Related papers: Chirality in a quaternionic representation of the …

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 previously formulated model for the evolution of the genetic code was shown to clarify why base triplets of some precursor amino acids differ by a single base from product amino acid codons, while others show less homology. First, the…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…

Protein representation learning is a challenging task that aims to capture the structure and function of proteins from their amino acid sequences. Previous methods largely ignored the fact that not all amino acids are equally important for…

The mathematical concept of q-deformations, in particular the one of qnumbers, is used to study the genetic code(s). After considering two kinds of q-numbers, for comparison, a phenomenological classification scheme of the genetic code…

Why is the genetic code the way it is? The most successful theory states that the codon assignments minimise the effects of errors arising in primordial living systems. Here a transversion is reported that leaves invariant degeneracy in the…

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model…

Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever) explanation of why living organisms have 4…

Chirality is a fundamental feature in all domains of nature, ranging from particle physics over electromagnetism to chemistry and biology. Chiral objects lack a mirror plane and inversion symmetry and therefore cannot be spatially aligned…

In the QCD analysis, when quarks are expressed in quaternion basis, the quark and its charge conjugate together are expressed by octonions and the octonion posesses the triality symmetry. Gluos are expressed by Pl\"ucker coordinates of…

New developments are presented in the framework of the model introduced by the authors in refs. [1,2] and in which nucleotides as well as codons are classified in crystal bases of the quantum group U_q(sl(2)+sl(2)) in the limit q -> 0. An…

The numerical optimization of continuous functions is a fundamental task in many scientific and engineering domains, ranging from mechanical design to training of artificial intelligence models. Among the most effective and widely used…

In the limit of large number of colors N the nucleon consisting of N quarks is heavy, and one can treat it semiclassically, like the large-Z Thomas--Fermi atom. The role of the semiclassical field binding the quarks in the nucleon is played…

Recently, Kulo\u{g}lu {\it et al.} \cite{Kul} introduced the higher order Horadam numbers. In this study, novel 3-parameter generalized quaternion sequences of higher order Horadam numbers, which have not been studied before, are defined by…

This paper introduces a novel idea for representation of individuals using quaternions in swarm intelligence and evolutionary algorithms. Quaternions are a number system, which extends complex numbers. They are successfully applied to…

In quantum mechanics, each conserved quantity (e.g., energy, position, linear momentum and angular momentum) is associated with a Hermitian operator. Its expected value can then be determined by performing a measurement on the wavefunction.…

The tendencies described in this work were revealed in the course of examination of adenine and uracil distribution in the mRNA encoding sequence. The study also discusses the usage of codons occupied by the amino acid arginine in the table…

The number of atoms in the four ribonucleotides uridine monophosphate, cytidine monophosphate, adenine monophosphate and guanine monophosphate is taken as a key parameter. A mathematical relation describing the condensation of the three…

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, G, A, U, C}, where the letter D represents one or more hypothetical bases with…

The genetic code has a high level of error robustness. Using values of hydrophobicity scales as a proxy for amino acid character, and the Mean Square measure as a function quantifying error robustness, a value can be obtained for a genetic…