Information Technology Reference
In-Depth Information
has no effect on its context within the developed program. Its context is a result
of the enzymes that choose it as an input source and the enzymes it chooses as
input sources. Whether an enzyme is chosen as an input source at a particular
location depends on its shape. Consequently, an enzyme's shape determines its
context.
In biology, it is common for a molecule's shape to reflect (in part) its function.
In enzyme GP, it is desirable that an enzyme's shape reflects its role within a
program, for this would entail that enzymes with similar shapes would have
similar roles. As such, during specificity satisfaction when an enzyme is selected
for input according to its similarity to the specificity, the chosen enzyme will
have a role similar to the preferred enzyme simply by definition of the process.
If this were not the case, then the context of the enzyme—which depends on its
inputs—would change considerably depending on which other enzymes were
present within the program.
Functionality is a definition of shape, where an enzyme's shape is derived
from its own activity and the activities of enzymes bound below it in the pro-
gram. The aim of functionality is to make an enzyme's context meaningful and
repeatable regardless of which other enzymes are present within a program.
A functionality is a point within functionality space. The easiest way to think
of functionality space is as an enzyme reference system where each location
characterizes a certain type of enzyme. Any enzyme can be referenced within
this space and, consequently, other enzymes can use it to specify the types of
enzymes they would prefer to receive input from.
Functionality space is a unitary vector space with a dimension for each mem-
ber of the set of available functions and terminals. A functionality, therefore,
is a vector with a component between 0 and 1 for each member of this set. A
simple functionality space is depicted in Figure 3.6. The functionality,
F
,ofa
particular enzyme is derived using the following equations:
F(enzyme)
=
(
1
−
inputbias)F (activity)
+
inputbias.F (specificities)
(1)
i
=
1
specificity
i
.strength(specificity
i
)
F(specificities)
=
i
=
1
strength(specificity
i
)
,
(2)
where
inputbias
is a constant and
n
is the number of specificities. Equation 1
states that the functionality of an enzyme is a weighted sum of the functionality
of its activity and the functionality of its specificities. The functionality of the
enzyme's activity,
F(activity)
, is a unit vector situated on the axis corresponding
to the enzyme's function. A specificity is defined by the functionality it would
like to match. The functionality of all the enzyme's specificities, defined in
Equation 2, is a normalized sum of each specificity weighted by its strength.
An illustrative example using these equations is shown in Figure 3.7.
