104,565 research outputs found
Noise residuals for GW150914 using maximum likelihood and numerical relativity templates
We reexamine the results presented in a recent work by Nielsen et al. [1], in
which the properties of the noise residuals in the 40\,ms chirp domain of
GW150914 were investigated. This paper confirmed the presence of strong (i.e.,
about 0.80) correlations between residual noise in the Hanford and Livingston
detectors in the chirp domain as previously seen by us [2] when using a
numerical relativity template given in [3]. It was also shown in [1] that a
so-called maximum likelihood template can reduce these statistically
significant cross-correlations. Here, we demonstrate that the reduction of
correlation and statistical significance is due to (i) the use of a peculiar
template which is qualitatively different from the properties of GW150914
originally published by LIGO, (ii) a suspicious MCMC chain, (iii) uncertainties
in the matching of the maximum likelihood (ML) template to the data in the
Fourier domain, and (iv) a biased estimation of the significance that gives
counter-intuitive results. We show that rematching the maximum likelihood
template to the data in the 0.2\,s domain containing the GW150914 signal
restores these correlations at the level of of those found in [1]. With
necessary corrections, the probability given in [1] will decrease by more than
one order of magnitude. Since the ML template is itself problematic, results
associated with this template are illustrative rather than final.Comment: Minor correction
Stability of Monitoring Weak Changes in Multiply Scattering Media with Ambient Noise Correlation: Laboratory Experiments
Previous studies have shown that small changes can be monitored in a
scattering medium by observing phase shifts in the coda. Passive monitoring of
weak changes through ambient noise correlation has already been applied to
seismology, acoustics and engineering. Usually, this is done under the
assumption that a properly reconstructed Green function as well as stable
background noise sources are necessary. In order to further develop this
monitoring technique, a laboratory experiment was performed in the 2.5MHz range
in a gel with scattering inclusions, comparing an active (pulse-echo) form of
monitoring to a passive (correlation) one. Present results show that
temperature changes in the medium can be observed even if the Green function
(GF) of the medium is not reconstructed. Moreover, this article establishes
that the GF reconstruction in the correlations is not a necessary condition:
the only condition to monitoring with correlation (passive experiment) is the
relative stability of the background noise structure
Exploring two-spin internal linear combinations for the recovery of the CMB polarization
We present a methodology to recover cosmic microwave background (CMB)
polarization in which the quantity is linearly combined at
different frequencies using complex coefficients. This is the most general
linear combination of the and Stokes parameters which preserves the
physical coherence of the residual contribution on the CMB estimation. The
approach is applied to the internal linear combination (ILC) and the internal
template fitting (ITF) methodologies. The variance of of the resulting map
is minimized to compute the coefficients of the linear combination. One of the
key aspects of this procedure is that it serves to account for a global
frequency-dependent shift of the polarization phase. Although in the standard
case, in which no global E-B transference depending on frequency is expected in
the foreground components, minimizing is
similar to minimizing and separately (as previous methodologies proceed), multiplying
and by different coefficients induces arbitrary changes in the
polarization angle and it does not preserve the coherence between the spinorial
components. The approach is tested on simulations, obtaining a similar residual
level with respect to the one obtained with other implementations of the ILC,
and perceiving the polarization rotation of a toy model with the frequency
dependence of the Faraday rotation.Comment: 14 pages, 8 figures, 2 tables. Accepted for publication in MNRA
Device-independent point estimation from finite data and its application to device-independent property estimation
The device-independent approach to physics is one where conclusions are drawn
directly from the observed correlations between measurement outcomes. In
quantum information, this approach allows one to make strong statements about
the properties of the underlying systems or devices solely via the observation
of Bell-inequality-violating correlations. However, since one can only perform
a {\em finite number} of experimental trials, statistical fluctuations
necessarily accompany any estimation of these correlations. Consequently, an
important gap remains between the many theoretical tools developed for the
asymptotic scenario and the experimentally obtained raw data. In particular, a
physical and concurrently practical way to estimate the underlying quantum
distribution has so far remained elusive. Here, we show that the natural
analogs of the maximum-likelihood estimation technique and the
least-square-error estimation technique in the device-independent context
result in point estimates of the true distribution that are physical, unique,
computationally tractable and consistent. They thus serve as sound algorithmic
tools allowing one to bridge the aforementioned gap. As an application, we
demonstrate how such estimates of the underlying quantum distribution can be
used to provide, in certain cases, trustworthy estimates of the amount of
entanglement present in the measured system. In stark contrast to existing
approaches to device-independent parameter estimations, our estimation does not
require the prior knowledge of {\em any} Bell inequality tailored for the
specific property and the specific distribution of interest.Comment: Essentially published version, but with the typo in Eq. (E5)
correcte
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
We consider the frequency domain form of proper orthogonal decomposition
(POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is
derived from a space-time POD problem for statistically stationary flows and
leads to modes that each oscillate at a single frequency. This form of POD goes
back to the original work of Lumley (Stochastic tools in turbulence, Academic
Press, 1970), but has been overshadowed by a space-only form of POD since the
1990s. We clarify the relationship between these two forms of POD and show that
SPOD modes represent structures that evolve coherently in space and time while
space-only POD modes in general do not. We also establish a relationship
between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are
in fact optimally averaged DMD modes obtained from an ensemble DMD problem for
stationary flows. Accordingly, SPOD modes represent structures that are dynamic
in the same sense as DMD modes but also optimally account for the statistical
variability of turbulent flows. Finally, we establish a connection between SPOD
and resolvent analysis. The key observation is that the resolvent-mode
expansion coefficients must be regarded as statistical quantities to ensure
convergent approximations of the flow statistics. When the expansion
coefficients are uncorrelated, we show that SPOD and resolvent modes are
identical. Our theoretical results and the overall utility of SPOD are
demonstrated using two example problems: the complex Ginzburg-Landau equation
and a turbulent jet
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