Related papers: The genetic code, 8-dimensional hypercomplex numbe…
This paper presents several notable properties of the matrix $\mathbb{U}$ shown to be related to the isomorphism between $H_4$ and $E_8$. The most significant of these properties is that $\mathbb{U}$.$\mathbb{U}$ is to rank 8 matrices what…
Hashing plays an important role in information retrieval, due to its low storage and high speed of processing. Among the techniques available in the literature, multi-modal hashing, which can encode heterogeneous multi-modal features into…
The overarching goal of this paper is to solve the word problem for a class of idempotent commutative monoids whose elements model population haplotypes. More specifically, we design an algebraic framework in which it is possible to unravel…
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…
We consider the problem of detecting and estimating the strength of association between a trait of interest and alleles or haplotypes in a small genomic region (e.g. a gene or a gene complex), when no direct information on that region is…
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…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…
The present paper is devoted to foundations of p-adic modelling in genomics. Considering nucleotides, codons, DNA and RNA sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms…
In this paper we have established relations of the genetic tables with magic and bimagic squares. Connections with Hamming distances, binomial coefficients are established. The idea of Gray code is applied. Shannon entropy of magic squares…
A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…
Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of…
Several genetic programming systems are created, each solving a different problem. In these systems, the median number of generations G needed to evolve a working program is measured. The behavior of G is observed as the difficulty of the…
Genetic algorithms are considered as an original way to solve problems, probably because of their generality and of their "blind" nature. But GAs are also unusual since the features of many implementations (among all that could be thought…
In this short paper, it is shown that the multiplet structure of the standard genetic code is derivable from the total number of nucleotides contained in 64 codons, 192, a small number. The degeneracy class-number is derived as the number…
The quantum enveloping algebra U_q(sl(2) \oplus sl(2)) in the limit q \to 0 is proposed as a symmetry algebra for the genetic code. In this approach the triplets of nucleotids or codons in the DNA chain are classified in crystal bases,…
A method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…
The holographic bound in physics constrains the complexity of life. The finite storage capability of information in the observable universe requires the protein linguistics in the evolution of life. We find that the evolution of genetic…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…
In the framework of algebraic topology the closed sequence of 4-dimensional polyhedra (algebraic polytopes) was defined. This sequence is started by the polytope {240}, discovered by Coxeter, and is determined by the second coordination…