Related papers: The genetic code, 8-dimensional hypercomplex numbe…
Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this…
The concepts of orthology, paralogy, and xenology play a key role in molecular evolution. Orthology and paralogy distinguish whether a pair of genes originated by speciation or duplication. The corresponding binary relations on a set of…
Optimizing a neural network's performance is a tedious and time taking process, this iterative process does not have any defined solution which can work for all the problems. Optimization can be roughly categorized into - Architecture and…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…
After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or…
The $\mathbb{Z}_2\mathbb{Z}_4\mathbb{Z}_8$-additive codes are subgroups of $\mathbb{Z}_2^{\alpha_1} \times \mathbb{Z}_4^{\alpha_2} \times \mathbb{Z}_8^{\alpha_3}$, and can be seen as linear codes over $\mathbb{Z}_2$ when…
A promising paradigm for achieving highly efficient deep neural networks is the idea of evolutionary deep intelligence, which mimics biological evolution processes to progressively synthesize more efficient networks. A crucial design factor…
Despite the thousands of genes implicated in age-related phenotypes, effective interventions for aging remain elusive, a lack of advance rooted in the multifactorial nature of longevity and the functional interconnectedness of the molecular…
Unit derived schemes applied to Hadamard matrices are used to construct and analyse linear block and convolutional codes. Codes are constructed to prescribed types, lengths and rates and multiple series of self-dual, dual-containing, linear…
We propose a message passing neural network architecture designed to be equivariant to column and row permutations of a matrix. We illustrate its advantages over traditional architectures like multi-layer perceptrons (MLPs), convolutional…
There are several 3+1 parameter quantities in physics (like vector + scalar potentials, 4-currents, space-time, 4-momentum). In most cases (but space-time), the 3- and the 1-parameter characterised elements of these quantities differ in the…
The class of non-commutative hypercomplex number systems (HNS) of 4-dimension constructed by using of non-commutative procedure of Grassman-Clifford doubling of 2-dimensional systems is investigated in the article. All HNS of this class are…
Genetic sequencing has become an increasingly affordable and accessible source of genomic data in computational biology. This data is often represented as $k$-mers, i.e., strings of some fixed length $k$ with symbols chosen from a reference…
Motivation: Gene regulatory interactions are of fundamental importance to various biological functions and processes. However, only a few previous computational studies have claimed success in revealing genome-wide regulatory landscapes…
Decoding the genome confers the capability to predict characteristics of the organism(phenotype) from DNA (genotype). We describe the present status and future prospects of genomic prediction of complex traits in humans. Some highly…
The structural parameters of alpha helix and some forms of DNA-structures are determined by methods of algebraic topology. These structures are locally periodic and correspond to the bifurcation point for minimal surfaces given by…
Clonal organisms present a particular challenge in population genetics because, in addition to the possible existence of replicates of the same genotype in a given sample, some of the hypotheses and concepts underlying classical population…
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge-type numerical invariants (called H-numbers) of any, not necessarily algebraic, link in $S^3$. They contain the same information as the…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
The macromolecules that encode and translate information in living systems, DNA and RNA, exhibit distinctive structural asymmetries, including homochirality or mirror image asymmetry and $3' - 5'$ directionality, that are invariant across…