Predicting Emergence from Cell’s Structure - Systematic Design for Emergence in Cellular Nonlinear Networks - page 125

7.5.3 Comparison with the Experimental Exponent of Growth

It is interesting to compare the experimentally determined exponent of growth
U with the newly defined measure. It turns out that for “explosive” behaviors, in
addition to Up

as defined in (7.27), the value of ua (uncertainty within the active
area) plays an important role for a much finer discrimination among behaviors. Let

us recall Table 5.2, where some representative genes from each observed behavioral

class were listed. Here the same list of genes is considered but with new informa-
( U tion added ) to allow a comparison.

p ,

ua

Table 7.1a Comparison between U (experimental index of growth) and U p , for several

genes selected in Chap. 5 as belonging to “passive” (a), “stable near edge” (b) or “edge” (c) be-
haviors.

ua

Category (a) (b) (c)

ID U, Up= ua ID U, Up=ua ID U, Up, ua

107
128
136
144
152
256
264
272
280
862

0, 0.65
0, 0.32
0, 0.4
0, 0.33
0, 0.41
0, 0.08
0, 0.17
0, 0.09
0, 0.17
0, 2 0.67
Small ua

104
108
111
112
115
116
119
120
123
124

0.46, 0.67
0.60, 0.99
0.64, 0.64
0.13, 0.6
0.11, 0.55
0.67, 0.92
0.34, 0.58
0.47, 0.68
0.25, 0.74
0.67, 0.99
Large ua

131
134
135
138
139
142
143
146
147
150

1, 0.66 0.66
1, 2 0.94
1, 0.74 0.74
1, 2 0.82
1, 0.91 0.91
1, 2 0.86
1, 0.77 0.77
1, 2 0.74
1, 0.75 0.75
1, 2 0.94
Large ua

Table 7.1b Comparison between U (experimental index of growth) and U p , f r

several genes selected in Chap. 5 as belonging to “unstable near edge” (d), “nested” (e) or
“explosive” (f) behaviors

ua

Category (d) (e) (f)

ID U, Up, ua ID U, Up, ua ID U, Up, ua

41
49
69
81
101
375
463
471

4.98, 1.5, 0.43
1.36, 1.5, 0.27
2.98, 1.5, 0.66
1.18, 1.5, 0.43
1.85, 1.5, 0.64
2.08, 1.5, 0.66
1.18, 1.5, 0.27
1.4, 1.5, 0.43

330
341
682
693

4, 2, 1
5, 2, 1
5, 2, 1
4, 2, 1

418
419
421
422
423
425
426
427
429
430

44.04 2 0.99
15.28 1.5 0.83
46.49 2 0.93
44.04 2 0.69
6.0 1.5 0.68
46.49 2 0.83
44.0 2 0.92
15.28 1.5 0.75
46.44 2 0.68
44.04 2 0.6
Large ua
Large ue

Small ue,
Medium ua

Largest ue
Largest ua

From the above it is clear that there is a direct relationship between the prob-
abilistic exponent of growth and the experimentally determined one. These simi-
larities allow to infer rules (translated into “sieves” as defined in Chap. 6) to select