Related papers: Harmonic mean as a determinant of the genetic code
The concepts of alpha- and beta-packets of the periodic table of chemical elements and chemical compounds are defined. The first of the 47 minerals alpha-packets is composed. In it all minerals are arranged in increasing Iav index of…
Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of…
We present a geometrical analysis of the protrusion statistics of side chains in more than 4,000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of C{\alpha}…
Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…
Several genetic programming systems are created, each solving a different problem. In these systems, the median number of generations G needed to evolve a working program is measured. The behavior of G is observed as the difficulty of the…
Let A be a nonempty finite set of relatively prime positive integers, and let p_A(n) denote the number of partitions of n with parts in A. An elementary arithmetic argument is used to obtain an asymptotic formula for p_A(n).
In several recent papers new gene-detection algorithms were proposed for detecting protein-coding regions without requiring learning dataset of already known genes. The fact that unsupervised gene-detection is possible closely connected to…
We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…
The standard genetic code is known to be robust to translation errors and point mutations. We studied how small modifications of the standard code affect its robustness. The robustness was assessed in terms of a proper stability function,…
We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.
In a previous paper, we saw how to create formulae for the sum of the terms of a harmonic progression of order $k$, $HP_k(n)$, with integer parameters, $a$ and $b$. In this new paper we make those formulae more general by lifting the…
A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the…
Understanding how genes interact and relate to each other is a fundamental question in biology. However, current practices for describing these relationships, such as drawing diagrams or graphs in a somewhat arbitrary manner, limit our…
A proper coloring $c$ of a simple graph $G$ is harmonious if, for every pair of distinct edges $uv,xy\in E(G)$, we have that $\{c(u),c(v)\}\neq \{c(x),c(y)\}$. The harmonious chromatic number of $G$, denoted by $h(G)$, is the least positive…
Given three positive integers $n,a,b$ with $n=ab$, we determine the base size of the symmetric group and of the alternating group of degree $n$ in their action on the set of partitions into $b$ parts having cardinality $a$.
Musical frequencies in Just Intonation are comprised of rational numbers. The structure of rational numbers is determined by prime factorisations. Just Intonation frequencies can be split into two components. The larger component uses only…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
How does the genome encode the form of the organism? What is the nature of this genomic code? Inspired by recent work in machine learning and neuroscience, we propose that the genome encodes a generative model of the organism. In this…
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…
How do genes affect cognitive ability or other human quantitative traits such as height or disease risk? Progress on this challenging question is likely to be significant in the near future. I begin with a brief review of psychometric…