Applications of Emergent Phenomena - Systematic Design for Emergence in Cellular Nonlinear Networks - page 138

processing architectures, high clock speeds and demand a large quantity of energy.
In [89] a different, lower complexity solution is proposed which employs emer-
gent computation of the type “unstable near edge” (Chap. 5). Instead of a highly
complex signal processor we build an “excitable membrane with temporal memory
(EMTM)” which slightly amplify any random spatial initial state, transforming a
temporal sequence applied only to a few cells of the membrane into a spatial

memory trace represented by the spatial state of the CA at the end of the temporal

sequence. CA arrays with no more than 20×20 cells can be used as EMTMs. Such
cellular arrays may be conveniently realized using FPGA technology or dedicated
hardware.
The computational complexity of the entire transformation scheme is reduced to
that of running the excitable membrane CA for the entire duration of the temporal
sequence (signal). Compared to HMM or other similar approaches it leads to a
dramatic reduction in the implementation complexity with positive impacts on the
power consumption.
Calvin [90] postulates a theory of a “cerebral code” emerging in the cerebral

cortex viewed as a cellular automata model. The method presented next can be
“ ”
artificial cortexes made of simple cells. Similar ideas, i.e. that of using special
dynamics of recurrent neural networks for signal processing [81] are also present
in the LSM (liquid state machines) [91] and Echo State Networks (ESN) [79]
theories, although for practical purposes they require a much higher implementa-
tion complexity.

regarded as a simple and practical possibility to create and use cerebral codes in

In what follows the EMTM method and its application for a sound recognition
problem is briefly discussed. For more details the reader is directed to [89].

8.3.1 Mapping Variable-Length Signals into Terminal States

Let us consider a signal defined as a discrete-time sequence s ( t ) with a certain

duration T (i.e. s ( t ) , t 1, 2 , K T . 'In many applications a signal has to be identi-

fied (or recognized) as belonging to a class. For instance, let us consider that our
signals come from a speaker and represents a segmented window of speech when

a particular word is spoken. In our experiments 20 different utterances of two

words, “zero” and “one” were considered'.

Let assume that we already identified a gene such that the CA behaves as an
EMTM (excitable membrane with temporal memory), a subject discussed
later. Then we are interested to map the variable length signal sequence
^ )

S into a fixed (predefined) sized binary matrix X (a terminal
state of the CA) to be used as a feature in a classification system. The following
algorithm is proposed to implement the function

s ( ), s ( 2 ),..., s ( T

. In the above <
represents the algorithm, which can be applied to any particular temporal se-
quence (or signal) S :

X < S