516 research outputs found
Continuous-time random walk theory of superslow diffusion
Superslow diffusion, i.e., the long-time diffusion of particles whose
mean-square displacement (variance) grows slower than any power of time, is
studied in the framework of the decoupled continuous-time random walk model. We
show that this behavior of the variance occurs when the complementary
cumulative distribution function of waiting times is asymptotically described
by a slowly varying function. In this case, we derive a general representation
of the laws of superslow diffusion for both biased and unbiased versions of the
model and, to illustrate the obtained results, consider two particular classes
of waiting-time distributions.Comment: 4 page
Limiting distributions of continuous-time random walks with superheavy-tailed waiting times
We study the long-time behavior of the scaled walker (particle) position
associated with decoupled continuous-time random walk which is characterized by
superheavy-tailed distribution of waiting times and asymmetric heavy-tailed
distribution of jump lengths. Both the scaling function and the corresponding
limiting probability density are determined for all admissible values of tail
indexes describing the jump distribution. To analytically investigate the
limiting density function, we derive a number of different representations of
this function and, by this way, establish its main properties. We also develop
an efficient numerical method for computing the limiting probability density
and compare our analytical and numerical results.Comment: 35 pages, 4 figure
First Amendment; Freedom of Speech; Commerical Speech and Advertising; Metpath, Inc. v. Imperato
The decision of Metpath, Inc. v. Imperato is indicative of the growing trend of the judiciary toward affording commercial speech the protective shield of the first amendment. As shown by Metpath, where the concern is advertising by a medical clinic, speech with commercial overtones is afforded protection where a public interest in the subject and content of the speech is demonstrated. However, the perimeters of such protection have not been defined by this or previous decisions
How does the quality of a prediction depend on the magnitude of the events under study?
We investigate the predictability of extreme events in time series. The focus of this work is to understand, under which circumstances large events are better predictable than smaller events. Therefore we use a simple prediction algorithm based on precursory structures which are identified via the maximum likelihood principle. Using theses precursory structures we predict threshold crossings in autocorrelated processes of order one, which are either Gaussian, exponentially or Pareto distributed. The receiver operating characteristic curve is used as a measure for the quality of predictions we find that the dependence on the event magnitude is closely linked to the probability distribution function of the underlying stochastic process. We evaluate this dependence on the probability distribution function numerically and in the Gaussian case also analytically. Furthermore, we study predictions of threshold crossings in correlated data, i.e., velocity increments of a free jet flow. The velocity increments in the free jet flow are in dependence on the time scale either asymptotically Gaussian or asymptotically exponential distributed. If we assume that the optimal precursory structures are used to make the predictions, we find that large threshold crossings are for all different types of distributions better predictable. These results are in contrast to previous results, obtained for the prediction of large increments, which showed a strong dependence on the probability distribution function of the underlying process
Directed transport in periodically rocked random sawtooth potentials
We study directed transport of overdamped particles in a periodically rocked
random sawtooth potential. Two transport regimes can be identified which are
characterized by a nonzero value of the average velocity of particles and a
zero value, respectively. The properties of directed transport in these regimes
are investigated both analytically and numerically in terms of a random
sawtooth potential and a periodically varying driving force. Precise conditions
for the occurrence of transition between these two transport regimes are
derived and analyzed in detail.Comment: 18 pages, 7 figure
Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers
It is shown that correlation function of the mean wind velocity generated by
a turbulent thermal convection (Rayleigh number ) exhibits
exponential decay with a very long correlation time, while corresponding
largest Lyapunov exponent is certainly positive. These results together with
the reconstructed phase portrait indicate presence of chaotic component in the
examined mean wind. Telegraph approximation is also used to study relative
contribution of the chaotic and stochastic components to the mean wind
fluctuations and an equilibrium between these components has been studied in
detail
Continuous-time random walk with a superheavy-tailed distribution of waiting times
We study the long-time behavior of the probability density associated with
the decoupled continuous-time random walk which is characterized by a
superheavy-tailed distribution of waiting times. It is shown that if the random
walk is unbiased (biased) and the jump distribution has a finite second moment
then the properly scaled probability density converges in the long-time limit
to a symmetric two-sided (an asymmetric one-sided) exponential density. The
convergence occurs in such a way that all the moments of the probability
density grow slower than any power of time. As a consequence, the reference
random walk can be viewed as a generic model of superslow diffusion. A few
examples of superheavy-tailed distributions of waiting times that give rise to
qualitatively different laws of superslow diffusion are considered.Comment: 7 page
Transition from phase to generalized synchronization in time-delay systems
The notion of phase synchronization in time-delay systems, exhibiting highly
non-phase-coherent attractors, has not been realized yet even though it has
been well studied in chaotic dynamical systems without delay. We report the
identification of phase synchronization in coupled nonidentical piece-wise
linear and in coupled Mackey-Glass time-delay systems with highly
non-phase-coherent regimes. We show that there is a transition from
non-synchronized behavior to phase and then to generalized synchronization as a
function of coupling strength. We have introduced a transformation to capture
the phase of the non-phase coherent attractors, which works equally well for
both the time-delay systems. The instantaneous phases of the above coupled
systems calculated from the transformed attractors satisfy both the phase and
mean frequency locking conditions. These transitions are also characterized in
terms of recurrence based indices, namely generalized autocorrelation function
, correlation of probability of recurrence (CPR), joint probability of
recurrence (JPR) and similarity of probability of recurrence (SPR). We have
quantified the different synchronization regimes in terms of these indices. The
existence of phase synchronization is also characterized by typical transitions
in the Lyapunov exponents of the coupled time-delay systems.Comment: Accepted for publication in CHAO
How to avoid potential pitfalls in recurrence plot based data analysis
Recurrence plots and recurrence quantification analysis have become popular
in the last two decades. Recurrence based methods have on the one hand a deep
foundation in the theory of dynamical systems and are on the other hand
powerful tools for the investigation of a variety of problems. The increasing
interest encompasses the growing risk of misuse and uncritical application of
these methods. Therefore, we point out potential problems and pitfalls related
to different aspects of the application of recurrence plots and recurrence
quantification analysis
Surrogate-assisted network analysis of nonlinear time series
The performance of recurrence networks and symbolic networks to detect weak
nonlinearities in time series is compared to the nonlinear prediction error.
For the synthetic data of the Lorenz system, the network measures show a
comparable performance. In the case of relatively short and noisy real-world
data from active galactic nuclei, the nonlinear prediction error yields more
robust results than the network measures. The tests are based on surrogate data
sets. The correlations in the Fourier phases of data sets from some surrogate
generating algorithms are also examined. The phase correlations are shown to
have an impact on the performance of the tests for nonlinearity.Comment: 9 pages, 5 figures, Chaos
(http://scitation.aip.org/content/aip/journal/chaos), corrected typo
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