Average-link clustering

The second approach used for linking clusters is termed the centroid link method. This method joins the centroids of the clusters instead of the nearest neighbors. The centroid is calculated as the average of the points within a cluster. Clustering using this approach with the same data as in Figure 4.8 is shown in Figure 4.10. 

Fig. 14. Plot of the g values g,g ) and of the average g value g vs rhombicity (UJ of (a) wild type (open symbol) and variant forms (closed symbols) of the Rieske protein in yeast bci complex where the residues Ser 183 and Tyr 185 forming hydrogen bonds into the cluster have been replaced by site-directed mutagenesis [Denke et al. (35) Merbitz-Zahradnik, T. Link, T. A., manuscript in preparation] and of (b) the Rieske cluster in membranes of Rhodobacter capsulatus in different redox states of the quinone pool and with inhibitors added [data from Ding et al. (79)]. The solid lines represent linear fits to the data points the dashed lines reproduce the fits to the g values of all Rieske and Rieske-type proteins shown in Fig. 13.

Another attribute of CA dynamics is the average size of clusters of cells. This is certainly influenced by the choice of J and Pb rules and should parallel some physical properties. Other attributes that can be measured and used to link with physical properties include the average number of joined faces of a molecule and the number of free cell faces. Each of these attributes has been exploited for their ability to relate to the physical properties. The choice of J and Pb rules, therefore, must be made with some attention to their attributes produced and their ability to mirror physical properties as a function of systematic rule changes. 

Figure 4.33. Layer formed by the linking of Mo6C18 clusters via extra Cl atoms (4 links per cluster). Each of these Cl atoms is shared between two clusters so, on average, 4/2 = 2C1 are added to each Mo6 group. Considering also the two unshared Cl atoms linked to each Mo octahedron we have an overall stoichiometric ratio of 6 Mo to (8 + 2 + 2) Cl corresponding to the di-halide Mo6C112. An isolated group formed by the 6 Mo octahedron with all (14) the surrounding Cl is shown in the next figure.

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