  We develop of a line of work initiated by Curto and Itskov towards
understanding the amount of information contained in the spike trains of
hippocampal place cells via topology considerations. Previously, it was
established that simply knowing which groups of place cells fire together in an
animal's hippocampus is sufficient to extract the global topology of the
animal's physical environment. We model a system where collections of place
cells group and ungroup according to short-term plasticity rules. In
particular, we obtain the surprising result that in experiments with spurious
firing, the accuracy of the extracted topological information decreases with
the persistence (beyond a certain regime) of the cell groups. This suggests
that synaptic transience, or forgetting, is a mechanism by which the brain
counteracts the effects of spurious place cell activity.
