We study long-range correlations and trends in time series extracted from the data of seismic events occurred from 1973 to 2011 in a rectangular region that contains mainly all the continental part of Colombia. The long-range correlations are detected by the calculation of the Hurst exponents...

Healthy sleep can be characterized by several stages: deep sleep, light sleep, and REM sleep. Here we show that these sleep stages lead to different autonomic regulation of breathing. Using the detrended fluctuation analysis up to the fourth order we find that breath-to-breath intervals and...

We review the present status of the studies of DNA sequences using methods of statistical physics. We present evidence, based on systematic studies of the entire GenBank database, supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the...

We examine the detrended fluctuation analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling which appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method...

We use the wavelet transform to explore the complexity of DNA sequences. Long-range correlations are clearly identified and shown to be related to the sequence GC content. The significance of this observation to gene evolution is discussed.

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations;...

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested...

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...