Algorithms for Kullback-Leibler Approximation of Probability Measures in Infinite Dimensions

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the Kullback-Leibler divergence as a distance and find the best Gaussian approximation by minimizing this distance. It then follows that the approximate Gaussian must be equivalent to the Gaussian reference measure, defining a natural function space setting for the underlying calculus of variations problem. We introduce a computational algorithm which is well-adapted to the required minimization, seeking to find the mean as a function, and parameterizing the covariance in two different ways: through low rank perturbations of the reference covariance; and through Schr\"odinger potential perturbations of the inverse reference covariance. Two applications are shown: to a nonlinear inverse problem in elliptic PDEs, and to a conditioned diffusion process. We also show how the Gaussian approximations we obtain may be used to produce improved pCN-MCMC methods which are not only well-adapted to the high-dimensional setting, but also behave well with respect to small observational noise (resp. small temperatures) in the inverse problem (resp. conditioned diffusion).Comment: 28 page

Cloning, purification and characterization of the 6-phospho-3-hexulose isomerase YckF from Bacillus subtilis

The enzyme 6-phospho-3-hexulose isomerase (YckF) from Bacillus subtilis has been prepared and crystallized in a form suitable for X-ray crystallographic analysis. Crystals were grown by the hanging-drop method at 291 K using polyethylene glycol 2000 monomethylether as precipitant. They diffract beyond 1.7 A using an in-house Cu Kalpha source and belong to either space group P6(5)22 or P6(1)22, with unit-cell parameters a = b = 72.4, c = 241.2 A, and have two molecules of YckF in the asymmetric unit

CATTLE AS ASSETS: ASSESSMENT OF NON-MARKET BENEFITS FROM CATTLE IN SMALLHOLDER KENYAN CROP-LIVESTOCK SYSTEMS

This paper uses data from a survey of two hundred and fifty cattle households in three cattle keeping systems; intensive, semi-intensive and extensive systems to estimate the value of non-market, socio-economic benefits of cattle in Kenya. These benefits of cattle keeping are of special importance in developing countries, where financial markets function poorly and opportunities for risk management through formal insurance generally absent. However, when estimating the total contribution of livestock, these non-market functions are often ignored since they are difficult to value, yet they may contribute to a better understanding of livestock production systems. The use of contingent valuation method is employed in this study to elicit these non-market values. Econometric estimations are then used to assess the factors influencing the non-market benefits function. The results indicate that these benefits are highly valued by cattle keepers and comprise approximately 20% of the animal's total value across the three systems. They are influenced by various production system and household related factors. Implications for policy are drawn.Livestock Production/Industries, QQ112, QQ118, DD223,

Earth, Air, Water, Oil: Regulating Fracking in the Monterey Shale with Health and Environment in Mind

“Earth, Air, Water, Oil: Regulating Fracking in the Monterey Shale with Health and Environment in Mind,” explores how hydraulic fracturing regulation in California’s oil-rich Monterey Shale will impact regional public health, including groundwater and air quality. This is achieved through a combination of case study and policy analysis on both the state and national level

Structure of the GH9 glucosidase/glucosaminidase from Vibrio cholerae

Glycoside hydrolase family 9 (GH9) of carbohydrate-processing enzymes primarily consists of inverting endoglucanases. A subgroup of GH9 enzymes are believed to act as exo-glucosidases or exo-glucosaminidases, with many being found in organisms of the family Vibrionaceae, where they are proposed to function within the chitin-catabolism pathway. Here, it is shown that the GH9 enzyme from the pathogen Vibrio cholerae (hereafter referred to as VC0615) is active on both chitosan-derived and β-glucoside substrates. The structure of VC0615 at 3.17 A ° resolution is reported from a crystal form with poor diffraction and lattice disorder. VC0615 was highly refractory to crystallization efforts, with crystals only appearing using a high protein concentration under conditions containing the precipitant poly-γ-glutamic acid (PGA). The structure is highly mobile within the crystal lattice, which is likely to reflect steric clashes between symmetry molecules which destabilize crystal packing. The overall tertiary structure of VC0615 is well resolved even at 3.17 A ° resolution, which has allowed the structural basis for the exo-glucosidase/glucosaminidase activity of this enzyme to be investigated

Oh, You Kid!

https://digitalcommons.library.umaine.edu/mmb-vp/3687/thumbnail.jp

Oh, You Kid!

https://digitalcommons.library.umaine.edu/mmb-vp/3686/thumbnail.jp

Coefficients for tests from a decision theoretic point of view

From a decision theoretic point of view a general coefficient for tests, d, is derived. The coefficient is applied to three kinds of decision situations. First, the situation is considered in which a true score is estimated by a function of the observed score of a subject on a test (point estimation). Using the squared error loss function and Kelley’s formula for estimating the true score, it is shown that d equals the reliability coefficient from classical test theory. Second, the situation is considered in which the observed scores are split into more than two categories and different decisions are made for the categories (multiple decision). The general form of the coefficient is derived, and two loss functions suited to multiple decision situations are described. It is shown that for the loss function specifying constant losses for the various combinations of categories on the true and on the observed scores, the coefficient can be computed under the assumptions of the beta-binomial model. Third, the situation is considered in which the observed scores are split into only two categories and different decisions are made for each category (dichotomous decisions). Using a loss function that specifies constant losses for combinations of categories on the true and observed score and the assumption of an increasing regression function of t on x, it is shown that coefficient d equals Loevinger’s coefficient H between true and observed scores. The coefficient can be computed under the assumption of the beta-binomial model. Finally, it is shown that for a linear loss function and Kelley’s formula for the regression of the true score on the observed score, the coefficient equals the reliability coefficient of classical test theory