We consider the low-temperature thermodynamic and magnetic properties of an ideal gas of particles obeying a generic fermion-like fractional statistics. The coefficients of the Sommerfeld expansion are calculated in terms of the central moments of the derivative of the density of entropy with...

We calculate the Hurst exponent H(t) of several time series by dynamical implementation of a recently proposed scaling technique: the detrending moving average (DMA). In order to assess the accuracy of the technique, we calculate the exponent H(t) for artificial series, simulating monofractal...

We calculate the Shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long-range correlated clusters introduced in [A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69 (2004) 026105]. We define three different measures of the entropy...

The Hurst exponent H of long range correlated series can be estimated by means of the detrending moving average (DMA) method. The computational tool, on which the algorithm is based, is the generalized variance σDMA2=1/(N-n)∑i=nN[y(i)-y˜n(i)]2, with y˜n(i)=1/n∑k=0ny(i-k) being the average...

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...