322 research outputs found
Fractal Descriptors in the Fourier Domain Applied to Color Texture Analysis
The present work proposes the development of a novel method to provide
descriptors for colored texture images. The method consists in two steps. In
the first, we apply a linear transform in the color space of the image aiming
at highlighting spatial structuring relations among the color of pixels. In a
second moment, we apply a multiscale approach to the calculus of fractal
dimension based on Fourier transform. From this multiscale operation, we
extract the descriptors used to discriminate the texture represented in digital
images. The accuracy of the method is verified in the classification of two
color texture datasets, by comparing the performance of the proposed technique
to other classical and state-of-the-art methods for color texture analysis. The
results showed an advantage of almost 3% of the proposed technique over the
second best approach.Comment: Chaos, Volume 21, Issue 4, 201
Levy distribution and long correlation times in supermarket sales
Sales data in a commodity market (supermarket sales to consumers) has been
analysed by studying the fluctuation spectrum and noise correlations. Three
related products (ketchup, mayonnaise and curry sauce) have been analysed. Most
noise in sales is caused by promotions, but here we focus on the fluctuations
in baseline sales. These characterise the dynamics of the market. Four hitherto
unnoticed effects have been found that are difficult to explain from simple
econometric models. These effects are: (1) the noise level in baseline sales is
much higher than can be expected for uncorrelated sales events; (2) weekly
baseline sales differences are distributed according to a broad non-Gaussian
function with fat tails; (3) these fluctuations follow a Levy distribution of
exponent alpha = 1.4, similar to financial exchange markets and in stock
markets; and (4) this noise is correlated over a period of 10 to 11 weeks, or
shows an apparent power law spectrum. The similarity to stock markets suggests
that models developed to describe these markets may be applied to describe the
collective behaviour of consumers.Comment: 19 pages, 7 figures, accepted for publication in Physica
The meta book and size-dependent properties of written language
Evidence is given for a systematic text-length dependence of the power-law
index gamma of a single book. The estimated gamma values are consistent with a
monotonic decrease from 2 to 1 with increasing length of a text. A direct
connection to an extended Heap's law is explored. The infinite book limit is,
as a consequence, proposed to be given by gamma = 1 instead of the value
gamma=2 expected if the Zipf's law was ubiquitously applicable. In addition we
explore the idea that the systematic text-length dependence can be described by
a meta book concept, which is an abstract representation reflecting the
word-frequency structure of a text. According to this concept the
word-frequency distribution of a text, with a certain length written by a
single author, has the same characteristics as a text of the same length pulled
out from an imaginary complete infinite corpus written by the same author.Comment: 7 pages, 6 figures, 1 tabl
Are European equity markets efficient? New evidence from fractal analysis
We report an empirical analysis of long-range dependence in the returns of eight stock market indices, using the Rescaled Range Analysis (RRA) to estimate the Hurst exponent. Monte Carlo and bootstrap simulations are used to construct critical values for the null hypothesis of no long-range dependence. The issue of disentangling short-range and long-range dependence is examined. Pre-filtering by fitting a (short-range) autoregressive model eliminates part of the long-range dependence when the latter is present, while failure to pre-filter leaves open the possibility of conflating short-range and long-range dependence. There is a strong evidence of long-range dependence for the small central European Czech stock market index PX-glob, and a weaker evidence for two smaller western European stock market indices, MSE (Spain) and SWX (Switzerland). There is little or no evidence of long-range dependence for the other five indices, including those with the largest capitalizations among those considered, DJIA (US) and FTSE350 (UK). These results are generally consistent with prior expectations concerning the relative efficiency of the stock markets examined
Spontaneous symmetry breaking in amnestically induced persistence
We investigate a recently proposed non-Markovian random walk model
characterized by loss of memories of the recent past and amnestically induced
persistence. We report numerical and analytical results showing the complete
phase diagram, consisting of 4 phases, for this system: (i) classical
nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence
and (iv) log-periodic persistence driven by negative feedback. The first two
phases possess continuous scale invariance symmetry, however log-periodicity
