10,551 research outputs found
Interference fringes with maximal contrast at finite coherence time
Interference fringes can result from the measurement of four-time fourth-order correlation functions of a wave field. These fringes have a statistical origin and, as a consequence, they show the greatest contrast when the coherence time of the field is finite. A simple acoustic experiment is presented in which these fringes are observed, and it is demonstrated that the contrast is maximal for partial coherence. Random telegraph phase noise is used to vary the field coherence in order to highlight the problem of interpreting this interference; for this noise, the Gaussian moment theorem may not be invoked to reduce the description of the interference to one in terms of first-order interference.M.W. Hamilto
Insights into neutralization of animal viruses gained from study of influenza virus
It has long been known that the binding of antibodies to viruses can result in a loss of infectivity, or neutralization, but little is understood of the mechanism or mechanisms of this process. This is probably because neutralization is a multifactorial phenomenon depending upon the nature of the virus itself, the particular antigenic site involved, the isotype of immunoglobulin and the ratio of virus to immunoglobulin (see below). Thus not only is it likely that neutralization of one virus will differ from another but that changing the circumstances of neutralization can change the mechanism itself. To give coherence to the topic we are concentrating this review on one virus, influenza type A which is itself well studied and reasonably well understood [1–3]. Reviews of the older literature can be found in references 4 to 7
An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations
Selection among alternative theoretical models given an observed data set is
an important challenge in many areas of physics and astronomy. Reversible-jump
Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for
performing Bayesian model selection, but it suffers from a fundamental
difficulty: it requires jumps between model parameter spaces, but cannot
efficiently explore both parameter spaces at once. Thus, a naive jump between
parameter spaces is unlikely to be accepted in the MCMC algorithm and
convergence is correspondingly slow. Here we demonstrate an interpolation
technique that uses samples from single-model MCMCs to propose inter-model
jumps from an approximation to the single-model posterior of the target
parameter space. The interpolation technique, based on a kD-tree data
structure, is adaptive and efficient in modest dimensionality. We show that our
technique leads to improved convergence over naive jumps in an RJMCMC, and
compare it to other proposals in the literature to improve the convergence of
RJMCMCs. We also demonstrate the use of the same interpolation technique as a
way to construct efficient "global" proposal distributions for single-model
MCMCs without prior knowledge of the structure of the posterior distribution,
and discuss improvements that permit the method to be used in
higher-dimensional spaces efficiently.Comment: Minor revision to match published versio
Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations
Modern problems in astronomical Bayesian inference require efficient methods
for sampling from complex, high-dimensional, often multi-modal probability
distributions. Most popular methods, such as Markov chain Monte Carlo sampling,
perform poorly on strongly multi-modal probability distributions, rarely
jumping between modes or settling on just one mode without finding others.
Parallel tempering addresses this problem by sampling simultaneously with
separate Markov chains from tempered versions of the target distribution with
reduced contrast levels. Gaps between modes can be traversed at higher
temperatures, while individual modes can be efficiently explored at lower
temperatures. In this paper, we investigate how one might choose the ladder of
temperatures to achieve more efficient sampling, as measured by the
autocorrelation time of the sampler. In particular, we present a simple,
easily-implemented algorithm for dynamically adapting the temperature
configuration of a sampler while sampling. This algorithm dynamically adjusts
the temperature spacing to achieve a uniform rate of exchanges between chains
at neighbouring temperatures. We compare the algorithm to conventional
geometric temperature configurations on a number of test distributions and on
an astrophysical inference problem, reporting efficiency gains by a factor of
1.2-2.5 over a well-chosen geometric temperature configuration and by a factor
of 1.5-5 over a poorly chosen configuration. On all of these problems a sampler
using the dynamical adaptations to achieve uniform acceptance ratios between
neighbouring chains outperforms one that does not.Comment: 21 pages, 21 figure
BDDC and FETI-DP under Minimalist Assumptions
The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary
simple abstract form. It is shown that their properties can be obtained from
only on a very small set of algebraic assumptions. The presentation is purely
algebraic and it does not use any particular definition of method components,
such as substructures and coarse degrees of freedom. It is then shown that
P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC
preconditioned operators are of the same algebraic form, and the standard
condition number bound carries over to arbitrary abstract operators of this
form. The equality of eigenvalues of BDDC and FETI-DP also holds in the
minimalist abstract setting. The abstract framework is explained on a standard
substructuring example.Comment: 11 pages, 1 figure, also available at
http://www-math.cudenver.edu/ccm/reports
Efficient method for measuring the parameters encoded in a gravitational-wave signal
Once upon a time, predictions for the accuracy of inference on
gravitational-wave signals relied on computationally inexpensive but often
inaccurate techniques. Recently, the approach has shifted to actual inference
on noisy signals with complex stochastic Bayesian methods, at the expense of
significant computational cost. Here, we argue that it is often possible to
have the best of both worlds: a Bayesian approach that incorporates prior
information and correctly marginalizes over uninteresting parameters, providing
accurate posterior probability distribution functions, but carried out on a
simple grid at a low computational cost, comparable to the inexpensive
predictive techniques.Comment: 17 pages, 5 figure
Multispace and Multilevel BDDC
BDDC method is the most advanced method from the Balancing family of
iterative substructuring methods for the solution of large systems of linear
algebraic equations arising from discretization of elliptic boundary value
problems. In the case of many substructures, solving the coarse problem exactly
becomes a bottleneck. Since the coarse problem in BDDC has the same structure
as the original problem, it is straightforward to apply the BDDC method
recursively to solve the coarse problem only approximately. In this paper, we
formulate a new family of abstract Multispace BDDC methods and give condition
number bounds from the abstract additive Schwarz preconditioning theory. The
Multilevel BDDC is then treated as a special case of the Multispace BDDC and
abstract multilevel condition number bounds are given. The abstract bounds
yield polylogarithmic condition number bounds for an arbitrary fixed number of
levels and scalar elliptic problems discretized by finite elements in two and
three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl
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