using the transformer can only extract information about the nodes. However, the covalent bonding and chirality of a drug molecule have a great influence on the pharmacological properties of the molecule, and these information are implied in the chemical bonds formed by the edges between the atoms. In addition, CNN methods for modelling cell lines genomics sequences can only perceive local rather than global information about the sequence. In order to solve the above problems, we propose the decoupled dual transformer structure with edge embedded for drug respond prediction (TransEDRP), which is used for the representation of cell line genomics and drug respectively. For the drug branch, we encoded the chemical bond information within the molecule as the embedding of the edge in the molecular graph, extracted the global structural and biochemical information of the drug molecule using graph transformer. For the branch of cell lines genomics, we use the multi-headed attention mechanism to globally represent the genomics sequence. Finally, the drug and genomics branches are fused to predict IC50 values through the transformer layer and the fully connected layer, which two branches are different modalities. Extensive experiments have shown that our method is better than the current mainstream approach in all evaluation indicators.

q-bio.BM↗

The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts

Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of the genetic system with Walsh functions and Hadamard matrices, which are known in theory of noise-immunity coding, digital communication and digital holography. Dyadic-shift decompositions of such genetic matrices lead to sets of sparse matrices. Each of these sets is closed in relation to multiplication and defines relevant algebra of hypercomplex numbers. It is shown that genetic Hadamard matrices are identical to matrix representations of Hamilton quaternions and its complexification in the case of unit coordinates. The diversity of known dialects of the genetic code is analyzed from the viewpoint of the genetic algebras. An algebraic analogy with Punnett squares for inherited traits is shown. Our results are used in analyzing genetic phenomena. The statement about existence of the geno-logic code in DNA and epigenetics on the base of the spectral logic of systems of Boolean functions is put forward. Our results show promising ways to develop algebraic-logical biology, in particular, in connection with the logic holography on Walsh functions.

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The matrix method of representation, analysis and classification of long genetic sequences

The article is devoted to a matrix method of comparative analysis of long nucleotide sequences by means of a presentation of each sequence in a form of three digital binary sequences. This method uses biochemical attributes of nucleotides and it also uses a possibility of presentation of every whole set of n-mers in a form of one of members of a Kronecker family of genetic matrices. Due to this method, a long nucleotide sequence can be visually represented as an individual fractal-like mosaic or another regular mosaic of binary type. In contrast to natural nucleotide sequences, artificial random sequences give non-regular patterns. Examples of binary mosaics of long nucleotide sequences are shown, including cases of human chromosomes and penicillins. Interpretation of binary presentations of nucleotide sequences from the point of view of Gray code is also tested. Possible reasons of genetic meaning of Kronecker multiplication of matrices are analyzed. The received results are discussed.

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Dyadic groups, dyadic trees and symmetries in long nucleotide sequences

The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with well-known notions of dyadic groups and dyadic-shift matrices. Matrix genetics shows relations of the genetic alphabets with some types of hypercomplex numbers including dual numbers and bicomplex numbers together with their extensions. A possibility of new approach is mentioned to simulate genetically inherited phenomena of biological spirals and phyllotaxis laws on the base of screw theory and Fibonacci matrices. Dyadic trees for sub-sets of triplets of the whole human genome are constructed. A new notion is put forward about square matrices with internal complementarities on the base of genetic matrices. Initial results of the study of such matrices are described. Our results testify that living matter possesses a profound algebraic essence. They show new promising ways to develop algebraic biology.

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Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices

The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C T; A G], where C, T, A, G are the letters of the genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the (4*4)-matrix of 16 duplets. The matrix [C T; A G] in the third Kronecker power is the (8*8)-matrix of 64 triplets. It is significant that peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of these genetic matrices. The article represents interesting mathematical properties of these mosaic matrices, which are connected with positional permutations inside duplets and triplets; with projector operators; with unitary matrices and cyclic groups, etc. Fractal genetic nets are proposed as a new effective tool to study long nucleotide sequences. Some results about revealing new symmetry principles of long nucleotide sequences are described.

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The degeneracy of the genetic code and Hadamard matrices

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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Matrix genetics, part 5: genetic projection operators and direct sums

The article is devoted to phenomena of symmetries and algebras in matrix presentations of the genetic code. The Kronecker family of the genetic matrices is investigated, which is based on the alphabetical matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. The matrix P=[C A; U G] in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. Peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix of 64 triplets. Phenomena of connections of this mosaic matrix (and many other genetic matrices) with projection operators are revealed. Taking into account an important role of projection operators in quantum mechanics, theory of digital codes, computer science, logic and in many other fields of applied mathematics, we study algebraic properties and biological meanings of these phenomena. Using of notions and formalisms of theory of finite-dimensional vector spaces in bioinformatics and theoretical biology is proposed on the bases of the described results.

