Related papers: The genetic code, 8-dimensional hypercomplex numbe…
We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric…
This paper introduces new tools for genomic signal processing, which can assist for genomic attribute extracting or describing biologically meaningful features embedded in a DNA. The codongrams and a2grams are offered as an alternative to…
In recent years the field of genetic programming has made significant advances towards automatic programming. Research and development of contemporary program synthesis methods, such as PushGP and Grammar Guided Genetic Programming, can…
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…
The aim of this paper is to study the behavior of Hodge-theoretic (intersection homology) genera and their associated characteristic classes under proper morphisms of complex algebraic varieties. We obtain formulae that relate (parametrized…
We provide a series of generic results regarding the structure of nodes in the retarded Green's function G of an interacting system, as exemplified by the extended Hubbard model. In particular: (1) due to an incompatibility between…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
Although algebraic graph theory based models have been widely applied in physical modeling and molecular studies, they are typically incompetent in the analysis and prediction of biomolecular properties when compared with other quantitative…
Current models for the folding of the human genome see a hierarchy stretching down from chromosome territories, through A/B compartments and TADs (topologically-associating domains), to contact domains stabilized by cohesin and CTCF.…
We introduce an algorithm to generate multivariate series of symbols from a finite alphabet with a given hierarchical structure of similarities. The target hierarchical structure of similarities is arbitrary, for instance the one obtained…
Hierarchical models are a powerful tool for high-throughput data with a small to moderate number of replicates, as they allow sharing information across units of information, for example, genes. We propose two such models and show its…
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…
The ranks and kernels of generalized Hadamard matrices are studied. It is proven that any generalized Hadamard matrix $H(q,\lambda)$ over $F_q$, $q>3$, or $q=3$ and $\gcd(3,\lambda)\not =1$, generates a self-orthogonal code. This result…
We develop a symbolic regression framework for extracting the governing mathematical expressions from observed data. The evolutionary approach, faiGP, is designed to leverage the properties of a function algebra that have been encoded into…
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…
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…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
We study the Hadamard product of the linear forms defining a hyperplane arrangement with those of its dual, which we view as generating an ideal in a certain polynomial ring. We use this ideal, which we call the ideal of pairs, to study…
A system-level genetic code is a hypothetical genetic code that exclusively or preferentially codes systems of interacting coadapted parts. System-level genetic codes differ from part-level genetic codes in which each discrete part is coded…
Discovering genes with similar functions across diverse biomedical contexts poses a significant challenge in gene representation learning due to data heterogeneity. In this study, we resolve this problem by introducing a novel model called…