Cell Assemblies (CAs) are the neural basis of both long and short termmemories. CAs, whose neurons persistently fire, are active short termmemories while the neurons are firing, and the memory ceases to beactive when the neurons stop firing. This paper provides simulationsof excitatory spiking neurons with small world topologies that persistfor several hundred milliseconds. Extending this model to includeshort term depression allows the CA to persist for several seconds, areasonable psychological duration. These CAs can be combined in asimple associative memory so that when three CAs are associated,ignition of two causes the third to ignite, while pairs ofunassociated CAs do not lead to the ignition of other CAs. Thismechanism has a larger capacity than a Hopfield net. A discussion ofthe current psychological theories, other mechanisms for short termmemory, the strengths and weaknesses of the paper's simulatedmodels, and proposed challenges are also provided.