where rk is the (instantaneous) firing frequency of the kth input neuron, and wk is the input weight for the kth synapse. Note that wk can be positive or negative (inhibitory inputs). There are N inputs to the single neuron. Unlike the RPFM SGL model, the output frequency of the leaky integrator neuron is not determined by a pulse generator and reset mechanism. Instead, the generator potential is passed through a no-memory nonlinearity, r = f(mp), to determine the instantaneous output frequency. Figure 9.2-1 illustrates four possible nonlinearities, or threshold functions, that can be used in NSL. Note that mp and r are analog variables.

In the NSL book (Weitzenfeld et al., 1999) some 11 CNS neural models applying NSL are described. All use very large numbers of neurons. In many ways, NSL is a bridge program between BNNs and ANNs. NSL can use more-detailed biological features of neurons than a typical ANN program; yet it also allows ANN structures to be simulated, albeit for neurophysiological purposes. The 11 example models in the NSL book include: Grossberg's adaptive resonance theory, Dev and House's depth perception, modeling the retina, receptive fields, the associative search network - landmark learning and hill climbing, a model of primate visual-motor conditional learning, the modular design of the oculomotor system in monkeys, the Crowley-Arbib saccade model, a cerebellar model of sensorimotor adaptation, learning to detour, and face recognition by dynamic link matching.

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