In this research the Hurst exponent <i>H</i> is used for quantifying the fractal features of LANDSAT images. The Hurst exponent is estimated by means of the Detrending Moving Average (DMA), an algorithm based on a generalized high-dimensional variance around a moving average low-pass filter. Hence, for a <i>two</i>-dimensional signal, the algorithm first generates an average response for different subarrays by varying the size of the moving low-pass filter. For each subarray the corresponding variance value is calculated by the difference between the original and the averaged signals. The value of the variance obtained at each subarray is then plotted on log-log axes, with the slope of the regression line corresponding to the Hurst exponent. The application of the algorithm to a set of LANDSAT imagery has allowed us to estimate the Hurst exponent of specific areas on Earth surface at subsequent time instances. According to the presented results, the value of the Hurst exponent is directly related to the changes in land use, showing a decreasing value when the area under study has been modified by natural processes or human intervention. Interestingly, natural areas presenting a gradual growth of man made activities or an increasing degree of pollution have a considerable reduction in their corresponding Hurst exponent.
The fractal properties of the clusters corresponding to the regions whose contour is a fractional brownian path have been extensively investigated. The clusters form a stationary sequence, which has been characterized by analyzing the <i>length</i>, the <i>lifetime</i> and the <i>area</i> of the single cluster. The rich fractal structure of the patterns has allowed to determine the time dependent Hurst exponent with great accuracy. We have also demonstrated that the cluster <i>area</i>, <i>length</i> and <i>lifetime</i> exhibit the characteristic scaling behavior of systems evolving through self-organized critical states.
The photocurrent noise has been investigated in Quantum Well
Infrared Photodetectors (QWIPs) having identical growth sequence,
layer width and composition, but different number of wells. It has
been found that the power spectral density exhibits characteristic
features related to the discrete structure of the device. This
behavior might be caused by the strong potential nonuniformity
arising as a consequence of the imbalance between the current
injected at the emitter and the stream of photoelectrons drifting
through the structure, which is also responsible for the anomalies
in the steady-state and transient photoconductivity. In the
present work, we will add further evidence to our preliminary
study by presenting results of the power spectral density obtained
by numerical solution of the continuity equation of the electrons
in the continuum state, with a discrete distribution of the
electric field in the active region, instead of the homogeneous one valid for conventional photodetectors.
Long-range correlation properties of financial stochastic time
series <i>y</i> have been investigated with the main aim to
demonstrate the ability of a recently proposed method to extract
the scaling parameters of a stochastic series. According to this
technique, the Hurst coefficient <i>H</i> is calculated by means of
the following function: EQUATION where <i>y</i><sub>n</sub>(<i>i</i>)is the moving average of <i>y</i>(<i>i</i>), defined as EQUATION the moving average window and <i>N</i><sub>max</sub> is the dimension of the stochastic series.
The method is called <i>Detrending Moving Average Analysis</i> (DMA) on account of the several analogies with the well-known <i>Detrended Fluctuation Analysis</i> (DFA). The DMA technique has been
widely tested on stochastic series with assigned <i>H</i> generated by
suitable algorithms. It has been demonstrated that the ability of
the proposed technique relies on very general grounds: the
function EQUATION generates indeed a sequence of clusters with power-law distribution of amplitudes and lifetimes. In particular the exponent of the distribution of cluster lifetime varies as the fractal dimension 2 - <i>H</i> of the series, as expected on the basis of the box-counting method. In the present paper we will report on the scaling coefficients of real data series (the BOBL and DAX German future) calculated by the DMA technique.