Bayesian error estimation in density-functional theory.

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.

D-penicillamine for primary biliary cirrhosis.

BACKGROUND: D-penicillamine is used for patients with primary biliary cirrhosis due to its hepatic copper decreasing and immunomodulatory potentials. The results from randomised clinical trials have been inconsistent. OBJECTIVES: To systematically review the beneficial and harmful effects of D-penicillamine for patients with primary biliary cirrhosis. SEARCH STRATEGY: We identified trials through electronic searches of The Cochrane Hepato-Biliary Group Controlled Trials Register (September 2003), The Cochrane Central Register of Controlled Trials on The Cochrane Library (Issue 3, 2003), MEDLINE (January 1966 to September 2003), EMBASE (January 1980 to September 2003), The Chinese Biomedical CD Database (January 1979 to August 2003), and LILACS (1982 to 2003); through manual searches of bibliographies; and by contacting authors of the trials and pharmaceutical companies. SELECTION CRITERIA: We included randomised clinical trials comparing D-penicillamine with placebo/no intervention or other control intervention irrespective of language, year of publication, and publication status. DATA COLLECTION AND ANALYSIS: Two reviewers independently assessed the methodological quality of the trials and extracted data, validated by a third reviewer. The primary outcomes were 1) mortality and 2) a combination of those who died or underwent liver transplantation. We analysed dichotomous outcomes as relative risk (RR) with 95% confidence interval (CI) by a fixed effect model and a random effects model. We investigated sources of heterogeneity by subgroup analyses and tested the robustness of our findings by sensitivity analyses. MAIN RESULTS: We included seven trials randomising 706 patients with primary biliary cirrhosis. D-penicillamine compared with placebo/no intervention tended to increase mortality (RR 1.34, 95% CI 1.09 to 1.64, fixed; RR 1.46, 95% CI 0.85 to 2.50, random). However, there was substantial heterogeneity. No significant differences were detected regarding the risks of mortality or liver transplantation, pruritus, liver complications, progression of liver histological stage, or the levels of liver biochemical variables (except alanine aminotransferase). D-penicillamine versus placebo/no intervention significantly increased the risk of adverse events (RR 3.11, 95% CI 2.33 to 4.16, fixed; RR 4.18, 95% CI 1.38 to 12.69, random). REVIEWERS' CONCLUSIONS: D-penicillamine did not appear to reduce the risk of mortality, but significantly increased the occurrences of adverse events in patients with primary biliary cirrhosis. We do not support the use of D-penicillamine for patients with primary biliary cirrhosis.

Triangular laser resonators with astigmatic compensation.

The magnitudes and locations of the beam waists in both the sagittal and the tangential planes have been found by means of the ABCD matrix method for a triangular resonator. Equilateral and isosceles resonators are discussed, and curves are given from which resonators with astigmatism-free beams can be designed. A frequency-doubled triangular Nd ring laser has been constructed after this design, and it is demonstrated that this laser emits a single longitudinal mode with a circular TEM(00) Gaussian beam.