Related papers: Chirality in a quaternionic representation of the …
The origin and organizing principles of the genetic code remain fundamental puzzles in life science. The vanishingly low probability of the natural codon-to-amino acid mapping arising by chance has spurred the hypothesis that its structure…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
In the QCD analysis, when quarks are expressed in quaternion basis, the product of quaternions are expressed by octonions and the octonion posesses the triality symmetry. Roles of triality in the gluon self energy calculation and finite…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
Since their first applications, Convolutional Neural Networks (CNNs) have solved problems that have advanced the state-of-the-art in several domains. CNNs represent information using real numbers. Despite encouraging results, theoretical…
Important aspects of the process of information storage and retrieval in DNA and RNA, and its evolution, are the role of the anticodons and associated $t$RNA's, and correlations between anticodons and amino acids; the degeneracy of the…
A new set of DNA base-nucleic acid codes and their hypercomplex number representation have been introduced for taking the probability of each nucleotide into full account. A new scoring system has been proposed to suit the hypercomplex…
We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra.
In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic…
Degeneracy is a salient feature of genetic codes, because there are more codons than amino acids. The conventional table for genetic codes suffers from an inability of illustrating a symmetrical nature among genetic base codes. In fact,…
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…
In a certain way, this paper presents the continuation of the previous one which discussed the harmonic structure of the genetic code (Rakocevic, 2004). Several new harmonic structures presented in this paper, through specific unity and…
Many modified genetic codes are found in specific genomes in which one or more codons have been reassigned to a different amino acid from that in the canonical code. We present a model that unifies four possible mechanisms for reassignment,…
Degeneracy of the genetic code is a biological way to minimize effects of the undesirable mutation changes. Degeneration has a natural description on the 5-adic space of 64 codons $\mathcal{C}_5 (64) = \{n_0 + n_1 5 + n_2 5^2 : n_i = 1, 2,…
Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and generalizes to higher dimension the theory of holomorphic functions in the complex plane.…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…
The information capacity of double-crossover (DX) tiles was successfully increased beyond a binary representation to higher base representations. By controlling the length and the position of DNA hairpins on the DX tile, ternary and senary…
Background The theoretical requirements for a genetic code were well defined and modeled by George Gamow and Francis Crick in the 50-es. Their models failed. However the valid Genetic Code, provided by Nirenberg and Matthaei in 1961,…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…