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In this paper we use the deformation procedure introduced in former work on deformed defects to investigate several new models for real scalar field. We introduce an interesting deformation function, from which we obtain two distinct…
We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the…
These lecture notes were written for a mini-course that was designed to introduce students and researchers to {\it $q$-series,} which are also called {\it basic hypergeometric series} because of the parameter $q$ that is used as a base in…
The genetic code maps the sixty-four nucleotide triplets (codons) to twenty amino-acids. While the biochemical details of this code were unraveled long ago, its origin is still obscure. We review information-theoretic approaches to the…
The poly-tRNA model was recently presented for the origin and evolution of genetic coding. This model has led to a rather precise description of what might have occurred at the beginning of protein synthesis in the first life form. Here, we…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Genetic information is encoded in a linear sequence of nucleotides, represented by letters ranging from thousands to billions. Mutations refer to changes in the DNA or RNA nucleotide sequence. Thus, mutation detection is vital in all areas…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
For $q$-ary $n$-sequences, we develop the concept of similarity functions that can be used (for $q=4$) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence…
The widely used genetic pleiotropic analysis of multiple phenotypes are often designed for examining the relationship between common variants and a few phenotypes. They are not suited for both high dimensional phenotypes and high…
Proteins, essential to biological systems, perform functions intricately linked to their three-dimensional structures. Understanding the relationship between protein structures and their amino acid sequences remains a core challenge in…
We propose a novel group testing method, termed semi-quantitative group testing, motivated by a class of problems arising in genome screening experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary pooling scheme that…
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic…
This thesis studies how the segmentation results, produced by convolutional neural networks (CNN), is different from each other when applied to small biomedical datasets. We use different architectures, parameters and hyper-parameters,…
A three-dimensional model of the genetic vocabulary is proposed in terms of determinative degree, an introduced characteristic of nucleotide, which reflects absolute difference between purin and pyrimidin bases in one DNA strand. In the…
A representation of the genetic code as a six-dimensional Boolean hypercube is described. This structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition. In this paper it is…
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical…
This article begins with an exploration of nonlinear codes ($\mathbb{F}_q$-linear subspaces of $\mathbb{F}_{q^m}^n$) which are generalizations of the familiar Reed-Solomon codes. This then leads to a wider exploration of nonlinear analogues…