804 research outputs found
Gridded and direct Epoch of Reionisation bispectrum estimates using the Murchison Widefield Array
We apply two methods to estimate the 21~cm bispectrum from data taken within
the Epoch of Reionisation (EoR) project of the Murchison Widefield Array (MWA).
Using data acquired with the Phase II compact array allows a direct bispectrum
estimate to be undertaken on the multiple redundantly-spaced triangles of
antenna tiles, as well as an estimate based on data gridded to the -plane.
The direct and gridded bispectrum estimators are applied to 21 hours of
high-band (167--197~MHz; =6.2--7.5) data from the 2016 and 2017 observing
seasons. Analytic predictions for the bispectrum bias and variance for point
source foregrounds are derived. We compare the output of these approaches, the
foreground contribution to the signal, and future prospects for measuring the
bispectra with redundant and non-redundant arrays. We find that some triangle
configurations yield bispectrum estimates that are consistent with the expected
noise level after 10 hours, while equilateral configurations are strongly
foreground-dominated. Careful choice of triangle configurations may be made to
reduce foreground bias that hinders power spectrum estimators, and the 21~cm
bispectrum may be accessible in less time than the 21~cm power spectrum for
some wave modes, with detections in hundreds of hours.Comment: 19 pages, 10 figures, accepted for publication in PAS
Bispectrum Inversion with Application to Multireference Alignment
We consider the problem of estimating a signal from noisy
circularly-translated versions of itself, called multireference alignment
(MRA). One natural approach to MRA could be to estimate the shifts of the
observations first, and infer the signal by aligning and averaging the data. In
contrast, we consider a method based on estimating the signal directly, using
features of the signal that are invariant under translations. Specifically, we
estimate the power spectrum and the bispectrum of the signal from the
observations. Under mild assumptions, these invariant features contain enough
information to infer the signal. In particular, the bispectrum can be used to
estimate the Fourier phases. To this end, we propose and analyze a few
algorithms. Our main methods consist of non-convex optimization over the smooth
manifold of phases. Empirically, in the absence of noise, these non-convex
algorithms appear to converge to the target signal with random initialization.
The algorithms are also robust to noise. We then suggest three additional
methods. These methods are based on frequency marching, semidefinite relaxation
and integer programming. The first two methods provably recover the phases
exactly in the absence of noise. In the high noise level regime, the invariant
features approach for MRA results in stable estimation if the number of
measurements scales like the cube of the noise variance, which is the
information-theoretic rate. Additionally, it requires only one pass over the
data which is important at low signal-to-noise ratio when the number of
observations must be large
The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
This article presents the first computation of the complete bispectrum of the
cosmic microwave background temperature anisotropies arising from the evolution
of all cosmic fluids up to second order, including neutrinos. Gravitational
couplings, electron density fluctuations and the second order Boltzmann
equation are fully taken into account. Comparison to limiting cases that
appeared previously in the literature are provided. These are regimes for which
analytical insights can be given. The final results are expressed in terms of
equivalent fNL for different configurations. It is found that for moments up to
lmax=2000, the signal generated by non-linear effects is equivalent to fNL~5
for both local-type and equilateral-type primordial non-Gaussianity.Comment: 44 pages, 8 figure
Testing Inflation with Large Scale Structure: Connecting Hopes with Reality
The statistics of primordial curvature fluctuations are our window into the
period of inflation, where these fluctuations were generated. To date, the
cosmic microwave background has been the dominant source of information about
these perturbations. Large scale structure is however from where drastic
improvements should originate. In this paper, we explain the theoretical
motivations for pursuing such measurements and the challenges that lie ahead.
In particular, we discuss and identify theoretical targets regarding the
measurement of primordial non-Gaussianity. We argue that when quantified in
terms of the local (equilateral) template amplitude
(), natural target levels of sensitivity are . We highlight that such levels are within
reach of future surveys by measuring 2-, 3- and 4-point statistics of the
galaxy spatial distribution. This paper summarizes a workshop held at CITA
(University of Toronto) on October 23-24, 2014.Comment: 27 pages + reference
Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity
We investigate several quantifiers of the electroencephalogram (EEG) signal
with respect to their ability to indicate depth of anesthesia. For 17 patients
anesthetized with Sevoflurane, three established measures (two spectral and one
based on the bispectrum), as well as a phase space based nonlinear correlation
index were computed from consecutive EEG epochs. In absence of an independent
way to determine anesthesia depth, the standard was derived from measured blood
plasma concentrations of the anesthetic via a pharmacokinetic/pharmacodynamic
model for the estimated effective brain concentration of Sevoflurane. In most
patients, the highest correlation is observed for the nonlinear correlation
index D*. In contrast to spectral measures, D* is found to decrease
monotonically with increasing (estimated) depth of anesthesia, even when a
"burst-suppression" pattern occurs in the EEG. The findings show the potential
for applications of concepts derived from the theory of nonlinear dynamics,
even if little can be assumed about the process under investigation.Comment: 7 pages, 5 figure
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