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Ta b l e 3 . 1 5 Descriptional indices of models given for the first 14 grammatical schemata
Grammatical
Number of
Number of
Total n. of
τ
interval
Best
τ
RMSE
10 3 min
10 3 min
schemata
models
regressors
monomials
(
)(
)
10 2
1
135
6
16
151 - 345
315
1
.
61
·
10 2
2
128
6
17
343 - 477
401
1
.
62
·
10 2
3
49
6
17
43 - 93
43
1
.
84
·
10 2
4
46
6
16
138 - 232
219
1
.
95
·
10 2
5
44
8
24
1-71
40
1
.
48
·
10 2
6
38
6
16
525 - 699
683
1
.
78
·
10 2
7
33
6
16
473 - 563
556
1
.
79
·
10 2
8
32
5
15
514 - 694
602
2
.
78
·
10 2
9
28
7
16
570 - 696
671
1
.
09
·
10 2
10
26
6
16
493 - 684
684
1
.
8
·
10 2
11
20
8
23
118 - 137
137
5
.
86
·
10 3
12
15
9
25
103 - 117
103
9
.
6
·
10 2
13
15
6
17
474 - 499
474
1
.
62
·
10 2
14
12
7
21
191 - 212
212
1
.
97
·
cannot be transformed. We call it the inertia of the substance (in a given state). The
difference between the whole quantity of a substance and its inertia is the quantity of
substance that can be partitioned among all reactions competing for it. MP systems
with reactivity parameters were the first kind of MP systems formally defined [92].
They are a special class of MP systems with regulators, which we call reactive MP
systems or MPR systems. When we want to refer to the MP systems defined in Def-
inition 3.1, we refer to them as MPF systems for distinguishing them from MPR
systems (MP will mean one of the two systems, MPF or MPR, according to the
context). In an MPR system, we denote by
ψ x the parameter providing the inertia of
substance x , and by f r (
r
R
)
which provides the reactivity of the reaction r .Letus
set by R (
the set of reactions consuming the substance x ,by S (
x
)
r
)
the reactants
r (
of reaction r ,by
the multiplicity of the reactant x in the rule r , and by s any
state of the system. Then, another parameter p r , x of (metabolic) reactance of the rule
r , with respect to the substance x , can be associated to any substance x
|
x
) |
S (
r
)
:
r (
x
/|
x
) |
p r , x (
s
)=
) .
(3.47)
ψ
(
s
)+ r R ( x )
f r (
s
x
Let min A be the minimum over a finite set A of numbers, conventionally extended
to the empty set by min 0
1. With these notations, the flux regulation maps of a
reactive MP system are given by:
=
S (
ϕ r (
s
)=
min
{
p r , x (
s
) |
x
r
)
f r (
s
) .
(3.48)
 
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