320 - canonization distance measure

In order to address this question, we conducted separate investigations into the spatial and temporal variation in O. excavata. For each sample, eigenscores from the PCA were plotted to facilitate visual examination of the data, and canonical variates analysis (CVA) was used to optimize any clustering. The smaller sample number required for the spatial and temporal analyses allowed a non-parametric MANOVA (NPMANOVA) to be conducted on the data using a Bray-Curtis distance measure, following the procedures described by Anderson (2001). 

It is clear that Eq. (85) is numerically reliable provided is sufficiently small. However, a detailed investigation in Ref. 69 reveals that can be as large as some ten percent of the diameter of a fluid molecule. Likewise, rj should not be smaller than, say, the distance at which the radial pair correlation function has its first minimum (corresponding to the nearest-neighbor shell). Under these conditions, and if combined with a neighbor list technique, savings in computer time of up to 40% over conventional implementations are measured for the first (canonical) step of the algorithm detailed in Sec. IIIB. These are achieved because, for pairwise interactions, only 1+ 2 contributions need to be computed here before i is moved U and F2), and only contributions need to be evaluated after i is displaced... 

Figures 7 and 8 plot deviations of total energies from FCI results for the various methods. It is clear that the CASSCF/L-CTD theory performs best out of all the methods smdied. (We recall that although the canonical transformation operator exp A does not explicitly include single excitations, the main effects are already included via the orbital relaxation in the CASSCF reference.) The absolute error of the CASSCF/L-CTD theory at equilibrium—1.57 mS (6-31G), 2.26 m j (cc-pVDZ)—is slightly better than that of CCSD theory—1.66m j (6-31G), 3.84 m j (cc-pVDZ) but unlike for the CCSD and CCSDT theories, the CASSCF/L-CTD error stays quite constant as the molecule is pulled apart while the CC theories exhibit a nonphysical turnover and a qualitatively incorrect dissociation curve. The largest error for the CASSCF/L-CTD method occurs at the intermediate bond distance of 1.8/ with an error of —2.34m (6-3IG), —2.42 mE j (cc-pVDZ). Although the MRMP curve is qualitatively correct, it is not quantitatively correct especially in the equilibrium region, with an error of 6.79 mEfi (6-3IG), 14.78 mEk (cc-pVDZ). One measure of the quality of a dissociation curve is the nonparallelity error (NPE), the absolute difference between the maximum and minimum deviations from the FCI energy. For MRMP the NPE is 4mE (6-3IG), 9mE, (cc-pVDZ), whereas for CASSCF/ L-CTD the NPE is 5 mE , (6-3IG), 6 mE , (cc-pVDZ), showing that the CASSCF/L-CTD provides a quantitative description of the bond breaking with a nonparallelity error competitive with that of MRMP.

Eirst a basic introduction into approaches of SDSL of proteins is given, followed by a summary of the important approaches for mobility measurements, accessibility studies, and distance determination. Finally, we will address IDPs. Since structure and dynamics of IDPs drastically depend on the environment and corresponding details are notoriously difficult to unravel by NMR or X-ray structure determination, SDSL EPR can significantly contribute in the investigation of those systems. To showcase the use of SDSL EPR in this field, recent results on a-synuclein being a canonical model among the IDPs are reviewed. 

Fig. 7.5 Classical and optimized MDS solutions calculated from the canonically transformed correlation surface from fig. 7.3. (A) The two-dimensional projection of the three-dimensional ( 2,3 = 99.2%) (or four-dimensional a2 4 = 99.98%) object found by the matrix method described by step 5 in the text. The coordinates for the points in A are the same as the first two columns of the matrix of eigenvectors in table 7.2A. The second diagram (B) is derived from the MDS optimization method discussed in step 6. The lines between points in both diagrams are obtained from the results of step 3 (table 7.1). Thus, B is more representative of the measured distance matrix. Both diagrams correspond to rotated and slightly distorted approximations to the reaction mechanism in fig.7.1. (From [1].)...

Physically, measures the probability of finding a particle at a distance ri2 from a particle held at the origin. Note that for a pair-wise additive potential in a canonical ensemble... 

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