Structure-Based Models of NO Diffusion in the Nervous System - Computational Neuroscience: A Comprehensive Approach - page 123

nervous systems in autonomous mobile robots and have allowed us to start exploring
the properties and potential functional roles of this kind of signalling in the genera-
tion of behaviour [20, 21]. We have named this class of ANNs GasNets. Our work
with these networks is briefly introduced in this section.
Since as yet we have no deep formal theory for such systems, we have found
the use of stochastic search methods (such as evolutionary algorithms) to be a very
helpful tool in this exploration. We have used the methods of evolutionary robotics to
explore the suitability of this class of networks for generating a range of behaviours
in a variety of autonomous robots [20, 21].

4.4.1 The GasNet model

In this strand of our work we have attempted to incorporate into ANNs, in an ab-
stracted form, some of the richness and complexity that characterises the temporal
and spatial dynamics of real neuronal signalling, especially chemical signalling by
gaseous transmitters. As these systems operate on different temporal and spatial
scales to electrical signalling, we have developed models in which electrical and in-
direct chemical signalling are controlled in ANNs by separate processes. Thus, we
developed the GasNet, a standard ANN augmented by a diffusing virtual gas which
can modulate the response of other neurons.
The 'electrical' network underlying the GasNet model is a discrete time-step, re-
current neural network with a variable number of nodes. These nodes are connected
by either excitatory (with a weight of +1) or inhibitory (with a weight of -1) links
with the output, O i , of node i at time-step n described by the following equation:

tanh k i O i =

∑ j ∈ C i w ji O n − 1

I i + + b i (4.53)

j

where C i is the set of nodes with connections to node i and w ji = ± 1 is a connection

weight. I i is the external (sensory) input to node i at time n , and b i is a genetically set
bias. Each node has a genetically set default transfer function parameter, k i , which
can be altered at each time-step according to the concentration of the diffusing 'gas'
at node i to give k i (as described later in the section on modulation).

4.4.2 Gas diffusion in the networks

In addition to this underlying network in which positive and negative 'signals' flow
between units, an abstract process loosely analogous to the diffusion of gaseous mod-
ulators is at play. Some units can emit virtual 'gases' which diffuse and are capable
of modulating the behaviour of other units. The networks occupy a 2D space; the
diffusion processes mean that the relative positioning of nodes is crucial to the func-
tioning of the network. The original GasNet diffusion model is controlled by two
genetically specified parameters, namely the radius of influence r and the rate of
build up and decay s . Spatially, the gas concentration varies as an inverse expo-
nential of the distance from the emitting node with a spread governed by r , with