Related papers: Harmonic mean as a determinant of the genetic code

Motivation: Protein sequence world is discrete as 20 amino acids (AA) while its structure world is continuous, though can be discretized into structural alphabets (SA). In order to reveal the relationship between sequence and structure, it…

The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C T; A G], where C, T, A, G are the letters of the genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the (4*4)-matrix…

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide…

Enzymes and proteins are live driven biochemicals, which has a dramatic impact over the environment, in which it is active. So, therefore, it is highly looked-for to build such a robust and highly accurate automatic and computational model…

Multiple sequence alignment is a basic procedure in molecular biology, and it is often treated as being essentially a solved computational problem. However, this is not so, and here I review the evidence for this claim, and outline the…

The hyperspherical harmonics (HH) provide a complete basis for the expansion of atomic wave functions, but even for two particles the number of harmonics for a given order is not trivial and, as the number of electrons increases, this…

Gauss's arithmetic-geometric mean (AGM) which is described by two variables iteration $(a_n, b_n)\rightarrow (a_{n+1}, b_{n+1})$ by $a_{n+1}=(a_n+b_n)/2,\ b_{n+1}=\sqrt{a_nb_n}$. We extend it to three variables iteration $(a_n, b_n,…

Each human genome is a 3 billion base pair set of encoding instructions. Decoding the genome using deep learning fundamentally differs from most tasks, as we do not know the full structure of the data and therefore cannot design…

We first compute the James' sectional category (secat) of the Ganea map g_k of any map f in terms of the sectional category of f: We show that secat(g_k) is the integer part of secat(f)/(k+1). Next we compute the relative category (relcat)…

We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…

All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reformulation of a result due to Heuvers in terms of a Cauchy…

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…

We Propose 22 unique Solutions to the Genetic Code. An Alternative Cracking, from the Perspective of a Mathematician.

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…

So far mutations analysis was performed in terms of transitions and trasversions, so on the basis of the molecule, or in terms of GC-content and isochors, through the quantification of GC->AT mutations over AT->GC mutations. We tried a…

In this paper the geometric mean of partial positive definite matrices with missing entries is considered. The weighted geometric mean of two sets of positive matrices is defined, and we show whether such a geometric mean holds certain…

The Dissertation is focused on the studies of associations between functional elements in human genome and their nucleotide structure. The asymmetry in nucleotide content (skew, bias) was chosen as the main feature for nucleotide structure.…

Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not…

Integrating the summary statistics from genome-wide association study (\textsc{gwas}) and expression quantitative trait loci (e\textsc{qtl}) data provides a powerful way of identifying the genes whose expression levels are potentially…

Equal temperament, in which semitones are tuned in the irrational ratio of $2^{1/12} : 1$, is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intonation, in which intervals are given by products of powers of…