1,000 research outputs found
Detrended fluctuation analysis for fractals and multifractals in higher dimensions
One-dimensional detrended fluctuation analysis (1D DFA) and multifractal
detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling
analysis of fractal and multifractal time series because of being accurate and
easy to implement. In this paper we generalize the one-dimensional DFA and
MF-DFA to higher-dimensional versions. The generalization works well when
tested with synthetic surfaces including fractional Brownian surfaces and
multifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze
two images from nature and experiment and nice scaling laws are unraveled.Comment: 7 Revtex pages inluding 11 eps figure
Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks
In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity
spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and
scaling functions, and methods used in their determination by means of Wavelet Transform Modulus
Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum
are presented. A method based on multifractal data analysis at network layer level by means of WTMM
is proposed for the detection of traffic anomalies in computer and telecommunication networks. The
chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimen-
sions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum
parameters is proposed for estimating queuing performance for the generalized multifractal traffic on
the input of a buffering device. It is shown that the multifractal character of traffic has significant impact
on queuing performance characteristics
On Multifractal Structure in Non-Representational Art
Multifractal analysis techniques are applied to patterns in several abstract
expressionist artworks, paintined by various artists. The analysis is carried
out on two distinct types of structures: the physical patterns formed by a
specific color (``blobs''), as well as patterns formed by the luminance
gradient between adjacent colors (``edges''). It is found that the analysis
method applied to ``blobs'' cannot distinguish between artists of the same
movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8.
The method can distinguish between different types of images, however, as
demonstrated by studying a radically different type of art. The data suggests
that the ``edge'' method can distinguish between artists in the same movement,
and is proposed to represent a toy model of visual discrimination. A ``fractal
reconstruction'' analysis technique is also applied to the images, in order to
determine whether or not a specific signature can be extracted which might
serve as a type of fingerprint for the movement. However, these results are
vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps
Parameters of the Magnetic Flux inside Coronal Holes
Parameters of magnetic flux distribution inside low-latitude coronal holes
(CHs) were analyzed. A statistical study of 44 CHs based on Solar and
Heliospheric Observatory (SOHO)/MDI full disk magnetograms and SOHO/EIT 284\AA
images showed that the density of the net magnetic flux, , does
not correlate with the associated solar wind speeds, . Both the area and
net flux of CHs correlate with the solar wind speed and the corresponding
spatial Pearson correlation coefficients are 0.75 and 0.71, respectively. A
possible explanation for the low correlation between and
is proposed. The observed non-correlation might be rooted in the structural
complexity of the magnetic field. As a measure of complexity of the magnetic
field, the filling factor, , was calculated as a function of spatial
scales. In CHs, was found to be nearly constant at scales above 2 Mm,
which indicates a monofractal structural organization and smooth temporal
evolution. The magnitude of the filling factor is 0.04 from the Hinode SOT/SP
data and 0.07 from the MDI/HR data. The Hinode data show that at scales smaller
than 2 Mm, the filling factor decreases rapidly, which means a mutlifractal
structure and highly intermittent, burst-like energy release regime. The
absence of necessary complexity in CH magnetic fields at scales above 2 Mm
seems to be the most plausible reason why the net magnetic flux density does
not seem to be related to the solar wind speed: the energy release dynamics,
needed for solar wind acceleration, appears to occur at small scales below 1
Mm.Comment: 6 figures, approximately 23 pages. Accepted in Solar Physic
Multiscale Fractal Descriptors Applied to Nanoscale Images
This work proposes the application of fractal descriptors to the analysis of
nanoscale materials under different experimental conditions. We obtain
descriptors for images from the sample applying a multiscale transform to the
calculation of fractal dimension of a surface map of such image. Particularly,
we have used the}Bouligand-Minkowski fractal dimension. We applied these
descriptors to discriminate between two titanium oxide films prepared under
different experimental conditions. Results demonstrate the discrimination power
of proposed descriptors in such kind of application
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