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. 2015 Nov 10;9:151. doi: 10.3389/fnsys.2015.00151

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Copyright © 2015 Brette.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution and reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Reduction of a spike-based model to a rate-based model. The spike model defines a relationship between presynaptic and postsynaptic spike trains through a function S. The rate model defines a relationship between rates through a function f. Rates are related to spikes through an observation function R. Reduction is possible when the diagram commutes: the composition of R and S equals the composition of f and R (mathematically, R o S = f o R). This is not generally possible because R is not invertible (many spike trains have the same rate).