Related papers: Chirality in a quaternionic representation of the …
The folding structure of the DNA molecule combined with helper molecules, also referred to as the chromatin, is highly relevant for the functional properties of DNA. The chromatin structure is largely determined by the underlying primary…
We consider Clifford algebras over the field of real or complex numbers as a quotient algebra without fixed basis. We present classification of Clifford algebra elements based on the notion of quaternion type. This classification allows us…
The usage frequencies for codons belonging to quartets are analized, over the whole exonic region, for 92 biological species. Correlation is put into evidence, between the usage frequencies of synonymous codons with third nucleotide A and C…
The genetic code is the function from the set of codons to the set of amino acids by which a DNA sequence encodes proteins. Since the codons also influence the shape of the DNA molecule itself, the same sequence that encodes a protein also…
The main properties of hypercomplex generalization of quaternion system as antiquaternion are presented in this article. Definitions and studied of antiquaternions conjugation are introduced, their norm and zero divisor, and how to perform…
We introduce combinatorial interpretability, a methodology for understanding neural computation by analyzing the combinatorial structures in the sign-based categorization of a network's weights and biases. We demonstrate its power through…
We show how chirality emerges naturally from an embedding of the standard model of particle physics into $E_{8(-24)}$. The well-known argument that there is no chiral theory of fundamental physics in $E_8$ is avoided by implementing…
In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having…
In this article we study an exact analogue of the cross-ratio for the algebra of quaternions H and use it to derive several interesting properties of quaternionic fractional linear transformations. In particular, we show that there exists a…
The notion of a quaternionic gerbe is presented as a new way of bundling algebraic structures over a four manifold. The structure groupoid of this fibration is described in some detail. The Euclidean conformal group R*SO(4) appears…
The underlying structure of the canonical amino acid substitution matrix (aaSM) is examined by considering stepwise improvements in the differential recognition of amino acids according to their chemical properties during the branching…
We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest do not necessarily follow a chi-square distribution and take the…
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…
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…
The presence of chirality in the main molecules of life may well be not just a structural artifact, but of pure biological advantage. The possibility of the existence of a phenomenon of a special mode of interaction, labeled as "chiral…
The research of developing a general methodology for the construction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of…
The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…
This letter reports complete sets of two-fold symmetries between partitions of the universal genetic code. By substituting bases at each position of the codons according to a fixed rule, it happens that properties of the degeneracy pattern…
Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are…