Correlated sampling method

A correlated sampling method, known as reweighting [39,40] is much more efficient. One samples a set of configurations Rj (usually several thousand points at least) according to some distribution function, usually taken to be the square of the wavefunction for some initial trial function ] f T(-R q o) -Then, the variational energy (or the variance) for trial function nearby in parameter space can be calculated by using the same set of points ... 

In order to assess the accuracy of the present method, we compared it with two other methods. One was the Track Etch detector manufactured by the Terradex Corp. (type SF). Simultaneous measurements with our detectors and the Terradex detectors in 207 locations were made over 10 months. The correlation coefficient between radon concentrations derived from these methods was 0.875, but the mean value by the Terradex method was about twice that by our detectors. The other method used was the passive integrated detector using activated charcoal which is in a canister (Iwata, 1986). After 24 hour exposure, the amount of radon absorbed in the charcoal was measured with Nal (Tl) scintillation counter. The method was calibrated with the grab sampling method using activated charcoal in the coolant and cross-calibrated with other methods. Measurements for comparison with the bare track detector were made in 57 indoor locations. The correlation coefficient between the results by the two methods was 0.323. In the case of comparisons in five locations where frequent measurements with the charcoal method were made or where the radon concentration was approximately constant, the correlation coefficient was 0.996 and mean value by the charcoal method was higher by only 12% than that by the present method. 

The Hamiltonian in Eq. (39) has bear used to calculate the adiahatic free energy as a function of the solvent coordinate using the umbrella sampling method, and reactive flux correlation function calculations have been used to determine the adiabatic rate constant. The results were qualitatively similar to the results based on the two-state model. 

Key experiments useful for substructure determination by NMR include the DEPT sequence (c.. Figs. 2.44-2.46) for analysis of CH multiplicities, as well as the two-dimensional CH correlation for identification of all CH bonds (e.g. Fig. 2.55 and Table 2.2) and localization of individual proton shifts. If, in addition, vicinal and longer-range proton-proton coupling relationships are known, all CH substructures of the sample molecule can be derived. Classical identification of homonuclear proton coupling relationships involves homonuclear proton decoupling. A two-dimensional proton-proton shift correlation would be an alternative and the complementary experiment to carbon-proton shift correlation. Several methods exist [68], Of those, the COSTsequence abbreviated from Correlation spectroscopy [69] is illustrated in Fig. 2.56. 

Straight line equation Correlation coefficient Number Comparative of samples method compared References... 

Straight line equation Correlation Number Comparative References coefficient of samples method compared ... 

Although there is good correlation of the ELISA results with both the standard GLC methods and with the bioassay results conducted under controlled conditions, unpublished results with clomazone indicate that the correlation of any soil analytical results (ELISA or GLC) with actual crop injury that is observed in the field is poor. This poor correlation between observed soil levels of clomazone, and the actual occurance of carryover injury in the field, indicates that factors unrelated to the soil analytical methods used, have a large impact on the ability to use soil residual levels as a predictive tool for this herbicide. An example of the impact of other factors can be seen with corn, where unpublished results attribute the poor correlation between detected soil levels of clomazone and observed injury in the field to several factors, which include differences in corn sensitivity toward clomazone, the method of clomazone application, application rate, soil type/organic matter levels, soil pH, soil sampling methods, time of corn injury assessment, interactions with other pesticides and environmental factors. 

In order to obtain the time lag between two sets of reflected light signals of known distance apart, points a and b, for particles in random movement, the cross-correlation function method is generally used in treating the signals. The cross-correlation function of two sets of random signals a t) and b(t) express the independence of the two sets of sampled data, i.e.,... 

Although the direct application of correlated sampling can be inefficient in a high-dimensional parameter space, it can be fruitfully combined with a standard minimization technique such as the steepest-descent method [24]. Consider again the trial wavefunction c) containing a parametric... 

This means that we can estimate the derivative of the energy with respect to a exactly, without using finite-difference methods. Still, the computational power needed to optimize more than a few parameters remains large, even including the savings from correlated sampling, because the fluctuations on this quantity can be large. 

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