185,402 research outputs found
Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching
MCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the
computation of complex target distributions as exemplified by huge datasets. We
offer in this paper an approach to reduce the computational costs of such
algorithms by a simple and universal divide-and-conquer strategy. The idea
behind the generic acceleration is to divide the acceptance step into several
parts, aiming at a major reduction in computing time that outranks the
corresponding reduction in acceptance probability. The division decomposes the
"prior x likelihood" term into a product such that some of its components are
much cheaper to compute than others. Each of the components can be sequentially
compared with a uniform variate, the first rejection signalling that the
proposed value is considered no further, This approach can in turn be
accelerated as part of a prefetching algorithm taking advantage of the parallel
abilities of the computer at hand. We illustrate those accelerating features on
a series of toy and realistic examples.Comment: 20 pages, 12 figures, 2 tables, submitte
Vectorial dissipative solitons in vertical-cavity surface-emitting Lasers with delays
We show that the nonlinear polarization dynamics of a vertical-cavity
surface-emitting laser placed into an external cavity leads to the formation of
temporal vectorial dissipative solitons. These solitons arise as cycles in the
polarization orientation, leaving the total intensity constant. When the cavity
round-trip is much longer than their duration, several independent solitons as
well as bound states (molecules) may be hosted in the cavity. All these
solutions coexist together and with the background solution, i.e. the solution
with zero soliton. The theoretical proof of localization is given by the
analysis of the Floquet exponents. Finally, we reduce the dynamics to a single
delayed equation for the polarization orientation allowing interpreting the
vectorial solitons as polarization kinks.Comment: quasi final resubmission version, 12 pages, 9 figure
An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation
We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a reliability of more than \%. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources
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Computational Methods for Parameter Estimation in Climate Models
Intensive computational methods have been used by Earth scientists in a wide range of problems in data inversion and uncertainty quantification such as earthquake epicenter location and climate projections. To quantify the uncertainties resulting from a range of plausible model configurations it is necessary to estimate a multidimensional probability distribution. The computational cost of estimating these distributions for geoscience applications is impractical using traditional methods such as Metropolis/Gibbs algorithms as simulation costs limit the number of experiments that can be obtained reasonably. Several alternate sampling strategies have been proposed that could improve on the sampling efficiency including Multiple Very Fast Simulated Annealing (MVFSA) and Adaptive Metropolis algorithms. The performance of these proposed sampling strategies are evaluated with a surrogate climate model that is able to approximate the noise and response behavior of a realistic atmospheric general circulation model (AGCM). The surrogate model is fast enough that its evaluation can be embedded in these Monte Carlo algorithms. We show that adaptive methods can be superior to MVFSA to approximate the known posterior distribution with fewer forward evaluations. However the adaptive methods can also be limited by inadequate sample mixing. The Single Component and Delayed Rejection Adaptive Metropolis algorithms were found to resolve these limitations, although challenges remain to approximating multi-modal distributions. The results show that these advanced methods of statistical inference can provide practical solutions to the climate model calibration problem and challenges in quantifying climate projection uncertainties. The computational methods would also be useful to problems outside climate prediction, particularly those where sampling is limited by availability of computational resources.National Science Foundation OCE-0415251CONACyT-Mexico 159764Institute for Geophysic
Pulse-Shape discrimination with the Counting Test Facility
Pulse shape discrimination (PSD) is one of the most distinctive features of
liquid scintillators. Since the introduction of the scintillation techniques in
the field of particle detection, many studies have been carried out to
characterize intrinsic properties of the most common liquid scintillator
mixtures in this respect. Several application methods and algorithms able to
achieve optimum discrimination performances have been developed. However, the
vast majority of these studies have been performed on samples of small
dimensions. The Counting Test Facility, prototype of the solar neutrino
experiment Borexino, as a 4 ton spherical scintillation detector immersed in
1000 tons of shielding water, represents a unique opportunity to extend the
small-sample PSD studies to a large-volume setup. Specifically, in this work we
consider two different liquid scintillation mixtures employed in CTF,
illustrating for both the PSD characterization results obtained either with the
processing of the scintillation waveform through the optimum Gatti's method, or
via a more conventional approach based on the charge content of the
scintillation tail. The outcomes of this study, while interesting per se, are
also of paramount importance in view of the expected Borexino detector
performances, where PSD will be an essential tool in the framework of the
background rejection strategy needed to achieve the required sensitivity to the
solar neutrino signals.Comment: 39 pages, 17 figures, submitted to Nucl. Instr. Meth.
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