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The Greenberg–Hastings Cellular Automaton is a three state two dimensional cellular automaton named after James M. Greenberg and Stuart Hastings, designed to model excitable media, One advantage of a CA model is ease of computation. The model can be understood quite well using simple "hand" calculations, not involving a computer. Another advantage is that, at least in this case, one can prove a theorem characterizing those initial conditions which lead to repetitive behavior.
The spike response model (SRM) is a spiking neuron model in which spikes are generated by either a deterministic or a stochastic threshold process. In the SRM, the membrane voltage V is described as a linear sum of the postsynaptic potentials (PSPs) caused by spike arrivals to which the effects of refractoriness and adaptation are added. The threshold is either fixed or dynamic. In the latter case it increases after each spike. The SRM is flexible enough to account for a variety of neuronal firing pattern in response to step current input. The SRM has also been used in the theory of computation to quantify the capacity of spiking neural networks; and in the neurosciences to predict the subthreshold voltage and the firing times of cortical neurons during stimulation with a time-dependent current stimulation. The name Spike Response Model points to the property that the two important filters and of the model can be interpreted as the response of the membrane potential to an incoming spike (response kernel , the PSP) and to an outgoing spike (response kernel , also called refractory kernel). The SRM has been formulated in continuous time and in discrete time. The SRM can be viewed as a generalized linear model (GLM) or as an (integrated version of) a generalized integrate-and-fire model with adaptation.
References
- ↑ H. R. Wilson and J. D. Cowan. "Excitatory and inhibitory interactions in localized populations of model neurons" Biophysical Journal, 12:1–24, 1972.
- ↑ H. R. Wilson and J. D. Cowan. "A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue" Kybernetik, 13:55–80, 1973.
- ↑ S. Amari. "Dynamics of pattern formation in lateral inhibition type neural fields" Biological Cybernetics, 27:77–87, 1977.
- ↑ Coombes, Stephen (2006). "Neural fields" (PDF). Scholarpedia. 1 (6): 1373. Bibcode:2006SchpJ...1.1373C. doi: 10.4249/scholarpedia.1373 .
- ↑ G. B. Ermentrout and J. D. Cowan. "A mathematical theory of visual hallucination patterns" Biological Cybernetics, 34:137–150, 1979.
- ↑ David H. Wolpert and Bruce J. MacLennan, "A Universal Field Computer That is Purely Linear", University of Tennessee, Knoxville, Department of Computer Science Technical Report CS-93-206, September 14, 1993, 28 pp.