26,732 research outputs found
Driving Markov chain Monte Carlo with a dependent random stream
Markov chain Monte Carlo is a widely-used technique for generating a
dependent sequence of samples from complex distributions. Conventionally, these
methods require a source of independent random variates. Most implementations
use pseudo-random numbers instead because generating true independent variates
with a physical system is not straightforward. In this paper we show how to
modify some commonly used Markov chains to use a dependent stream of random
numbers in place of independent uniform variates. The resulting Markov chains
have the correct invariant distribution without requiring detailed knowledge of
the stream's dependencies or even its marginal distribution. As a side-effect,
sometimes far fewer random numbers are required to obtain accurate results.Comment: 16 pages, 4 figure
A rational spectral collocation method with adaptively transformed Chebyshev grid points
A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are approximated by the locations of poles of Chebyshev-PadƩ approximants. Numerical experiments on two time-dependent problems, one with finite time blow-up and one with a moving front, indicate that the method far outperforms the standard Chebyshev spectral collocation method for problems whose solutions have singularities in the complex plan close to [-1,1]
A nonparametric HMM for genetic imputation and coalescent inference
Genetic sequence data are well described by hidden Markov models (HMMs) in
which latent states correspond to clusters of similar mutation patterns. Theory
from statistical genetics suggests that these HMMs are nonhomogeneous (their
transition probabilities vary along the chromosome) and have large support for
self transitions. We develop a new nonparametric model of genetic sequence
data, based on the hierarchical Dirichlet process, which supports these self
transitions and nonhomogeneity. Our model provides a parameterization of the
genetic process that is more parsimonious than other more general nonparametric
models which have previously been applied to population genetics. We provide
truncation-free MCMC inference for our model using a new auxiliary sampling
scheme for Bayesian nonparametric HMMs. In a series of experiments on male X
chromosome data from the Thousand Genomes Project and also on data simulated
from a population bottleneck we show the benefits of our model over the popular
finite model fastPHASE, which can itself be seen as a parametric truncation of
our model. We find that the number of HMM states found by our model is
correlated with the time to the most recent common ancestor in population
bottlenecks. This work demonstrates the flexibility of Bayesian nonparametrics
applied to large and complex genetic data
Faster K-Means Cluster Estimation
There has been considerable work on improving popular clustering algorithm
`K-means' in terms of mean squared error (MSE) and speed, both. However, most
of the k-means variants tend to compute distance of each data point to each
cluster centroid for every iteration. We propose a fast heuristic to overcome
this bottleneck with only marginal increase in MSE. We observe that across all
iterations of K-means, a data point changes its membership only among a small
subset of clusters. Our heuristic predicts such clusters for each data point by
looking at nearby clusters after the first iteration of k-means. We augment
well known variants of k-means with our heuristic to demonstrate effectiveness
of our heuristic. For various synthetic and real-world datasets, our heuristic
achieves speed-up of up-to 3 times when compared to efficient variants of
k-means.Comment: 6 pages, Accepted at ECIR 201
Complete spatial characterization of an optical wavefront using a variable-separation pinhole pair
We present a technique for measuring the transverse spatial properties of an
optical wavefront. Intensity and phase profiles are recovered by analysis of a
series of interference patterns produced by the combination of a scanning
X-shaped slit and a static horizontal slit; the spatial coherence may be found
from the same data. We demonstrate the technique by characterizing high
harmonic radiation generated in a gas cell, however the method could be
extended to a wide variety of light sources.Comment: 4 pages, 3 figures, 1 tabl
Rhinologic changes in Wegener's granulomatosis
Twenty-eight patients with a clinical diagnosis of sinonasal Wegener's granulomatosis were referred for imaging during the period 1990-2001. Of these, 10 had clinical symptoms and signs confined to the nose and sinuses and 18 had classical systemic Wegener's. The computed tomography (CT) and magnetic resonance (MRI) scans of the series were reviewed by a panel of one otolaryngologist and two radiologists. From the total of 28 patients, 85.7 per cent showed non-specific mucosal thickening in the nasal cavity or paranasal sinuses, 75 per cent showed evidence of bone destruction, and 50 per cent new bone formation in the walls of the sinus cavities. In addition the orbit was affected in 30 per cent of patients.The diagnosis of systemic Wegener's granulomatosis is made clinically but the condition may present characteristic features on imaging by CT and MRI. In a patient without a history of previous sinonasal surgery, a combination of bone destruction and new bone formation on CT is virtually diagnostic of Wegener's especially when accompanied on MRI by a fat signal from the sclerotic sinus wall. These changes are important diagnostically in localized sinonasal Wegener's granulomatosis where the clinical diagnosis may be uncertain and the cANCA test can be negative
A comparison of the physiological consequences of head-loading and back-loading for African and European women
The aim is to quantify the physiological cost of head-load carriage and to examine the āfree rideā hypothesis for head-load carriage in groups of women differing in their experience of head-loading. Twenty-four Xhosa women [13 experienced head-loaders (EXP), 11 with no experience of head-loading (NON)] attempted to carry loads of up to 70% of body mass on both their heads and backs whilst walking on a treadmill at a self-selected walking speed. Expired air was collected throughout. In a second study nine women, members of the British Territorial Army, carried similar loads, again at a self-selected speed. Maximum load carried was greater for the back than the head (54.7 Ā± 15.1 vs. 40.8 Ā± 13.2% BM, P <0.0005). Considering study one, head-loading required a greater oxygen rate than back-loading (10.1 Ā± 2.6 vs. 8.8 Ā± 2.3 ml kg bodymassā1 minā1, P = 0.043, for loads 10ā25% BM) regardless of previous head-loading experience (P = 0.333). Percentage changes in oxygen consumption associated with head-loading were greater than the proportional load added in both studies but were smaller than the added load for the lighter loads carried on the back in study 1. All other physiological variables were consistent with changes in oxygen consumption. The data provides no support for the āfree rideā hypothesis for head-loading although there is some evidence of energy saving mechanisms for back-loading at low speed/load combinations. Investigating the large individual variation in response may help in identifying combinations of factors that contribute to improved economy
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