1,671 research outputs found
Effect of nonlinear filters on detrended fluctuation analysis
We investigate how various linear and nonlinear transformations affect the
scaling properties of a signal, using the detrended fluctuation analysis (DFA).
Specifically, we study the effect of three types of transforms: linear,
nonlinear polynomial and logarithmic filters. We compare the scaling properties
of signals before and after the transform. We find that linear filters do not
change the correlation properties, while the effect of nonlinear polynomial and
logarithmic filters strongly depends on (a) the strength of correlations in the
original signal, (b) the power of the polynomial filter and (c) the offset in
the logarithmic filter. We further investigate the correlation properties of
three analytic functions: exponential, logarithmic, and power-law. While these
three functions have in general different correlation properties, we find that
there is a broad range of variable values, common for all three functions,
where they exhibit identical scaling behavior. We further note that the scaling
behavior of a class of other functions can be reduced to these three typical
cases. We systematically test the performance of the DFA method in accurately
estimating long-range power-law correlations in the output signals for
different parameter values in the three types of filters, and the three
analytic functions we consider.Comment: 12 pages, 7 figure
Simulation of Jahn-Teller-Dicke Magnetic Structural Phase Transition with Trapped Ions
We study theoretically the collective Ee Jahn-Teller-Dicke
distortion in a system of trapped ions. We focus in the limit of infinite range
interactions in which an ensemble of effective spins interacts with two
collective vibrational modes with U(1) symmetric couplings. Our model is
exactly solvable in the thermodynamical limit and it is amenable to be solved
by exact numerical diagonalization for a moderate number of ions. We show that
trapped ions are ideally suited to study the emergence of spontaneous symmetry
breaking of a continuous symmetry and magnetic structural phase transition in a
mesoscopic system.Comment: 19 pages, 7 figure
Effect of nonstationarities on detrended fluctuation analysis
Detrended fluctuation analysis (DFA) is a scaling analysis method used to
quantify long-range power-law correlations in signals. Many physical and
biological signals are ``noisy'', heterogeneous and exhibit different types of
nonstationarities, which can affect the correlation properties of these
signals. We systematically study the effects of three types of
nonstationarities often encountered in real data. Specifically, we consider
nonstationary sequences formed in three ways: (i) stitching together segments
of data obtained from discontinuous experimental recordings, or removing some
noisy and unreliable parts from continuous recordings and stitching together
the remaining parts -- a ``cutting'' procedure commonly used in preparing data
prior to signal analysis; (ii) adding to a signal with known correlations a
tunable concentration of random outliers or spikes with different amplitude,
and (iii) generating a signal comprised of segments with different properties
-- e.g. different standard deviations or different correlation exponents. We
compare the difference between the scaling results obtained for stationary
correlated signals and correlated signals with these three types of
nonstationarities.Comment: 17 pages, 10 figures, corrected some typos, added one referenc
Characterization of Sleep Stages by Correlations of Heartbeat Increments
We study correlation properties of the magnitude and the sign of the
increments in the time intervals between successive heartbeats during light
sleep, deep sleep, and REM sleep using the detrended fluctuation analysis
method. We find short-range anticorrelations in the sign time series, which are
strong during deep sleep, weaker during light sleep and even weaker during REM
sleep. In contrast, we find long-range positive correlations in the magnitude
time series, which are strong during REM sleep and weaker during light sleep.
We observe uncorrelated behavior for the magnitude during deep sleep. Since the
magnitude series relates to the nonlinear properties of the original time
series, while the signs series relates to the linear properties, our findings
suggest that the nonlinear properties of the heartbeat dynamics are more
pronounced during REM sleep. Thus, the sign and the magnitude series provide
information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte
Scale Invariance in the Nonstationarity of Physiological Signals
We introduce a segmentation algorithm to probe temporal organization of
heterogeneities in human heartbeat interval time series. We find that the
lengths of segments with different local values of heart rates follow a
power-law distribution. This scale-invariant structure is not a simple
consequence of the long-range correlations present in the data. We also find
that the differences in mean heart rates between consecutive segments display a
common functional form, but with different parameters for healthy individuals
and for patients with heart failure. This finding may provide information into
the way heart rate variability is reduced in cardiac disease.Comment: 13 pages, 5 figures, corrected typo
Magnitude and Sign Correlations in Heartbeat Fluctuations
We propose an approach for analyzing signals with long-range correlations by
decomposing the signal increment series into magnitude and sign series and
analyzing their scaling properties. We show that signals with identical
long-range correlations can exhibit different time organization for the
magnitude and sign. We find that the magnitude series relates to the nonlinear
properties of the original time series, while the sign series relates to the
linear properties. We apply our approach to the heartbeat interval series and
find that the magnitude series is long-range correlated, while the sign series
is anticorrelated and that both magnitude and sign series may have clinical
applications.Comment: 4 pages,late
Memory beyond memory in heart beating: an efficient way to detect pathological conditions
We study the long-range correlations of heartbeat fluctuations with the
method of diffusion entropy. We show that this method of analysis yields a
scaling parameter that apparently conflicts with the direct evaluation
of the distribution of times of sojourn in states with a given heartbeat
frequency. The strength of the memory responsible for this discrepancy is given
by a parameter , which is derived from real data. The
distribution of patients in the (, )-plane yields a neat
separation of the healthy from the congestive heart failure subjects.Comment: submitted to Physical Review Letters, 5 figure
Influence of corruption on economic growth rate and foreign investments
In order to investigate whether government regulations against corruption can
affect the economic growth of a country, we analyze the dependence between
Gross Domestic Product (GDP) per capita growth rates and changes in the
Corruption Perceptions Index (CPI). For the period 1999-2004 on average for all
countries in the world, we find that an increase of CPI by one unit leads to an
increase of the annual GDP per capita by 1.7 %. By regressing only European
transition countries, we find that CPI = 1 generates increase of the
annual GDP per capita by 2.4 %. We also analyze the relation between foreign
direct investments received by different countries and CPI, and we find a
statistically significant power-law functional dependence between foreign
direct investment per capita and the country corruption level measured by the
CPI. We introduce a new measure to quantify the relative corruption between
countries based on their respective wealth as measured by GDP per capita.Comment: 8 pages, 3 figures, elsart styl
Observation of Magnetic Moments in the Superconducting State of YBaCuO
Neutron Scattering measurements for YBaCuO have identified
small magnetic moments that increase in strength as the temperature is reduced
below and further increase below . An analysis of the data shows
the moments are antiferromagnetic between the Cu-O planes with a correlation
length of longer than 195 \AA in the - plane and about 35 \AA along the
c-axis. The origin of the moments is unknown, and their properties are
discusssed both in terms of Cu spin magnetism and orbital bond currents.Comment: 9 pages, and 4 figure
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