194 research outputs found
Multifractal analyses of row sum signals of elementary cellular automata
We first apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial
multifractal time series of three different binomial parameters and find that
the WTMM method indicates an enhanced difference between the fractal components
than the known theoretical result. Next, we make use of the same methods for
the time series of the row sum signals of the two complementary ECA pairs of
rules (90,165) and (150,105) for ten initial conditions going from a single 1
in the central position up to a set of ten 1's covering the ten central
positions in the first row. Since the members of the pairs are actually similar
from the statistical point of view, we can check which method is the most
stable numerically by recording the differences provided by the methods between
the two members of the pairs for various important quantities of the scaling
analyses, such as the multifractal support, the most frequent Holder exponent,
and the Hurst exponent and considering as the better one the method that
provides the minimum differences. According to this criterion, our results show
that the MFDFA performs better than WT-MFDFA and WTMM in the case of the
multifractal support, while for the other two scaling parameters the WT-MFDFA
is the best. The employed set of initial conditions does not generate any
specific trend in the values of the multifractal parametersComment: 23 pages including an appendix and 11 figures, extended version
accepted for publication by Physica
Scaling analyses based on wavelet transforms for the Talbot effect
The fractal properties of the transverse Talbot images are analysed with two
well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the
wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We
use the widths of the singularity spectra, Delta alpha=alpha_H-alpha_min, as a
characteristic feature of these Talbot images. The tau scaling exponents of the
q moments are linear in q within the two methods, which proves the
monofractality of the transverse diffractive paraxial field in the case of
these imagesComment: 9 pages, 6 figures, version accepted at Physica
Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the
time series of the elementary cellular automata (ECA) for possible
(multi)fractal behavior. They eliminated the polynomial background at^b through
the direct fitting of the polynomial coefficients a and b. We here reconsider
their work eliminating the polynomial trend by means of the multifractal-based
detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution
property is employed to filter out the trend in a more speedy way than the
direct polynomial fitting and also with respect to the wavelet transform
modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet
transform is used to calculate the trend as a local feature that enters the
so-called details signal. We illustrate our result for three representative ECA
rules: 90, 105, and 150. We confirm their multifractal behavior and provide our
results for the scaling parametersComment: 8 pages, 5 figures, 21 reference
Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the
time series of the elementary cellular automata (ECA) for possible
(multi)fractal behavior. They eliminated the polynomial background at^b through
the direct fitting of the polynomial coefficients a and b. We here reconsider
their work eliminating the polynomial trend by means of the multifractal-based
detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution
property is employed to filter out the trend in a more speedy way than the
direct polynomial fitting and also with respect to the wavelet transform
modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet
transform is used to calculate the trend as a local feature that enters the
so-called details signal. We illustrate our result for three representative ECA
rules: 90, 105, and 150. We confirm their multifractal behavior and provide our
results for the scaling parametersComment: 8 pages, 5 figures, 21 reference
Talbot effect for dispersion in linear optical fibers and a wavelet approach
We shortly recall the mathematical and physical aspects of Talbot's
self-imaging effect occurring in near-field diffraction. In the rational
paraxial approximation, the Talbot images are formed at distances z=p/q, where
p and q are coprimes, and are superpositions of q equally spaced images of the
original binary transmission (Ronchi) grating. This interpretation offers the
possibility to express the Talbot effect through Gauss sums. Here, we pay
attention to the Talbot effect in the case of dispersion in optical fibers
presenting our considerations based on the close relationships of the
mathematical representations of diffraction and dispersion. Although dispersion
deals with continuous functions, such as gaussian and supergaussian pulses,
whereas in diffraction one frequently deals with discontinuous functions, the
mathematical correspondence enables one to characterize the Talbot effect in
the two cases with minor differences. In addition, we apply, for the first time
to our knowledge, the wavelet transform to the fractal Talbot effect in both
diffraction and fiber dispersion. In the first case, the self similar character
of the transverse paraxial field at irrational multiples of the Talbot distance
is confirmed, whereas in the second case it is shown that the field is not self
similar for supergaussian pulses. Finally, a high-precision measurement of
irrational distances employing the fractal index determined with the wavelet
transform is pointed outComment: 15 text pages + 7 gif figs, accepted at Int. J. Mod. Phys. B, final
version of a contribution at ICSSUR-Besancon (May/05). Color figs available
from the first autho
Improvement and analysis of a pseudo random bit generator by means of cellular automata
In this paper, we implement a revised pseudo random bit generator based on a
rule-90 cellular automaton. For this purpose, we introduce a sequence matrix
H_N with the aim of calculating the pseudo random sequences of N bits employing
the algorithm related to the automaton backward evolution. In addition, a
multifractal structure of the matrix H_N is revealed and quantified according
to the multifractal formalism. The latter analysis could help to disentangle
what kind of automaton rule is used in the randomization process and therefore
it could be useful in cryptanalysis. Moreover, the conditions are found under
which this pseudo random generator passes all the statistical tests provided by
the National Institute of Standards and Technology (NIST)Comment: 20 pages, 12 figure
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