The statistical properties of the size distribution of DNA segments separating identical oligonucleotides are studied. For representative eukaryotes (Homo sapiens, Mus musculus, Saccharomyces cereviciae, Oryza sativa, Arabidopsis thaliana) we have demonstrated the existence of long-range...

In the given paper, we consider the scaling features of long letter sequences like human writings, discretized images and discretized financial data. Using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate...

Arrival sequences for several marathon races, including New York City and Chicago ones, have been analyzed using an internet freely available database. By means of the Allan factor statistics, time-clustering phenomena has been detected in the sequence and this indicates that at certain time...

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 function-based multifractal formalism, and prove that both...

This article shows numerically that the variance of the stretching exponents for two-dimensional chaotic area-preserving systems grows asymptotically as a linear function of time, although an intermediate anomalous power-law scaling may occur. This implies that the autocorrelation function of...

We have analyzed third position in codons and have observed strong long-range correlations along DNA sequence. We have shown that the correlations are caused mostly by asymmetric replication. In the analysis, we have used a DNA walk (spider analysis Cebrat et al., Microbial Comparative Genomics...

We study the localization of electronic wave functions in the one-dimensional Anderson model with diagonal disorder, where the site energies are long-range correlated. We find different behavior at the band edge and at the band center. Close to the band edge, the correlations lead to a decrease...

We introduce and develop new techniques to quantify DNA patchiness, and characteristics of their mosaic structure. These techniques, which involve calculating two functions, α(ℓ) and β(ℓ), measure correlation exponents at length scale ℓ and detect distinct characteristic patch sizes...

Multifractal random walks (MRW) correspond to simple solvable “stochastic volatility” processes. Moreover, they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that they are able to...

We have studied the stimulated discharge dynamics of fusimotor neurons by applying the wavelet transform technique and by adopting that the neuronal discharge dynamics is manifested by the random time series of interspike intervals. We found two different power-law type behaviors along...