In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 82, 041103(R) (2010)] we introduced the effective-energy technique to calculate in an accurate and numerically efficient manner the GW self-energy as well as the polarizability, which is required to evaluate the screened Coulomb interaction W. In this work we show that the effective-energy technique can be used to further simplify the expression for the polarizability without a significant loss of accuracy. In contrast to standard sum-over-state methods where huge summations over empty states are required, our approach only requires summations over occupied states. The three simplest approximations we obtain for the polarizability are explicit functionals of an independent- or quasi-particle one-body reduced density matrix. We provide evidence of the numerical accuracy of this simplified effective-energy technique as well as an analysis of our method.
The aim of this study was to evaluate the effectiveness of manual and rotary instrumentation techniques for removing root fillings after different storage times. Twenty-four canals from palatal roots of human maxillary molars were instrumented and filled with gutta-percha and zinc-oxide eugenol-based sealer (Endofill) , and were stored in saline for 6 years. Non-aged control specimens were treated in the same manner and stored for 1 week. All canals were retreated using hand files or ProTaper Universal NiTi rotary system. Radiographs were taken to determine the amount of remaining material in the canals. The roots were vertically split, the halves were examined with a clinical microscope and the obtained images were digitized. The images were evaluated with AutoCAD software and the percentage of residual material was calculated. Data were analyzed with two-way ANOVA and Tukey's test at 5% significance level. There was no statistically significant differences (p>0.05) between the manual and rotary techniques for filling material removal regardless the ageing effect on endodontic sealers. When only the age of the filling material was analyzed microscopically, non-aged fillings that remained on the middle third of the canals presented a higher percentage of material remaining (p
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The increasing complexity and runtime of environmental models lead to the current situation that the calibration of all model parameters or the estimation of all of their uncertainty is often computationally infeasible. Hence, techniques to determine the sensitivity of model parameters are used to identify most important parameters or model processes. All subsequent model calibrations or uncertainty estimation procedures focus then only on these subsets of parameters and are hence less computational demanding. While the examination of the convergence of calibration and uncertainty methods is state-of-the-art, the convergence of the sensitivity methods is usually not checked. If any, bootstrapping of the sensitivity results is used to determine the reliability of the estimated indexes. Bootstrapping, however, might as well become computationally expensive in case of large model outputs and a high number of bootstraps. We, therefore, present a Model Variable Augmentation (MVA) approach to check the convergence of sensitivity indexes without performing any additional model run. This technique is method- and model-independent. It can be applied either during the sensitivity analysis (SA) or afterwards. The latter case enables the checking of already processed sensitivity indexes. To demonstrate the method independency of the convergence testing method, we applied it to three widely used, global SA methods: the screening method known as Morris method or Elementary Effects (Morris 1991, Campolongo et al., 2000), the variance-based Sobol' method (Solbol' 1993, Saltelli et al. 2010) and a derivative-based method known as Parameter Importance index (Goehler et al. 2013). The new convergence testing method is first scrutinized using 12 analytical benchmark functions (Cuntz & Mai et al. 2015) where the true indexes of aforementioned three methods are known. This proof of principle shows that the method reliably determines the uncertainty of the SA results when different 2ff7e9595c
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