1,754 research outputs found
Parametric, nonparametric and parametric modelling of a chaotic circuit time series
The determination of a differential equation underlying a measured time
series is a frequently arising task in nonlinear time series analysis. In the
validation of a proposed model one often faces the dilemma that it is hard to
decide whether possible discrepancies between the time series and model output
are caused by an inappropriate model or by bad estimates of parameters in a
correct type of model, or both. We propose a combination of parametric
modelling based on Bock's multiple shooting algorithm and nonparametric
modelling based on optimal transformations as a strategy to test proposed
models and if rejected suggest and test new ones. We exemplify this strategy on
an experimental time series from a chaotic circuit where we obtain an extremely
accurate reconstruction of the observed attractor.Comment: 19 pages, 8 Fig
Tempting long-memory - on the interpretation of DFA results
We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than Ī±=0.5 for large scales does not necessarily imply long-memory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously
Cessation of X-ray Pulsation of GX 1+4
We report results from our weekly monitoring campaign on the X-ray pulsar GX
1+4 with the {\em Rossi X-ray Timing Explorer} satellite. The spin-down trend
of GX 1+4 was continuing, with the pulsar being at its longest period ever
measured (about 138.7 s). At the late stage of the campaign, the source entered
an extended faint state, when its X-ray (2-60 keV) flux decreased significantly
to an average level of . It was
highly variable in the faint state; the flux dropped to as low as . In several observations during this
period, the X-ray pulsation became undetectable. We can, therefore, conclude
conservatively that the pulsed fraction, which is normally 70%
(peak-to-peak), must have decreased drastically in those cases. This is very
similar to what was observed of GX 1+4 in 1996 when it became similarly faint
in X-ray. In fact, the flux at which the cessation of X-ray pulsation first
occurred is nearly the same as it was in 1996. We suggest that we have, once
again, observed the propeller effect in GX 1+4, a phenomenon that is predicted
by theoretical models of accreting X-ray pulsars.Comment: 13 pages, 9 figures (available at
http://www.physics.purdue.edu/~cui/ftp/cuifigs.tar.gz). To appear in Ap
Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1
We analyze the variability in the X-ray lightcurves of the black hole
candidate Cygnus X-1 by linear and nonlinear time series analysis methods.
While a linear model describes the over-all second order properties of the
observed data well, surrogate data analysis reveals a significant deviation
from linearity. We discuss the relation between shot noise models usually
applied to analyze these data and linear stochastic autoregressive models. We
debate statistical and interpretational issues of surrogate data testing for
the present context. Finally, we suggest a combination of tools from linear
andnonlinear time series analysis methods as a procedure to test the
predictions of astrophysical models on observed data.Comment: 15 pages, to appear in Phys. Rev.
Phase synchronization from noisy univariate signals
We present methods for detecting phase synchronization of two
unidirectionally coupled, self-sustained noisy oscillators from a signal of the
driven oscillator alone. One method detects soft, another hard phase locking.
Both are applied to the problem of detecting phase synchronization in von
Karman vortex flow meters.Comment: 4 pages, 4 figure
Disorder-Induced Shift of Condensation Temperature for Dilute Trapped Bose Gases
We determine the leading shift of the Bose-Einstein condensation temperature
for an ultracold dilute atomic gas in a harmonic trap due to weak disorder by
treating both a Gaussian and a Lorentzian spatial correlation for the quenched
disorder potential. Increasing the correlation length from values much smaller
than the geometric mean of the trap scale and the mean particle distance to
much larger values leads first to an increase of the positive shift to a
maximum at this critical length scale and then to a decrease.Comment: Author information under
http://www.theo-phys.uni-essen.de/tp/ags/pelster_di
Correlated X-ray and Optical Variability in Mkn 509
We present results of a 3 year monitoring campaign of the Seyfert 1 galaxy
Markarian 509, using X-ray data from the Rossi X-ray Timing Explorer (RXTE) and
optical data taken by the SMARTS consortium. Both light curves show significant
variations, and are strongly correlated with the optical flux leading the X-ray
flux by 15 days. The X-ray power spectrum shows a steep high-frequency slope of
-2.0, breaking to a slope of -1.0 at at timescale of 34 days. The lag from
optical to X-ray emission is most likely caused by variations in the accretion
disk propagating inward.Comment: 13 pages, 3 figures. Accepted for publication in the Astrophysical
Journa
Talking quiescence: a rigorous theory that supports parallel composition, action hiding and determinisation
The notion of quiescence - the absence of outputs - is vital in both
behavioural modelling and testing theory. Although the need for quiescence was
already recognised in the 90s, it has only been treated as a second-class
citizen thus far. This paper moves quiescence into the foreground and
introduces the notion of quiescent transition systems (QTSs): an extension of
regular input-output transition systems (IOTSs) in which quiescence is
represented explicitly, via quiescent transitions. Four carefully crafted rules
on the use of quiescent transitions ensure that our QTSs naturally capture
quiescent behaviour.
