18,093 research outputs found
Range entropy: A bridge between signal complexity and self-similarity
Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for
temporal complexity analysis of real-world phenomena. However, their
relationship with the Hurst exponent as a measure of self-similarity is not
widely studied. Additionally, ApEn and SampEn are susceptible to signal
amplitude changes. A common practice for addressing this issue is to correct
their input signal amplitude by its standard deviation. In this study, we first
show, using simulations, that ApEn and SampEn are related to the Hurst exponent
in their tolerance r and embedding dimension m parameters. We then propose a
modification to ApEn and SampEn called range entropy or RangeEn. We show that
RangeEn is more robust to nonstationary signal changes, and it has a more
linear relationship with the Hurst exponent, compared to ApEn and SampEn.
RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1
(minimum entropy) and it has no need for signal amplitude correction. Finally,
we demonstrate the clinical usefulness of signal entropy measures for
characterisation of epileptic EEG data as a real-world example.Comment: This is the revised and published version in Entrop
Difference image photometry with bright variable backgrounds
Over the last two decades the Andromeda Galaxy (M31) has been something of a
test-bed for methods aimed at obtaining accurate time-domain relative
photometry within highly crowded fields. Difference imaging methods, originally
pioneered towards M31, have evolved into sophisticated methods, such as the
Optimal Image Subtraction (OIS) method of Alard & Lupton (1998), that today are
most widely used to survey variable stars, transients and microlensing events
in our own Galaxy. We show that modern difference image (DIA) algorithms such
as OIS, whilst spectacularly successful towards the Milky Way bulge, may
perform badly towards high surface brightness targets such as the M31 bulge.
Poor results can occur in the presence of common systematics which add spurious
flux contributions to images, such as internal reflections, scattered light or
fringing. Using data from the Angstrom Project microlensing survey of the M31
bulge, we show that very good results are usually obtainable by first
performing careful photometric alignment prior to using OIS to perform
point-spread function (PSF) matching. This separation of background matching
and PSF matching, a common feature of earlier M31 photometry techniques, allows
us to take full advantage of the powerful PSF matching flexibility offered by
OIS towards high surface brightness targets. We find that difference images
produced this way have noise distributions close to Gaussian, showing
significant improvement upon results achieved using OIS alone. We show that
with this correction light-curves of variable stars and transients can be
recovered to within ~10 arcseconds of the M31 nucleus. Our method is simple to
implement and is quick enough to be incorporated within real-time DIA
pipelines. (Abridged)Comment: 12 pages. Accepted for publication in MNRAS. Includes an expanded
discussion of DIA testing and results, including additional lightcurve
example
Fast, scalable, Bayesian spike identification for multi-electrode arrays
We present an algorithm to identify individual neural spikes observed on
high-density multi-electrode arrays (MEAs). Our method can distinguish large
numbers of distinct neural units, even when spikes overlap, and accounts for
intrinsic variability of spikes from each unit. As MEAs grow larger, it is
important to find spike-identification methods that are scalable, that is, the
computational cost of spike fitting should scale well with the number of units
observed. Our algorithm accomplishes this goal, and is fast, because it
exploits the spatial locality of each unit and the basic biophysics of
extracellular signal propagation. Human intervention is minimized and
streamlined via a graphical interface. We illustrate our method on data from a
mammalian retina preparation and document its performance on simulated data
consisting of spikes added to experimentally measured background noise. The
algorithm is highly accurate
High signal-to-noise ratio observations and the ultimate limits of precision pulsar timing
We demonstrate that the sensitivity of high-precision pulsar timing
experiments will be ultimately limited by the broadband intensity modulation
that is intrinsic to the pulsar's stochastic radio signal. That is, as the peak
flux of the pulsar approaches that of the system equivalent flux density,
neither greater antenna gain nor increased instrumental bandwidth will improve
timing precision. These conclusions proceed from an analysis of the covariance
matrix used to characterise residual pulse profile fluctuations following the
template matching procedure for arrival time estimation. We perform such an
analysis on 25 hours of high-precision timing observations of the closest and
brightest millisecond pulsar, PSR J0437-4715. In these data, the standard
deviation of the post-fit arrival time residuals is approximately four times
greater than that predicted by considering the system equivalent flux density,
mean pulsar flux and the effective width of the pulsed emission. We develop a
technique based on principal component analysis to mitigate the effects of
shape variations on arrival time estimation and demonstrate its validity using
a number of illustrative simulations. When applied to our observations, the
method reduces arrival time residual noise by approximately 20%. We conclude
that, owing primarily to the intrinsic variability of the radio emission from
PSR J0437-4715 at 20 cm, timing precision in this observing band better than 30
- 40 ns in one hour is highly unlikely, regardless of future improvements in
antenna gain or instrumental bandwidth. We describe the intrinsic variability
of the pulsar signal as stochastic wideband impulse modulated self-noise
(SWIMS) and argue that SWIMS will likely limit the timing precision of every
millisecond pulsar currently observed by Pulsar Timing Array projects as larger
and more sensitive antennae are built in the coming decades.Comment: 16 pages, 9 figures, accepted for publication in MNRAS. Updated
version: added DOI and changed manuscript to reflect changes in the final
published versio
Frequency-Dependent Template Profiles for High Precision Pulsar Timing
Pulsar timing experiments require high fidelity template profiles in order to
minimize the biases in pulse time-of-arrival (TOA) measurements and their
uncertainties. Efforts to acquire more precise TOAs given fixed effective area
of telescopes, finite receiver noise, and limited integration time have led
pulsar astronomers to the solution of implementing ultra-wideband receivers.
