Related papers: Multifractal analysis of DNA walks and trails
The multifractal detrended fluctuation analysis of time series is able to reveal the presence of long-range correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the…
The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested…
In this paper we treat some fractal and statistical features of the DNA sequences. First, a fractal record model of DNA sequence is proposed by mapping DNA sequences to integer sequences, followed by R/S analysis of the model and…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
This paper develops a theory for characterisation of DNA sequences based on their measure representation. The measures are shown to be random cascades generated by an infinitely divisible distribution. This probability distribution is…
We introduce a simple model for DNA evolution. Using the method of Peng et al.$^1$, we investigate the fractal properties of the system. For small chains and chains of intermediate size we find a fractal exponent that indicates the…
We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are…
Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation…
We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the…
This paper examines two methods for finding whether long-range correlations exist in DNA: a fractal measure and a mutual information technique. We evaluate the performance and implications of these methods in detail. In particular we…
Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
With the help of one-dimensional random Potts-like model we study the origins of fine structure observed on differential melting profiles of double-stranded DNA. We assess the effects of sequence arrangement on DNA melting curves through…
A theory is presented of the longitudinal dispersion of DNA under equilibrium confined in a nanochannel. Orientational fluctuations of the DNA chain build up to give rise to substantial fluctuations of the coil in the longitudinal direction…
In this paper, we review the literature on statistical long-range correlation in DNA sequences. We examine the current evidence for these correlations, and conclude that a mixture of many length scales (including some relatively long ones)…
Herein it is shown that in order to study the statistical properties of DNA sequences in bacterial chromosomes it suffices to consider only one half of the chromosome because they are similar to its corresponding complementary sequence in…
We study statistical properties of DNA chains of thirteen microbial complete genomes. We find that the power spectrum of several of the sequences studied flattens off in the low frequency limit. This implies that the correlation length in…
The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available…
The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a…