We present the building blocks for a comprehensive theory on QTSs supporting
parallel composition, action hiding and determinisation. In particular, we
prove that these operations preserve all the aforementioned rules.
Additionally, we provide a way to transform existing IOTSs into QTSs, allowing
even IOTSs as input that already contain some quiescent transitions. As an
important application, we show how our QTS framework simplifies the fundamental
model-based testing theory formalised around ioco.Comment: In Proceedings MBT 2012, arXiv:1202.582
Mass Measurements of AGN from Multi-Lorentzian Models of X-ray Variability. I. Sampling Effects in Theoretical Models of the rms^2-M_BH Correlation
Recent X-ray variability studies suggest that the log of the square of the
fractional rms variability amplitude, rms^2, seems to correlate with the log of
the AGN black-hole mass, M_BH, with larger black holes being less variable for
a fixed time interval. This has motivated the theoretical modeling of the
rms^2-M_BH correlation with the aim of constraining AGN masses based on X-ray
variability. A viable approach to addressing this problem is to assume an
underlying power spectral density with a suitable mass dependence, derive the
functional form of the rms^2-M_BH correlation for a given sampling pattern, and
investigate whether the result is consistent with the observations. For
simplicity, previous studies, inspired by the similarities shared by the timing
properties of AGN and X-ray binaries, have explored model power spectral
densities characterized by broken power laws. and ignored, in general, the
distorting effects that the particular sampling pattern imprints in the
observed power spectral density. Motivated by the latest timing results from
X-ray binaries, obtained with RXTE, we propose that AGN broad-band noise
spectra consist of a small number of Lorentzian components. This assumption
allows, for the first time, to fully account for sampling effects in
theoretical models of X-ray variability in an analytic manner. We show that,
neglecting sampling effects when deriving the fractional rms from the model
power spectral density can lead to underestimating it by a factor of up to 80%
with respect to its true value for the typical sampling patterns used to
monitor AGN. We discuss the implications of our results for the derivation of
AGN masses using theoretical models of the rms^2-M_BH correlation. (Abridged)Comment: The Astrophysical Journal, in press, 11 pages, 6 figure
Neuron dynamics in the presence of 1/f noise
Interest in understanding the interplay between noise and the response of a
non-linear device cuts across disciplinary boundaries. It is as relevant for
unmasking the dynamics of neurons in noisy environments as it is for designing
reliable nanoscale logic circuit elements and sensors. Most studies of noise in
non-linear devices are limited to either time-correlated noise with a
Lorentzian spectrum (of which the white noise is a limiting case) or just white
noise. We use analytical theory and numerical simulations to study the impact
of the more ubiquitous "natural" noise with a 1/f frequency spectrum.
Specifically, we study the impact of the 1/f noise on a leaky integrate and
fire model of a neuron. The impact of noise is considered on two quantities of
interest to neuron function: The spike count Fano factor and the speed of
neuron response to a small step-like stimulus. For the perfect (non-leaky)
integrate and fire model, we show that the Fano factor can be expressed as an
integral over noise spectrum weighted by a (low pass) filter function. This
result elucidates the connection between low frequency noise and disorder in
neuron dynamics. We compare our results to experimental data of single neurons
in vivo, and show how the 1/f noise model provides much better agreement than
the usual approximations based on Lorentzian noise. The low frequency noise,
however, complicates the case for information coding scheme based on interspike
intervals by introducing variability in the neuron response time. On a positive
note, the neuron response time to a step stimulus is, remarkably, nearly
optimal in the presence of 1/f noise. An explanation of this effect elucidates
how the brain can take advantage of noise to prime a subset of the neurons to
respond almost instantly to sudden stimuli.Comment: Phys. Rev. E in pres
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