  The idea of using metaplastic synapses to incorporate the separate storage of
long- and short-term memories via an array of hidden states was put forward in
the cascade model of Fusi et al. In this paper, we devise and investigate two
models of a metaplastic synapse based on these general principles. The main
difference between the two models lies in their available mechanisms of decay,
when a contrarian event occurs after the build-up of a long-term memory. In one
case, this leads to the conversion of the long-term memory to a short-term
memory of the opposite kind, while in the other, a long-term memory of the
opposite kind may be generated as a result. Appropriately enough, the response
of both models to short-term events is not affected by this difference in
architecture. On the contrary, the transient response of both models, after
long-term memories have been created by the passage of sustained signals, is
rather different. The asymptotic behaviour of both models is, however,
characterised by power-law forgetting with the same universal exponent.