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Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles

The article continues an analysis of the genetic 8-dimensional Yin-Yang-algebra. This algebra was revealed in a course of matrix researches of structures of the genetic code and it was described in the author's articles arXiv:0803.3330 and arXiv:0805.4692. The article presents data about many kinds of cyclic permutations of elements of the genetic code in the genetic (8x8)-matrix [C A; U G](3) of 64 triplets, where C, A, U, G are letters of the genetic alphabet. These cyclic permutations lead to such reorganizations of the matrix form of presentation of the initial genetic Yin-Yang-algebra that arisen matrices serve as matrix forms of presentations of new Yin-Yang-algebras as well. They are connected algorithmically with Hadamard matrices. The discovered existence of a hierarchy of the cyclic changes of types of genetic Yin-Yang-algebras allows thinking about new algebraic-genetic models of cyclic processes in inherited biological systems including models of cyclic metamorphoses of animals. These cycles of changes of the genetic 8-dimensional algebras and of their 8-dimensional numeric systems have many analogies with famous facts and doctrines of modern and ancient physiology, medicine, etc. This viewpoint proposes that the famous idea by Pythagoras (about organization of natural systems in accordance with harmony of numerical systems) should be combined with the idea of cyclic changes of Yin-Yang-numeric systems in considered cases. This second idea reminds of the ancient idea of cyclic changes in nature. From such algebraic-genetic viewpoint, the notion of biological time can be considered as a factor of coordinating these hierarchical ensembles of cyclic changes of types of the genetic multi-dimensional algebras.

q-bio.GN↗

Matrix genetics, part 3: the evolution of the genetic code from the viewpoint of the genetic octave Yin-Yang-algebra

The set of known dialects of the genetic code (GC) is analyzed from the viewpoint of the genetic octave Yin-Yang-algebra. This algebra was described in the previous author's publications. The algebra was discovered on the basis of structural features of the GC in the matrix form of its presentation ("matrix genetics"). The octave Yin-Yang-algebra is considered as the pre-code or as the model of the GC. From the viewpoint of this algebraic model, for example, the sets of 20 amino acids and of 64 triplets consist of sub-sets of "male", "female" and "androgynous" molecules, etc. This algebra permits to reveal hidden peculiarities of the structure and evolution of the GC and to propose the conception of "sexual" relationships among genetic molecules. The first results of the analysis of the GC systems from such algebraic viewpoint say about the close connection between evolution of the GC and this algebra. They include 8 evolutionary rules of the dialects of the GC. The evolution of the GC is appeared as the struggle between male and female beginnings. The hypothesis about new biophysical factor of "sexual" interactions among genetic molecules is put forward. The matrix forms of presentation of elements of the genetic octave Yin-Yang-algebra are connected with Hadamard matrices by means of the simple U-algorithm. Hadamard matrices play a significant role in the theory of quantum computers, in particular. It gives new opportunities for possible understanding the GC systems as quantum computer systems. Revealed algebraic properties of the GC permit to put forward the problem of algebraization of bioinformatics on the basis of the algebras of the GC. Our investigation is connected with the question: what is life from the viewpoint of algebra? The algebraic version of the origin of the GC is discussed.

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Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)

Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20 amino acids and stop-signals. This mosaic genetic matrix is connected with the matrix form of presentation of the special 8-dimensional Yin-Yang-algebra and of its particular 4-dimensional case. The special algorithm, which is based on features of genetic molecules, exists to transform the mosaic genomatrix into the matrices of these algebras. Two new numeric systems are defined by these 8-dimensional and 4-dimensional algebras: genetic Yin-Yang-octaves and genetic tetrions. Their comparison with quaternions by Hamilton is presented. Elements of new "genovector calculation" and ideas of "genetic mechanics" are discussed. These algebras are considered as models of the genetic code and as its possible pre-code basis. They are related with binary oppositions of the Yin-Yang type and they give new opportunities to investigate evolution of the genetic code. The revealed fact of the relation between the genetic code and these genetic algebras is discussed in connection with the idea by Pythagoras: "All things are numbers". Simultaneously these genetic algebras can be utilized as the algebras of genetic operators in biological organisms. The described results are related with the problem of algebraization of bioinformatics. They take attention to the question: what is life from the viewpoint of algebra?

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