Exponents of Growth - Systematic Design for Emergence in Cellular Nonlinear Networks - page 90

Fig. 5.18. Functional dependence between all possible pairs of complexity measures.
Each point in a graph corresponds to a particular cell ID among the entire set of 262,144
possible cells

In order to give a quantitative description of that dependence, the following
simple statistical operations were performed:
Each complexity measure sequence representing a stochastic was normalized
such that results in a zero mean and a covariance of one sequence. Then mutual
correlations between all six possible pairs are calculated. The results are shown in
Table 5.4.

Table 5.4. Mutual correlations between the four measures for emergence introduced in
Chaps. 4 and 5

U Trans Clus Var

U 1 -0.19 -0.55 0.15

Trans -0.19 1 0.238 -0.23

Clus -0.55 0.238 1 -0.317

Var 0.15 -0.23 -0.317 1

The highest correlation (0.55) is between U and Clus. Indeed, as we already
observed, genes with explosive behaviors (large U ) are in many cases associated
with “random-like” noise generators characterized by a value of Clus around 0.5.
The weakest correlation (0.15) is between the variance Var of the clustering
coefficient and the exponent of growth U . Thus, the introduction of the variance
as a complexity measures gives enough new information to characterize the CA
behaviors.