2,581 research outputs found
Measurement of Parity Violation in the Early Universe using Gravitational-wave Detectors
A stochastic gravitational-wave background (SGWB) is expected to arise from
the superposition of many independent and unresolved gravitational-wave
signals, of either cosmological or astrophysical origin. Some cosmological
models (characterized, for instance, by a pseudo-scalar inflaton, or by some
modification of gravity) break parity, leading to a polarized SGWB. We present
a new technique to measure this parity violation, which we then apply to the
recent results from LIGO to produce the first upper limit on parity violation
in the SGWB, assuming a generic power-law SGWB spectrum across the LIGO
sensitive frequency region. We also estimate sensitivity to parity violation of
the future generations of gravitational-wave detectors, both for a power-law
spectrum and for a model of axion inflation. This technique offers a new way of
differentiating between the cosmological and astrophysical sources of the
isotropic SGWB, as astrophysical sources are not expected to produce a
polarized SGWB.Comment: 5 pages, 2 figures, 1 tabl
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
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