9,898 research outputs found
Composing Scalable Nonlinear Algebraic Solvers
Most efficient linear solvers use composable algorithmic components, with the
most common model being the combination of a Krylov accelerator and one or more
preconditioners. A similar set of concepts may be used for nonlinear algebraic
systems, where nonlinear composition of different nonlinear solvers may
significantly improve the time to solution. We describe the basic concepts of
nonlinear composition and preconditioning and present a number of solvers
applicable to nonlinear partial differential equations. We have developed a
software framework in order to easily explore the possible combinations of
solvers. We show that the performance gains from using composed solvers can be
substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table
PURIFY: a new approach to radio-interferometric imaging
In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a minimization problem for image reconstruction. This approach was shown, in theory and through simulations in a simple discrete visibility setting, to have the potential to outperform significantly CLEAN and its evolutions. In this work, we leverage the versatility of convex optimization in solving minimization problems to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted relies on the simultaneous-direction method of multipliers (SDMM), and contrasts with the current major-minor cycle structure of CLEAN and its evolutions, which in particular cannot handle the state-of-the-art minimization problems under consideration where neither the regularization term nor the data term are differentiable functions. We release a beta version of an SDMM-based imaging software written in C and dubbed PURIFY (http://basp-group.github.io/purify/) that handles various sparsity priors, including our recent average sparsity approach SARA. We evaluate the performance of different priors through simulations in the continuous visibility setting, confirming the superiority of SARA
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Overview of Constitutional Challenges to NSA Collection Activities and Recent Developments
[Excerpt] Beginning in the summer of 2013, media reports of foreign intelligence activities conducted by the National Security Agency (NSA) have been published and are apparently based on unauthorized disclosures of classified information by Edward Snowden, a former NSA contractor. The reports have focused on two main NSA collection activities conducted under the auspices of the Foreign Intelligence Surveillance Act (FISA) of 1978. The first is the bulk collection of telephony metadata for domestic and international telephone calls. The second involves the interception of Internet-based communications and is targeted at foreigners who are not within the United States, but may also inadvertently acquire the communications of U.S. persons.
As the public’s awareness of these programs has grown, Members of Congress and the public have increasingly voiced concerns about the constitutionality of these programs. This report provides a description of these two programs and the various constitutional challenges that have arisen in judicial forums with respect to each. Although a brief overview of the constitutional arguments and issues raised in the assorted cases is included, a detailed analysis or evaluation of those arguments is beyond the scope of this report
A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I
A new fast Bayesian approach is introduced for the detection of discrete
objects immersed in a diffuse background. This new method, called PowellSnakes,
speeds up traditional Bayesian techniques by: i) replacing the standard form of
the likelihood for the parameters characterizing the discrete objects by an
alternative exact form that is much quicker to evaluate; ii) using a
simultaneous multiple minimization code based on Powell's direction set
algorithm to locate rapidly the local maxima in the posterior; and iii)
deciding whether each located posterior peak corresponds to a real object by
performing a Bayesian model selection using an approximate evidence value based
on a local Gaussian approximation to the peak. The construction of this
Gaussian approximation also provides the covariance matrix of the uncertainties
in the derived parameter values for the object in question. This new approach
provides a speed up in performance by a factor of `hundreds' as compared to
existing Bayesian source extraction methods that use MCMC to explore the
parameter space, such as that presented by Hobson & McLachlan. We illustrate
the capabilities of the method by applying to some simplified toy models.
Furthermore PowellSnakes has the advantage of consistently defining the
threshold for acceptance/rejection based on priors which cannot be said of the
frequentist methods. We present here the first implementation of this technique
(Version-I). Further improvements to this implementation are currently under
investigation and will be published shortly. The application of the method to
realistic simulated Planck observations will be presented in a forthcoming
publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted
for publication in MNRA
Multi-Detector Multi-Component spectral matching and applications for CMB data analysis
We present a new method for analyzing multi--detector maps containing
contributions from several components. Our method, based on matching the data
to a model in the spectral domain, permits to estimate jointly the spatial
power spectra of the components and of the noise, as well as the mixing
coefficients. It is of particular relevance for the analysis of
millimeter--wave maps containing a contribution from CMB anisotropies.Comment: 15 pages, 7 Postscript figures, submitted to MNRA
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