1,940 research outputs found
Singular value decomposition applied to compact binary coalescence gravitational-wave signals
We investigate the application of the singular value decomposition to
compact-binary, gravitational-wave data-analysis. We find that the truncated
singular value decomposition reduces the number of filters required to analyze
a given region of parameter space of compact binary coalescence waveforms by an
order of magnitude with high reconstruction accuracy. We also compute an
analytic expression for the expected signal-loss due to the singular value
decomposition truncation.Comment: 4 figures, 6 page
ZAP -- Enhanced PCA Sky Subtraction for Integral Field Spectroscopy
We introduce Zurich Atmosphere Purge (ZAP), an approach to sky subtraction
based on principal component analysis (PCA) that we have developed for the
Multi Unit Spectrographic Explorer (MUSE) integral field spectrograph. ZAP
employs filtering and data segmentation to enhance the inherent capabilities of
PCA for sky subtraction. Extensive testing shows that ZAP reduces sky emission
residuals while robustly preserving the flux and line shapes of astronomical
sources. The method works in a variety of observational situations from sparse
fields with a low density of sources to filled fields in which the target
source fills the field of view. With the inclusion of both of these situations
the method is generally applicable to many different science cases and should
also be useful for other instrumentation. ZAP is available for download at
http://muse-vlt.eu/science/tools.Comment: 12 pages, 7 figures, 1 table. Accepted to MNRA
A comparative study on global wavelet and polynomial models for nonlinear regime-switching systems
A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems
A machine learning approach to portfolio pricing and risk management for high-dimensional problems
We present a general framework for portfolio risk management in discrete
time, based on a replicating martingale. This martingale is learned from a
finite sample in a supervised setting. The model learns the features necessary
for an effective low-dimensional representation, overcoming the curse of
dimensionality common to function approximation in high-dimensional spaces. We
show results based on polynomial and neural network bases. Both offer superior
results to naive Monte Carlo methods and other existing methods like
least-squares Monte Carlo and replicating portfolios.Comment: 30 pages (main), 10 pages (appendix), 3 figures, 22 table
Wavelet methods in speech recognition
In this thesis, novel wavelet techniques are developed to improve parametrization of
speech signals prior to classification. It is shown that non-linear operations carried out
in the wavelet domain improve the performance of a speech classifier and consistently
outperform classical Fourier methods. This is because of the localised nature of the
wavelet, which captures correspondingly well-localised time-frequency features
within the speech signal. Furthermore, by taking advantage of the approximation
ability of wavelets, efficient representation of the non-stationarity inherent in speech
can be achieved in a relatively small number of expansion coefficients. This is an
attractive option when faced with the so-called 'Curse of Dimensionality' problem of
multivariate classifiers such as Linear Discriminant Analysis (LDA) or Artificial
Neural Networks (ANNs). Conventional time-frequency analysis methods such as the
Discrete Fourier Transform either miss irregular signal structures and transients due to
spectral smearing or require a large number of coefficients to represent such
characteristics efficiently. Wavelet theory offers an alternative insight in the
representation of these types of signals.
As an extension to the standard wavelet transform, adaptive libraries of wavelet and
cosine packets are introduced which increase the flexibility of the transform. This
approach is observed to be yet more suitable for the highly variable nature of speech
signals in that it results in a time-frequency sampled grid that is well adapted to
irregularities and transients. They result in a corresponding reduction in the
misclassification rate of the recognition system. However, this is necessarily at the
expense of added computing time.
Finally, a framework based on adaptive time-frequency libraries is developed which
invokes the final classifier to choose the nature of the resolution for a given
classification problem. The classifier then performs dimensionaIity reduction on the
transformed signal by choosing the top few features based on their discriminant power. This approach is compared and contrasted to an existing discriminant wavelet
feature extractor.
The overall conclusions of the thesis are that wavelets and their relatives are capable
of extracting useful features for speech classification problems. The use of adaptive
wavelet transforms provides the flexibility within which powerful feature extractors
can be designed for these types of application
Effective-one-body waveforms for binary neutron stars using surrogate models
Gravitational-wave observations of binary neutron star systems can provide
information about the masses, spins, and structure of neutron stars. However,
this requires accurate and computationally efficient waveform models that take
<1s to evaluate for use in Bayesian parameter estimation codes that perform
10^7 - 10^8 waveform evaluations. We present a surrogate model of a nonspinning
effective-one-body waveform model with l = 2, 3, and 4 tidal multipole moments
that reproduces waveforms of binary neutron star numerical simulations up to
merger. The surrogate is built from compact sets of effective-one-body waveform
amplitude and phase data that each form a reduced basis. We find that 12
amplitude and 7 phase basis elements are sufficient to reconstruct any binary
neutron star waveform with a starting frequency of 10Hz. The surrogate has
maximum errors of 3.8% in amplitude (0.04% excluding the last 100M before
merger) and 0.043 radians in phase. The version implemented in the LIGO
Algorithm Library takes ~0.07s to evaluate for a starting frequency of 30Hz and
~0.8s for a starting frequency of 10Hz, resulting in a speed-up factor of ~10^3
- 10^4 relative to the original Matlab code. This allows parameter estimation
codes to run in days to weeks rather than years, and we demonstrate this with a
Nested Sampling run that recovers the masses and tidal parameters of a
simulated binary neutron star system.Comment: 17 pages, 11 figures, submitted to PR
- …