Memory as an organizer of dynamic modules in a network of potential interactions

Networks are amongst the most common tools to
describe interactions in a spatial form. One failing of networks is
that often there is little differentiation between the links of
potential interactions and those that are actually active in a
specific time or space. In this paper, we aim to show how spatial
organization of a network of potential interactions effect the
pattern formation and reproducibility of sub-patterns in the
network. We further show that even a short memory of the path
taken can radically effect the network characteristics and
placement of the most common modules.
While memory helps the reproducibility of some dynamic
patterns by creating a bias in the direction of learned patterns,
the spatial organization does this by limiting the individual
stochasticity. In both cases these forces increase the probability of
a pattern to recur. We see that memory effects are highly
dependent on the connectivity of the network. In high
connectivity networks memory cannot effect the results much.
This makes sense when the connectivity is seen as a measure of
the stochastic potential of the network, e. g., if there are many
connections from a node, then a memory remembering a specific
path passing through that node will not create much bias in the
directional preferences.
Many real networks are sparse. In light of this observation and
our confirming simulation results, we may conclude that there
should be a connectivity constraint for a network system to be
able to use memory to create specific sub-modules in its network
of potential interactions.