This solution, however, has run up against the problem that pulse profile
shapes evolve with frequency, which raises the question of how to properly
measure and analyze TOAs obtained using template-matching methods. This paper
proposes a new method for one facet of this problem, that of template profile
generation, and demonstrates it on the well-timed millisecond pulsar
J1713+0747. Specifically, we decompose pulse profile evolution into a linear
combination of basis eigenvectors, the coefficients of which change slowly with
frequency such that their evolution is modeled simply by a sum of low degree
piecewise polynomial spline functions. These noise-free, high fidelity,
frequency-dependent templates can be used to make measurements of so-called
"wideband TOAs" simultaneously with an estimate of the instantaneous dispersion
measure. The use of wideband TOAs is becoming important for pulsar timing array
experiments, as the volume of datasets comprised of conventional, subbanded
TOAs are quickly becoming unwieldly for the Bayesian analyses needed to uncover
latent gravitational wave signals. Although motivated by high precision timing
experiments, our technique is applicable in more general pulsar observations.Comment: 16 pages, 6 figures, accepted to Ap
Pulsar data analysis with PSRCHIVE
PSRCHIVE is an open-source, object-oriented, scientific data analysis
software library and application suite for pulsar astronomy. It implements an
extensive range of general-purpose algorithms for use in data calibration and
integration, statistical analysis and modeling, and visualisation. These are
utilised by a variety of applications specialised for tasks such as pulsar
timing, polarimetry, radio frequency interference mitigation, and pulse
variability studies. This paper presents a general overview of PSRCHIVE
functionality with some focus on the integrated interfaces developed for the
core applications.Comment: 21 pages, 5 figures; tutorial presented at IPTA 2010 meeting in
Leiden merged with talk presented at 2011 pulsar conference in Beijing;
includes further research and development on algorithms for RFI mitigation
and TOA bias correctio
Astrometric calibration and performance of the Dark Energy Camera
We characterize the ability of the Dark Energy Camera (DECam) to perform
relative astrometry across its 500~Mpix, 3 deg^2 science field of view, and
across 4 years of operation. This is done using internal comparisons of ~4x10^7
measurements of high-S/N stellar images obtained in repeat visits to fields of
moderate stellar density, with the telescope dithered to move the sources
around the array. An empirical astrometric model includes terms for: optical
distortions; stray electric fields in the CCD detectors; chromatic terms in the
instrumental and atmospheric optics; shifts in CCD relative positions of up to
~10 um when the DECam temperature cycles; and low-order distortions to each
exposure from changes in atmospheric refraction and telescope alignment. Errors
in this astrometric model are dominated by stochastic variations with typical
amplitudes of 10-30 mas (in a 30 s exposure) and 5-10 arcmin coherence length,
plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of
these atmospheric distortions is not closely related to the seeing. Given an
astrometric reference catalog at density ~0.7 arcmin^{-2}, e.g. from Gaia, the
typical atmospheric distortions can be interpolated to 7 mas RMS accuracy (for
30 s exposures) with 1 arcmin coherence length for residual errors. Remaining
detectable error contributors are 2-4 mas RMS from unmodelled stray electric
fields in the devices, and another 2-4 mas RMS from focal plane shifts between
camera thermal cycles. Thus the astrometric solution for a single DECam
exposure is accurate to 3-6 mas (0.02 pixels, or 300 nm) on the focal plane,
plus the stochastic atmospheric distortion.Comment: Submitted to PAS
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