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An autapse is a synapse that a neuron forms with itself. They have been hypothesized to serve as short-term analog memory storage.[1]
  1. Seung, HS; Lee, DD; Reis, BY; Tank, DW (2000). "The Autapse: A Simple Illustration of Short-Term Analog Memory Storage by Tuned Synaptic Feedback", J. Computational Neuroscience 9:171-185. doi: 10.1023/A:1008971908649.