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6
Sieves for Selection of Genes According
to Desired Behaviors
6.1 Introduction
So far we introduced and discussed four nearly-orthogonal measures of emergence
(the
exponent of growth
, the
variance
, the
transient length,
and the
clustering
coefficient
) capable to give a synthetic description of the emergent behavior in a
cellular array (CA, CNN or Small Worlds network) with a given cell (usually
specified by its family name and the particular ID).
In Chap. 4 we saw that with the help of these measures it is possible to draw
maps transforming the ID (cell genes) space into a behavioral space where each
cell is associated with a point. The position of this point within the behavioral
space gives a hint about the behavioral particularities of the cellular array without
a need to further simulate it.
In practical applications of cellular automata quite often the following problem
(called
design for emergence
) occurs: Given a desired behavior, often specified in
natural language, find one or more cellular systems (CNNs CAs, Small World
networks, etc.) capable to exhibit this behavior. Unless a description with meas-
ures of emergence is available, answering the above question is a matter of trial
and error with a lot of wasted time to simulate and observe the dynamical evolution
of the cellular automata. Instead, defining families of CA cells and automatically
calculating the reduced set of measures of complexities for small size cellular
arrays allows for the automation of the search process. It also makes possible to
apply optimization algorithms with numerically specified objective function and
therefore complex design for emergence problems can be solved in due time.
The focus of this chapter is on a methodology to design “sieves”, i.e. functional
constraints applied to one or more of the previously defined
emergence measures
such that desired genes may be selected from a larger pool. This larger pool may
be an entire family of cells, or a large population of cells selected randomly within
a very large family. The computational limitation is given by the available time to
compute the emergence measure for all cells within the selected pool. As we will
see in Chap. 7, introducing an
analytically defined exponent of growth
makes pos-
sible a substantial reduction of computational demands, since emergent properties
may be predicted entirely based on cell and neighborhood properties, without
simulating the CA.
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