Related papers: Multifractal characterisation of complete genomes
Statistical analysis of bacteria genomes texts has been performed on the basis of 20 complete genomes origin from Genebank. It has been revealed that the word ranked distributions are quite well approximated by logarithmic law. Results…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
Modern genomics experiments measure functional behaviors for many thousands of DNA sequences. We suggest that, especially when these sequences are chosen at random, it is natural to compute correlation functions between sequences and…
We propose a general and formal statistical framework for multiple tests of association between known fixed features of a genome and unknown parameters of the distribution of variable features of this genome in a population of interest. The…
Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the…
2D display is a fast and economical way of visualizing polymorphism and comparing genomes, which is based on the separation of DNA fragments in two steps, according first to their size and then to their sequence composition. In this paper,…
A rapid and low-cost method to sequence DNA would usher in a revolution in medicine. We propose and theoretically show the feasibility of a protocol for sequencing based on the distributions of transverse electrical currents of…
We show that every interval in the homomorphism order of finite undirected graphs is either universal or a gap. Together with density and universality this "fractal" property contributes to the spectacular properties of the homomorphism…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of…
Among the statistical models employed to approximate nonlinear interactions in biological and psychological processes, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, a…
From a mathematical and statistical point of view, a segment of a DNA strand can be viewed as a sequence of four-state (A, C, G, T) trials. We consider distributions of runs and patterns related to run lengths of multi-state sequences,…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…