Related papers: Harmonic mean as a determinant of the genetic code
Use is made of rigorous definitions for the terms normal, natural, and harmonic to reveal a number of unfamiliar aspects about them. The Gaussian distribution is not sufficient to determine who is normal, and fluctuations above or below a…
The rank ordered distribution of the codon usage frequencies for 123 bacteriae is best fitted by a three parameters function that is the sum of a constant, an exponential and a linear term in the rank n. The parameters depend (two…
Proteins employ the information stored in the genetic code and translated into their sequences to carry out well-defined functions in the cellular environment. The possibility to encode for such functions is controlled by the balance…
The main statistical distributions applicable to the analysis of genome architecture and genome tracks are briefly discussed and critically assessed. Although the observed features in distributions of element lengths can be equally well…
The underlying structure of the canonical amino acid substitution matrix (aaSM) is examined by considering stepwise improvements in the differential recognition of amino acids according to their chemical properties during the branching…
Quantitative criteria are proposed to identify genes (and sets of genes) whose expression marks a specific brain region (or a set of brain regions). Gene-expression energies, obtained for thousands of mouse genes by numerization of in-situ…
Background. The large-scale pattern of distribution of genes on the chromosomes in the known animal genomes is not well characterized. We hypothesized that individual genes will be distributed on chromosomes in a mathematically ordered…
The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by…
A molecular dynamics calculation of the amino acid polar requirement is presented and used to score the canonical genetic code. Monte Carlo simulation shows that this computational polar requirement has been optimized by the canonical…
Genetic Algorithms (GA) are a powerful tool for stochastic optimisation and non-parametric symbolic regression, already widely used in cosmology. They are capable of reconstructing analytical functions directly from data points without…
Statistical methodology plays a crucial role in drug regulation. Decisions by the FDA or EMA are typically made based on multiple primary studies testing the same medical product, where the two-trials rule is the standard requirement,…
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…
An ordered set-partition (or preferential arrangement) of n labeled elements represents a single ``hierarchy''; these are enumerated by the ordered Bell numbers. In this note we determine the number of ``hierarchical orderings'' or…
We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius $n$ centered at the root, we prove that, although the size of the boundary is of order $n$, most of the harmonic measure is supported…
In matrix theory, a well established relation $(AB)^{T}=B^{T}A^{T}$ holds for any two matrices $A$ and $B$ for which the product $AB$ is defined. Here $T$ denote the usual transposition. In this work, we explore the possibility of deriving…
A theoretical construction of the genetic material establishes the unique and ideal character of DNA. A similar conclusion is reached for amino acids and proteins.
We consider Gibbs distributions, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval…
Gene expression programming, a genotype/phenotype genetic algorithm (linear and ramified), is presented here for the first time as a new technique for the creation of computer programs. Gene expression programming uses character linear…
Let $G=\mathop{A\ast B}\limits_C$ be an amalgamated product of finite rank free groups $A$, $B$ and $C$. We introduce atomic measures and corresponding asymptotic densities on a set of normal forms of elements in $G$. We also define two…
The genetic code is nearly universal, and the arrangement of the codons in the standard codon table is highly non-random. The three main concepts on origin and evolution of the code are the stereochemical theory; the coevolution theory; and…