Related papers: Quaternionic representation of the genetic code
Recent work has studied the interplay between a galaxy's history and its observable properties using "genetically modified" cosmological zoom simulations. The approach systematically generates alternative histories for a halo, while keeping…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
Living organisms are the most complex, interesting and significant objects regarding all substructures of the universe. Life science is regarded as a science of the 21st century and one can expect great new discoveries in the near futures.…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
We have presented the basic knowledge on the structure of molecules coding the genetic information, mechanisms of transfer of this information from DNA to proteins and phenomena connected with replication of DNA. In particular, we have…
In this article, we discuss how a kind of hybrid computation, which employs symbolic, numeric, classic, and quantum algorithms, allows us to conduct Hartree-Fock electronic structure computation of molecules. In the proposed algorithm, we…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
A primordial genetic code is proposed, having only four codons assigned, GGC meaning glycine, GAC meaning aspartate/glutamate, GCC meaning alanine-like and GUC meaning valine-like. Pathways of ambiguity reduction enlarged the codon…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
Rotary Positional Embeddings (RoPE) have demonstrated exceptional performance as a positional encoding method, consistently outperforming their baselines. While recent work has sought to extend RoPE to higher-dimensional inputs, many such…
The genetic code maps the sixty-four nucleotide triplets (codons) to twenty amino-acids. Some argue that the specific form of the code with its twenty amino-acids might be a 'frozen accident' because of the overwhelming effects of any…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
Using the crystal basis model of the genetic code, a set of relations between the physical-chemical properties of the amino acids are derived and compared with the experimental data. A prevision for the not yet measured thermodynamical…
Quaternion derivatives in the mathematical literature are typically defined only for analytic (regular) functions. However, in engineering problems, functions of interest are often real-valued and thus not analytic, such as the standard…
In this work it is shown that 20 canonical amino acids (AAs) within genetic code appear to be a whole system with strict distinction in Genetic Code Table (GCT) into some different quantums: 20, 23, 61 amino acid molecules. These molecules…
The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
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…