  Various neurophysiological and cognitive functions are based on transferring
information between spiking neurons via a complex system of synaptic
connections. In particular, the capacity of presynaptic inputs to influence the
postsynaptic outputs---the efficacy of the synapses---plays a principal role in
all aspects of hippocampal neurophysiology. However, a direct link between the
information processed at the level of individual synapses and the animal's
ability to form memories at the organismal level has not yet been fully
understood. Here, we investigate the effect of synaptic transmission
probabilities on the ability of the hippocampal place cell ensembles to produce
a cognitive map of the environment. Using methods from algebraic topology, we
find that weakening synaptic connections increase spatial learning times,
produce topological defects in the large-scale representation of the ambient
space and restrict the range of parameters for which place cell ensembles are
capable of producing a map with correct topological structure. On the other
hand, the results indicate a possibility of compensatory phenomena, namely that
spatial learning deficiencies may be mitigated through enhancement of neuronal
activity.
