14 research outputs found
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
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
Long-range correlation and multifractality in Bach's Inventions pitches
We show that it can be considered some of Bach pitches series as a stochastic
process with scaling behavior. Using multifractal deterend fluctuation analysis
(MF-DFA) method, frequency series of Bach pitches have been analyzed. In this
view we find same second moment exponents (after double profiling) in ranges
(1.7-1.8) in his works. Comparing MF-DFA results of original series to those
for shuffled and surrogate series we can distinguish multifractality due to
long-range correlations and a broad probability density function. Finally we
determine the scaling exponents and singularity spectrum. We conclude fat tail
has more effect in its multifractality nature than long-range correlations.Comment: 18 page, 6 figures, to appear in JSTA
Spectroscopic investigation of quantum confinement effects in ion implanted silicon-on-sapphire films
Crystalline Silicon-on-Sapphire (SOS) films were implanted with boron (B)
and phosphorous (P) ions. Different samples, prepared by varying the ion
dose in the range to 5 x and ion energy in the range
150-350 keV, were investigated by the Raman spectroscopy, photoluminescence
(PL) spectroscopy and glancing angle x-ray diffraction (GAXRD). The Raman
results from dose dependent B implanted samples show red-shifted and
asymmetrically broadened Raman line-shape for B dose greater than
ions cm. The asymmetry and red shift in the Raman line-shape is
explained in terms of quantum confinement of phonons in silicon nanostructures
formed as a result of ion implantation. PL spectra shows size dependent visible
luminescence at 1.9 eV at room temperature, which confirms the presence
of silicon nanostructures. Raman studies on P implanted samples were also
done as a function of ion energy. The Raman results show an amorphous top SOS
surface for sample implanted with 150 keV P ions of dose 5 x ions
cm. The nanostructures are formed when the P energy is increased to
350 keV by keeping the ion dose fixed. The GAXRD results show consistency with
the Raman results.Comment: 9 Pages, 6 Figures and 1 Table, \LaTex format To appear in
SILICON(SPRINGER
Effect of Trends on Detrended Fluctuation Analysis
Detrended fluctuation analysis (DFA) is a scaling analysis method used to
estimate long-range power-law correlation exponents in noisy signals. Many
noisy signals in real systems display trends, so that the scaling results
obtained from the DFA method become difficult to analyze. We systematically
study the effects of three types of trends -- linear, periodic, and power-law
trends, and offer examples where these trends are likely to occur in real data.
We compare the difference between the scaling results for artificially
generated correlated noise and correlated noise with a trend, and study how
trends lead to the appearance of crossovers in the scaling behavior. We find
that crossovers result from the competition between the scaling of the noise
and the ``apparent'' scaling of the trend. We study how the characteristics of
these crossovers depend on (i) the slope of the linear trend; (ii) the
amplitude and period of the periodic trend; (iii) the amplitude and power of
the power-law trend and (iv) the length as well as the correlation properties
of the noise. Surprisingly, we find that the crossovers in the scaling of noisy
signals with trends also follow scaling laws -- i.e. long-range power-law
dependence of the position of the crossover on the parameters of the trends. We
show that the DFA result of noise with a trend can be exactly determined by the
superposition of the separate results of the DFA on the noise and on the trend,
assuming that the noise and the trend are not correlated. If this superposition
rule is not followed, this is an indication that the noise and the superimposed
trend are not independent, so that removing the trend could lead to changes in
the correlation properties of the noise.Comment: 20 pages, 16 figure
The effect of annealing conditions on the red photoluminescence of nanocrystalline Si/SiO 2 films
Nanocrystalline Si (nc-Si) embedded in a SiO2 matrix, fabricated by plasma CVD and a subsequent post-treatment shows a broad red photoluminescence (PL). In this paper, the effects of annealing temperature, atmosphere and time on the red PL from 1.75 to 1.5 eV have been investigated in detail. It is found that the spectral shift and the PL intensity from 1.75 to 1.5 eV show a strong and unique dependence on annealing conditions. For a PL approximately 1.75 eV, upon 400 °C forming gas annealing, the spectral shift and the peak intensity versus accumulation annealing times show a novel temporal oscillation. This unique dependence and the novel temporal oscillation behavior, which have not been reported in porous silicon, exclude nc-Si itself as the source of the red PL. Instead they favor oxygen thermal donors (TDs)-like defect states as PL centers. This is in consensus with our earlier results of defect studies using electron spin resonance in this system. Furthermore, two PL centers in this red PL were distinguished according to their variance in annealing temperature- and time-dependence. The spectral change between 1.5 and 1.75 eV upon annealing conditions can be qualitatively explained by using the formation and annihilation kinetics of two oxygen TDs-like defect state