A multi-layered competitive neural network is presented for learning to achieve pattern recognition in a manner invariant to linear and/or nonlinear coordinate transformations such as projection, shift, rotation, magnification and so on. The transformed input patterns stored in the network are multiplied by the Jacobian of the transformation, an aspect shown to be essential for the transformation invariance. The network also has excellent generalization ability as has been verified by computer simulation.
Stochastic depression behavior of EPSPs which has been investigated experimentally by Markram and Tsodyks is analyzed using a probabilistic postsynapse model involving a 2-state receptor type and the Morris-Lecar equations. The analysis explains the depression and stationary properties of EPSPs on the basis of saturation and recovery characteristics of the receptor mechanisms. Furthermore, the “after pairing effect” is caused by changes in the receptor sensitivity, according to the present model. The model predictions with various action potential frequencies are in good agreement with the experimental results.