Nearest neighbour histogram

Fig. 1.6 Black phosphorus and arsenic nearest neighbour histograms, showing the number of atoms in a given neighbouring shell versus the normalized shell distance cfmin is the nearest neighbour distance). Note the different location of the maximum gap between phosphorus and arsenic. After Daams etai (1991).

See also Fig. 3.8. where the nearest-neighbour number (NNN) of the two atomic species is evidently eight. A list and the histogram of the atomic distances with the corresponding number of the equidistant neighbours are shown in Fig. 3.17. The resulting CNE is 14. In Fig. 3.31 the derivative CsCl superstructure MnCu2Al type... 

Fig. 10.13. Nearest neighbour spacing distribution of the energy levels of the one-dimensional hehum atom in the three energy regimes of Fig. 10.12(a) - (c), respectively. Histograms numerical data. Smooth lines Wignerian distribution. (Adapted from Bliimel and Reinhardt (1995).)...

The discriminant analysis techniques discussed above rely for their effective use on a priori knowledge of the underlying parent distribution function of the variates. In analytical chemistry, the assumption of multivariate normal distribution may not be valid. A wide variety of techniques for pattern recognition not requiring any assumption regarding the distribution of the data have been proposed and employed in analytical spectroscopy. These methods are referred to as non-parametric methods. Most of these schemes are based on attempts to estimate P(x g > and include histogram techniques, kernel estimates and expansion methods. One of the most common techniques is that of K-nearest neighbours. 

These nucleotides had compositions that were characteristic of the DNA under study (and of the DNase used). Since the pereentages of the termini formed by DNases from bacterial DNAs were linearly related to their GC levels (Fig. 1.3A), a useful way to show the results from the DNAs under examination was to plot difference histograms like those of Fig. 1.3B. This approach extended the nearest neighbour analysis of dinucleotide frequencies (Josse et al., 1961) to a frequency approach involving the sequences, at least four... 

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