1,825 research outputs found
The human ECG - nonlinear deterministic versus stochastic aspects
We discuss aspects of randomness and of determinism in electrocardiographic
signals. In particular, we take a critical look at attempts to apply methods of
nonlinear time series analysis derived from the theory of deterministic
dynamical systems. We will argue that deterministic chaos is not a likely
explanation for the short time variablity of the inter-beat interval times,
except for certain pathologies. Conversely, densely sampled full ECG recordings
possess properties typical of deterministic signals. In the latter case,
methods of deterministic nonlinear time series analysis can yield new insights.Comment: 6 pages, 9 PS figure
Nonlinear projective filtering I: Background in chaos theory
We derive a locally projective noise reduction scheme for nonlinear time
series using concepts from deterministic dynamical systems, or chaos theory. We
will demonstrate its effectiveness with an example with known deterministic
dynamics and discuss methods for the verification of the results in the case of
an unknown deterministic system.Comment: 4 pages, PS figures, needs nolta.st
Nonlinear time-series analysis revisited
In 1980 and 1981, two pioneering papers laid the foundation for what became
known as nonlinear time-series analysis: the analysis of observed
data---typically univariate---via dynamical systems theory. Based on the
concept of state-space reconstruction, this set of methods allows us to compute
characteristic quantities such as Lyapunov exponents and fractal dimensions, to
predict the future course of the time series, and even to reconstruct the
equations of motion in some cases. In practice, however, there are a number of
issues that restrict the power of this approach: whether the signal accurately
and thoroughly samples the dynamics, for instance, and whether it contains
noise. Moreover, the numerical algorithms that we use to instantiate these
ideas are not perfect; they involve approximations, scale parameters, and
finite-precision arithmetic, among other things. Even so, nonlinear time-series
analysis has been used to great advantage on thousands of real and synthetic
data sets from a wide variety of systems ranging from roulette wheels to lasers
to the human heart. Even in cases where the data do not meet the mathematical
or algorithmic requirements to assure full topological conjugacy, the results
of nonlinear time-series analysis can be helpful in understanding,
characterizing, and predicting dynamical systems
Nonlinear projective filtering I: Application to real time series
We discuss applications of nonlinear filtering of time series by locally
linear phase space projections. Noise can be reduced whenever the error due to
the manifold approximation is smaller than the noise in the system. Examples
include the real time extraction of the fetal electrocardiogram from abdominal
recordings.Comment: 4 pages, PS figures, needs nolta.st
Differential Landauer's principle
Landauer's principle states that the erasure of information must be a
dissipative process. In this paper, we carefully analyze the recording and
erasure of information on a physical memory. On the one hand, we show that in
order to record some information, the memory has to be driven out of
equilibrium. On the other hand, we derive a differential version of Landauer's
principle: We link the rate at which entropy is produced at every time of the
erasure process to the rate at which information is erased.Comment: 11 pages, 6 figure
Recurrence time analysis, long-term correlations, and extreme events
The recurrence times between extreme events have been the central point of
statistical analyses in many different areas of science. Simultaneously, the
Poincar\'e recurrence time has been extensively used to characterize nonlinear
dynamical systems. We compare the main properties of these statistical methods
pointing out their consequences for the recurrence analysis performed in time
series. In particular, we analyze the dependence of the mean recurrence time
and of the recurrence time statistics on the probability density function, on
the interval whereto the recurrences are observed, and on the temporal
correlations of time series. In the case of long-term correlations, we verify
the validity of the stretched exponential distribution, which is uniquely
defined by the exponent , at the same time showing that it is
restricted to the class of linear long-term correlated processes. Simple
transformations are able to modify the correlations of time series leading to
stretched exponentials recurrence time statistics with different ,
which shows a lack of invariance under the change of observables.Comment: 9 pages, 7 figure
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
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