160,802 research outputs found
The rotational modes of relativistic stars: Numerical results
We study the inertial modes of slowly rotating, fully relativistic compact
stars. The equations that govern perturbations of both barotropic and
non-barotropic models are discussed, but we present numerical results only for
the barotropic case. For barotropic stars all inertial modes are a hybrid
mixture of axial and polar perturbations. We use a spectral method to solve for
such modes of various polytropic models. Our main attention is on modes that
can be driven unstable by the emission of gravitational waves. Hence, we
calculate the gravitational-wave growth timescale for these unstable modes and
compare the results to previous estimates obtained in Newtonian gravity (i.e.
using post-Newtonian radiation formulas). We find that the inertial modes are
slightly stabilized by relativistic effects, but that previous conclusions
concerning eg. the unstable r-modes remain essentially unaltered when the
problem is studied in full general relativity.Comment: RevTeX, 29 pages, 31 eps figure
Deconvolution of spectra for intimate mixtures
Visible to near infrared reflectance spectra of macroscopic mixtures have been shown to be linear combinations of the reflections of the pure mineral components in the mixture. However, for microscopic mixtures the mixing systematics are in general nonlinear. The systematics may be linearized by conversion of reflectance to single scattering albedo (w), where the equations which relate reflectance to w depend on the method of data collection. Several proposed mixing models may be used to estimate mineral abundances from the reflectance spectra of intimate mixtures. These models are summarized and a revised model is presented. A noniterative (linear) least squares approach was used for curve fitting and the data, measured as bi-directional reflectance with incidence and emergence angles of 30 and 0 deg were converted to w by a simplified version of Hapke's equation for bi-directional reflectance. This model was tested with two mixture series composed of 45 to 75 micron particles: an anorthite-enstatite series and an olivine-magnetite series. The data indicate that the simplified Hapke's equation may be used to convolve reflectance spectra into mineral abundances if appropriate endmembers are known or derived from other techniques. For surfaces that contain a significant component of very low albedo material, a somewhat modified version of this technique will need to be developed. Since the abundances are calculated using a noniterative approach, the application of this method is especially efficient for large spectral data sets, such as those produced by mapping spectrometers
Nonparametric Estimation of Multi-View Latent Variable Models
Spectral methods have greatly advanced the estimation of latent variable
models, generating a sequence of novel and efficient algorithms with strong
theoretical guarantees. However, current spectral algorithms are largely
restricted to mixtures of discrete or Gaussian distributions. In this paper, we
propose a kernel method for learning multi-view latent variable models,
allowing each mixture component to be nonparametric. The key idea of the method
is to embed the joint distribution of a multi-view latent variable into a
reproducing kernel Hilbert space, and then the latent parameters are recovered
using a robust tensor power method. We establish that the sample complexity for
the proposed method is quadratic in the number of latent components and is a
low order polynomial in the other relevant parameters. Thus, our non-parametric
tensor approach to learning latent variable models enjoys good sample and
computational efficiencies. Moreover, the non-parametric tensor power method
compares favorably to EM algorithm and other existing spectral algorithms in
our experiments
Spectral Sequence Motif Discovery
Sequence discovery tools play a central role in several fields of
computational biology. In the framework of Transcription Factor binding
studies, motif finding algorithms of increasingly high performance are required
to process the big datasets produced by new high-throughput sequencing
technologies. Most existing algorithms are computationally demanding and often
cannot support the large size of new experimental data. We present a new motif
discovery algorithm that is built on a recent machine learning technique,
referred to as Method of Moments. Based on spectral decompositions, this method
is robust under model misspecification and is not prone to locally optimal
solutions. We obtain an algorithm that is extremely fast and designed for the
analysis of big sequencing data. In a few minutes, we can process datasets of
hundreds of thousand sequences and extract motif profiles that match those
computed by various state-of-the-art algorithms.Comment: 20 pages, 3 figures, 1 tabl
A Method of Moments for Mixture Models and Hidden Markov Models
Mixture models are a fundamental tool in applied statistics and machine
learning for treating data taken from multiple subpopulations. The current
practice for estimating the parameters of such models relies on local search
heuristics (e.g., the EM algorithm) which are prone to failure, and existing
consistent methods are unfavorable due to their high computational and sample
complexity which typically scale exponentially with the number of mixture
components. This work develops an efficient method of moments approach to
parameter estimation for a broad class of high-dimensional mixture models with
many components, including multi-view mixtures of Gaussians (such as mixtures
of axis-aligned Gaussians) and hidden Markov models. The new method leads to
rigorous unsupervised learning results for mixture models that were not
achieved by previous works; and, because of its simplicity, it offers a viable
alternative to EM for practical deployment
Application of FTIR spectroscopy for the determination of virgin coconut oil in binary mixtures with olive oil and palm oil.
Rapid Fourier transform infrared (FTIR) spectroscopy combined with attenuated total reflectance (ATR) was applied for quantitative analysis of virgin coconut oil (VCO) in binary mixtures with olive oil (OO) and palm oil (PO). The spectral bands correlated with VCO, OO, PO; blends of VCO and OO; VCO and PO were scanned, interpreted, and identified. Two multivariate calibration methods, partial least square (PLS) and principal component regression (PCR), were used to construct the calibration models that correlate between actual and FTIR-predicted values of VCO contents in the mixtures at the FTIR spectral frequencies of 1,120–1,105 and 965–960 cm−1. The calibration models obtained were cross validated using the “leave one out” method. PLS at these frequencies showed the best calibration model, in terms of the highest coefficient of determination (R 2) and the lowest of root mean standard error of calibration (RMSEC) with R 2 = 0.9992 and RMSEC = 0.756, respectively, for VCO in mixture with OO. Meanwhile, the R 2 and RMSEC values obtained for VCO in mixture with PO were 0.9996 and 0.494, respectively. In general, FTIR spectroscopy serves as a suitable technique for determination of VCO in mixture with the other oils
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