Correlation graph between various

Figure 5 Correlation graph between various exchange, exchange-correlation methods, and OEP for C2H4 all 6 occupied valence orbitals. Prom Ref. [55].

Fig. 12.5 The general scheme of the Monte Carlo optimization used as the basis of caleulation of optimal descriptors. The row Correlation weight contains graphical images of various features (extracted from graph or SMILES) characterized by positive values of the correlation weights (they are indicated by white color) or by negative values of correlation weights (those are indieated by black color). Blocked (rare) features have correlation weights which are fixed to be equal to zero (indicated by grey b ). The R(X,Y) is correlation coefficient between descriptor and endpoint...

A numerical value associated with chemical constitution that can be used to correlate chemical structure with various physical properties, chemical reactivity, or biological reactivity. The numerical basis tor topological indices is provided (depending on how a molecular graph is converted into a numerical value) by either the adjacency matrix or the topological distance matrix. In the latter, the topological distance between two vertices is the number of edges in the shortest path between these. 

In Figure 2 the relationship between the number of observations and the probability of a chance correlation with ten screened variables for various r2 values is shown. From the graph corresponding to r2 0.8 it may be seen that the probability of encountering a chance correlation at this level is about 22 for ten observations, reaching zero for 23 observations. 

Figure 5 shows the relationship between observations and variables for a chance correlation probability of 1 or less for various r2 levels. The linear relationships shown are each statistically significant at the p < 0.0001 level. This graph permits the determination of the number of observations required to screen, for example, ten variables while keeping the probability of encountering a chance correlation with r2 0.8 at the 1 level or less. From the graph it can be estimated that this number of observations is about 20. For r2 0.9> the number required is less,... 

To summarize all copolymers. Fig. 7.82 reproduces a three-dimensional plot of the Barton equation, as it was used throughout this chapter. This graph allows the correlation between the three types of projections possible and shown in various parts of this chapter. The two effects that must be added for a full description are the specific interactions (see Fig. 7.69, Schneider equation) and the broadening of the glass transition, available from heat capacity analysis. 

Figure 17 The various correiations between NMR parameters and locai Ti geometry are shown. The graph in (A) depicts the reiationship between Siso and the mean bond length in TiOg units. Cq( TI) is shown to be directly correlated to the amount of shear strain in (B) TiOg and (C) Ti04 units see Ref. [42] for more information about shear strain. Note that iso is referenced to SrTiOs (see Table 1 and main text). Reprinted with permission from Ref. [49], Copyright 2002 American Chemical Society.

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