breaks this symmetry. Instead, log-periodic motion satisfies discrete scale
invariance symmetry, with complex rather than real fractal dimensions. We find
for log-periodic persistence evidence not only of statistical but also of
geometric self-similarity.Comment: 4 pages, 2 color fig
Amnestically induced persistence in random walks
We study how the Hurst exponent depends on the fraction of the
total time remembered by non-Markovian random walkers that recall only the
distant past. We find that otherwise nonpersistent random walkers switch to
persistent behavior when inflicted with significant memory loss. Such memory
losses induce the probability density function of the walker's position to
undergo a transition from Gaussian to non-Gaussian. We interpret these findings
of persistence in terms of a breakdown of self-regulation mechanisms and
discuss their possible relevance to some of the burdensome behavioral and
psychological symptoms of Alzheimer's disease and other dementias.Comment: 4 pages, 3 figs, subm. to Phys. Rev. Let
The rate of entropy increase at the edge of chaos
Under certain conditions, the rate of increase of the statistical entropy of
a simple, fully chaotic, conservative system is known to be given by a single
number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This
connection is here generalized to a simple dissipative system, the logistic
map, and especially to the chaos threshold of the latter, the edge of chaos. It
is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon
entropy is not appropriate. Instead, the non-extensive entropy , must be used. The latter contains a
parameter q, the entropic index which must be given a special value
(for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos
under consideration. The same q^* enters also in the description of the
sensitivity to initial conditions, as well as in that of the multifractal
spectrum of the attractor.Comment: 6 pages, Latex, 4 figures included, final version accepted for
publication in Physics Letters
How a plantar pressure-based, tongue-placed tactile biofeedback modifies postural control mechanisms during quiet standing
The purpose of the present study was to determine the effects of a plantar
pressure-based, tongue-placed tactile biofeedback on postural control
mechanisms during quiet standing. To this aim, sixteen young healthy adults
were asked to stand as immobile as possible with their eyes closed in two
conditions of No-biofeedback and Biofeedback. Centre of foot pressure (CoP)
displacements, recorded using a force platform, were used to compute the
horizontal displacements of the vertical projection the centre of gravity
(CoGh) and those of the difference between the CoP and the vertical projection
of the CoG (CoP-CoGv). Altogether, the present findings suggest that the main
way the plantar pressure-based, tongue-placed tactile biofeedback improves
postural control during quiet standing is via both a reduction of the
correction thresholds and an increased efficiency of the corrective mechanism
involving the CoGh displacements
Identifying financial crises in real time
Following the thermodynamic formulation of multifractal measure that was
shown to be capable of detecting large fluctuations at an early stage, here we
propose a new index which permits us to distinguish events like financial
crisis in real time . We calculate the partition function from where we obtain
thermodynamic quantities analogous to free energy and specific heat. The index
is defined as the normalized energy variation and it can be used to study the
behavior of stochastic time series, such as financial market daily data. Famous
financial market crashes - Black Thursday (1929), Black Monday (1987) and
Subprime crisis (2008) - are identified with clear and robust results. The
method is also applied to the market fluctuations of 2011. From these results
it appears as if the apparent crisis of 2011 is of a different nature from the
other three. We also show that the analysis has forecasting capabilities.Comment: 8 pages, 6 figure
The origin of power-law distributions in deterministic walks: the influence of landscape geometry
We investigate the properties of a deterministic walk, whose locomotion rule
is always to travel to the nearest site. Initially the sites are randomly
distributed in a closed rectangular ( landscape and, once
reached, they become unavailable for future visits. As expected, the walker
step lengths present characteristic scales in one () and two () dimensions. However, we find scale invariance for an intermediate
geometry, when the landscape is a thin strip-like region. This result is
induced geometrically by a dynamical trapping mechanism, leading to a power law
distribution for the step lengths. The relevance of our findings in broader
contexts -- of both deterministic and random walks -- is also briefly
discussed.Comment: 7 pages, 11 figures. To appear in Phys. Rev.
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