Vector correlation patterns

Finally, MET was imparted the matrix form similar to that of IET. A newly developed original method based on the many-particle master equation led to an infinite hierarchy for vector correlation patterns (VCPs) that can be truncated in two different ways [43,44], The simplest one reproduces the conventional IET, while the other allows a general modification of the kernel, resulting in the matrix formulation of MET applicable to complex multistage reactions. 

Using a redundant internal coordinate set as in the case of Figures 3e - 3h, a significant improvement of all correlation patterns can be observed. This has to do with the fact that with increasing size of the redundant parameter set c-vectors adopt more the form of a-vectors [19]. For example, in the case of the noruedundant internal coordinate set the average overlap between adiabatic and c-vectors is 0.69, which means that the two types of internal mode vectors are... 

Figure 4.28. Correlation graph for file PROFILE.dat. The facts that (a) 23 out of 55 combinations yield probabilities of error below p = 0.04 (42% expected due to chance alone =8%) and (b) that they fall into a clear pattern makes it highly probable that the peak areas [%] of the corresponding chromatograms follow a hidden set of rules. This is borne out by plotting the vectors two by two. Because a single-sided test is used, p cannot exceed 0.5.

Unfortunately, the experimental data cannot be correlated directly with the crystal structure, because some of the information needed is lost in recording the X-ray intensity pattern. Indeed, the diffracted X-ray beam is a vector, and it has both an intensity and a phase angle. The information concerning phase angle is lost during measurement of the X-ray intensity. The phase angle could, perhaps, be recorded by a holographic method, but X-ray lasers do not as yet exist. 

Fig. 18. One-dimensional model for visualisation of the surface lattice by a blunt tip based on the Moire mechanism, a The signal, which is measured by the detector during lateral sliding of the two lattices over each other, represents a superposition of the two wave vectors k and 1 b The regular pattern vanishes when the correlation between the lattices is disturb ed by the irregular surface structure c The regular pattern retains though a single atom defect emerges in the surface lattice...

Alignment-free Pharmacophore Patterns -A Correlation-vector Approach ... 

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