Over the periods 1998-2002 and 2009-2011, the S&P-500 Index went from persistence to anti-persistence mode, as measured by the Hurst index H. To uncover the reasons that characterize such a change, this paper uses a simple method that consists in treating quasi self-similar segments of the Index...

Three distinct methods, namely, the spectral density, the multifractal random walk approach, and the multifractal detrended fluctuation analysis are utilized to study the properties of four distinct types of well logs from three oil and gas fields, namely, the natural gamma ray emission, neutron...

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 the other half. This is due to the inverse bilateral...

We discuss a family of clusters C corresponding to the region whose boundary is formed by a fractional Brownian path y(i) and by the moving average function yn(i)≡1n∑k=0n−1y(i−k). Our model generates fractal directed patterns showing spatio-temporal complexity, and we demonstrate that...

After a brief introduction we review the nonperturbative weak noise approach to the Kardar–Parisi–Zhang (KPZ) equation in one dimension. We argue that the strong coupling aspects of the KPZ equation are related to the existence of localized propagating domain walls or solitons representing...

The multifractal dimensionality Dq as a function of q expresses the distribution of measure over space. When all the moments scale with resolution in exactly the same way, we have a flat spectrum, and a single monofractal dimensionality. We argue that for multifractal spectra the scaling of the...