Dykstra's Algorithm and a Representation of the Moore–Penrose Inverse

AbstractThe convergence of Lardy's series representation of the Moore–Penrose inverse of a closed unbounded linear operator is proved via Dykstra's alternating projection algorithm

Nonstationary lterated Tikhonov Regularization

A convergence rate is established for nonstationary iterated Tikhonov regularization, applied to ill-posed problems involving closed, densely defined linear operators, under general conditions on the iteration parameters. lt is also shown that an order-optimal accuracy is attained when a certain a posteriori stopping rule is used to determine the iteration number

Dublin Core Metadata Harvested Through OAI-PMH

The introduction in 2001 of the Open Archives Initiative Protocol for Metadata Harvesting (OAI-PMH) increased interest in and awareness of metadata quality issues relevant to digital library interoperability and the use of harvested metadata to build "union catalogs" of digital information resources. Practitioners have offered wide-ranging advice to metadata authors and have suggested metrics useful for measuring the quality of shareable metadata. Is there evidence of changes in metadata practice in response to such advice and/or as a result of an increased awareness of the importance of metadata interoperability? This paper looks at metadata records created over a six-year period that have been harvested by the University of Illinois at Urbana Champaign, and reports on quantitative and qualitative analyses of changes observed over time in shareable metadata quality.IMLS National Leadership Grant LG-02-02-0281published or submitted for publicationis peer reviewe

Validation of a spectral correction procedure for sun and sky reflections in above-water reflectance measurements

A three-component reflectance model (3C) is applied to above-water radiometric measurements to derive remote-sensing reflectance Rrs (λ). 3C provides a spectrally resolved offset Δ(λ) to correct for residual sun and sky radiance (Rayleigh- and aerosol-scattered) reflections on the water surface that were not represented by sky radiance measurements. 3C is validated with a data set of matching above- and below-water radiometric measurements collected in the Baltic Sea, and compared against a scalar offset correction Δ. Correction with Δ(λ) instead of Δ consistently reduced the (mean normalized root-mean-square) deviation between Rrs (λ) and reference reflectances to comparable levels for clear (Δ: 14.3 ± 2.5 %, Δ(λ): 8.2 ± 1.7 %), partly clouded (Δ: 15.4 ± 2.1 %, Δ(λ): 6.5 ± 1.4 %), and completely overcast (Δ: 10.8 ± 1.7 %, Δ(λ): 6.3 ± 1.8 %) sky conditions. The improvement was most pronounced under inhomogeneous sky conditions when measurements of sky radiance tend to be less representative of surface-reflected radiance. Accounting for both sun glint and sky reflections also relaxes constraints on measurement geometry, which was demonstrated based on a semi-continuous daytime data set recorded in a eutrophic freshwater lake in the Netherlands. Rrs (λ) that were derived throughout the day varied spectrally by less than 2 % relative standard deviation. Implications on measurement protocols are discussed. An open source software library for processing reflectance measurements was developed and is made publicly available

The equivalence of fluctuation scale dependence and autocorrelations

We define optimal per-particle fluctuation and correlation measures, relate fluctuations and correlations through an integral equation and show how to invert that equation to obtain precise autocorrelations from fluctuation scale dependence. We test the precision of the inversion with Monte Carlo data and compare autocorrelations to conditional distributions conventionally used to study high-$p_t$ jet structure.Comment: 10 pages, 9 figures, proceedings, MIT workshop on correlations and fluctuations in relativistic nuclear collision

Variability of adjacency effects in sky reflectance measurements

Sky reflectance Rsky(l) is used to correct in situ reflectance measurements in the remote detection of water colour. We analysed the directional and spectral variability in Rsky(l) due to adjacency effects against an atmospheric radiance model. The analysis is based on one year of semi-continuous Rsky(l) observations that were recorded in two azimuth directions. Adjacency effects contributed to Rsky(l) dependent on season and viewing angle, and predominantly in the near-infrared (NIR). For our test area, adjacency effects spectrally resembled a generic vegetation spectrum. The adjacency effect was weakly dependent on the magnitude of Rayleigh- and aerosol-scattered radiance. Reflectance differed between viewing directions 5.4 +/- 6.3% for adjacency effects and 21.0 +/- 19.8% for Rayleigh- and aerosol-scattered Rsky(l), in the NIR. It is discussed under which conditions in situ water reflectance observations require dedicated correction for adjacency effects. We provide an open source implementation of our method to aid identification of such conditions. Copyright 2017 Optical Society of America

On the condensed density of the generalized eigenvalues of pencils of Hankel Gaussian random matrices and applications

Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which allows to get a closed form approximation of the condensed density of the generalized eigenvalues of the pencils. Implications of this result for solving several moments problems are discussed and some numerical examples are provided.Comment: 30 pages, 16 figures, better approximations provide

On deconvolution problems: numerical aspects

An optimal algorithm is described for solving the deconvolution problem of the form ${\bf k}u:=\int_0^tk(t-s)u(s)ds=f(t)$ given the noisy data $f_\delta$, $||f-f_\delta||\leq \delta.$ The idea of the method consists of the representation ${\bf k}=A(I+S)$, where $S$ is a compact operator, $I+S$ is injective, $I$ is the identity operator, $A$ is not boundedly invertible, and an optimal regularizer is constructed for $A$. The optimal regularizer is constructed using the results of the paper MR 40#5130.Comment: 7 figure