1,387 research outputs found
Genetic Code and Number Theory
Living organisms are the most complex, interesting and significant objects
regarding all substructures of the universe. Life science is regarded as a
science of the 21st century and one can expect great new discoveries in the
near futures. This article contains an introductory brief review of genetic
information, its coding and translation of genes to proteins through the
genetic code. Some theoretical approaches to the modelling of the genetic code
are presented. In particular, connection of the genetic code with number theory
is considered and the role of -adic numbers is underlined.Comment: 15 pages. To apper in "Modern Topics in Science", a book of invited
papers (Eds. R. Constantinescu, G. Djordjevic, Lj. Nesic
BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction
A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN
Implementation of the Combined--Nonlinear Condensation Transformation
We discuss several applications of the recently proposed combined
nonlinear-condensation transformation (CNCT) for the evaluation of slowly
convergent, nonalternating series. These include certain statistical
distributions which are of importance in linguistics, statistical-mechanics
theory, and biophysics (statistical analysis of DNA sequences). We also discuss
applications of the transformation in experimental mathematics, and we briefly
expand on further applications in theoretical physics. Finally, we discuss a
related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press
On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source
In this paper, we develop an explicit formula allowing to compute the first k
moments of the random count of a pattern in a multi-states sequence generated
by a Markov source. We derive efficient algorithms allowing to deal both with
low or high complexity patterns and either homogeneous or heterogenous Markov
models. We then apply these results to the distribution of DNA patterns in
genomic sequences where we show that moment-based developments (namely:
Edgeworth's expansion and Gram-Charlier type B series) allow to improve the
reliability of common asymptotic approximations like Gaussian or Poisson
approximations
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