360 research outputs found
Improvement of speech recognition by nonlinear noise reduction
The success of nonlinear noise reduction applied to a single channel
recording of human voice is measured in terms of the recognition rate of a
commercial speech recognition program in comparison to the optimal linear
filter. The overall performance of the nonlinear method is shown to be
superior. We hence demonstrate that an algorithm which has its roots in the
theory of nonlinear deterministic dynamics possesses a large potential in a
realistic application.Comment: see urbanowicz.org.p
Dynamical estimates of chaotic systems from Poincar\'e recurrences
We show that the probability distribution function that best fits the
distribution of return times between two consecutive visits of a chaotic
trajectory to finite size regions in phase space deviates from the exponential
statistics by a small power-law term, a term that represents the deterministic
manifestation of the dynamics, which can be easily experimentally detected and
theoretically estimated. We also provide simpler and faster ways to calculate
the positive Lyapunov exponents and the short-term correlation function by
either realizing observations of higher probable returns or by calculating the
eigenvalues of only one very especial unstable periodic orbit of low-period.
Finally, we discuss how our approaches can be used to treat data coming from
complex systems.Comment: subm. for publication. Accepted fpr publication in Chao
Moses, Noah and Joseph effects in Levy walks
We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the 'Joseph effect' (Mandelbrot and Wallis 1968 Water Resour. Res.4 909), fat-tails of the increment probability density lead to a 'Noah effect' (Mandelbrot and Wallis 1968 Water Resour. Res.4 909), and non-stationarity, to the 'Moses effect' (Chen et al 2017 Phys. Rev. E 95 042141). After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled Levy walk, compare our results to theoretical predictions, and discuss the generality of the method
Generalized (m,k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend
We have translated fractional Brownian motion (FBM) signals into a text based
on two ''letters'', as if the signal fluctuations correspond to a constant
stepsize random walk. We have applied the Zipf method to extract the
exponent relating the word frequency and its rank on a log-log plot. We have
studied the variation of the Zipf exponent(s) giving the relationship between
the frequency of occurrence of words of length made of such two letters:
is varying as a power law in terms of . We have also searched how
the exponent of the Zipf law is influenced by a linear trend and the
resulting effect of its slope. We can distinguish finite size effects, and
results depending whether the starting FBM is persistent or not, i.e. depending
on the FBM Hurst exponent . It seems then numerically proven that the Zipf
exponent of a persistent signal is more influenced by the trend than that of an
antipersistent signal. It appears that the conjectured law
only holds near . We have also introduced considerations based on the
notion of a {\it time dependent Zipf law} along the signal.Comment: 24 pages, 12 figures; to appear in Int. J. Modern Phys
The backbone of the climate network
We propose a method to reconstruct and analyze a complex network from data
generated by a spatio-temporal dynamical system, relying on the nonlinear
mutual information of time series analysis and betweenness centrality of
complex network theory. We show, that this approach reveals a rich internal
structure in complex climate networks constructed from reanalysis and model
surface air temperature data. Our novel method uncovers peculiar wave-like
structures of high energy flow, that we relate to global surface ocean
currents. This points to a major role of the oceanic surface circulation in
coupling and stabilizing the global temperature field in the long term mean
(140 years for the model run and 60 years for reanalysis data). We find that
these results cannot be obtained using classical linear methods of multivariate
data analysis, and have ensured their robustness by intensive significance
testing.Comment: 6 pages, 5 figure
Analysis of a Japan government intervention on the domestic agriculture market
We investigate an economic system in which one large agent - the Japan
government changes the environment of numerous smaller agents - the Japan
agriculture producers by indirect regulation of prices of agriculture goods.
The reason for this intervention was that before the oil crisis in 1974 Japan
agriculture production prices exhibited irregular and large amplitude changes.
By means of analysis of correlations and a combination of singular spectrum
analysis (SSA), principal component analysis (PCA), and time delay phase space
construction (TDPSC) we study the influence of the government measures on the
domestic piglet prices and production in Japan. We show that the government
regulation politics was successful and leaded (i) to a decrease of the
nonstationarities and to increase of predictability of the piglet price; (ii)
to a coupling of the price and production cycles; (iii) to increase of
determinism of the dynamics of the fluctuations of piglet price around the year
average price. The investigated case is an example confirming the thesis that a
large agent can change in a significant way the environment of the small agents
in complex (economic or financial) systems which can be crucial for their
survival or extinction.Comment: 10 pages, 6 figures presented at APFA5, Torino, Italy,
29.06-01.07.200
Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions
We study the long-time behavior of decoupled continuous-time random walks
characterized by superheavy-tailed distributions of waiting times and symmetric
heavy-tailed distributions of jump lengths. Our main quantity of interest is
the limiting probability density of the position of the walker multiplied by a
scaling function of time. We show that the probability density of the scaled
walker position converges in the long-time limit to a non-degenerate one only
if the scaling function behaves in a certain way. This function as well as the
limiting probability density are determined in explicit form. Also, we express
the limiting probability density which has heavy tails in terms of the Fox
-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur
Nonperiodic Oscillations of Pressure in a Spark Ignition Engine
We report our results on non-periodic experimental time series of pressure in
a spark ignition engine. The experiments were performed for a low rotational
velocity of a crankshaft and a relatively large spark advance angle. We show
that the combustion process has many chaotic features. Surprisingly, the
reconstructed attractor has a characteristic butterfly shape similar to a
chaotic attractor of Lorentz type. The suitable recurrence plot shows that the
dynamics of the combustion is a nonlinear multidimensional process mediated by
stochastic noise.Comment: Latex, 6 pages, 5 figure
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