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Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions

Figure 2

A dendritic non-linearity enables the computation of linearly non-separable Boolean functions.

(A) Number of computable representative positive Boolean functions depending on the number of input variables and on the type of synaptic integration: purely linear (lin∶black), linear with a spiking dendritic sub-unit (spk∶green), linear with saturating dendritic sub-unit (sat∶blue). In red is the maximal number of positive representative functions computable for a given , this number is taken from [37] as the number of functions in condition lin (black). Upper panel: number of computable functions (in bold are lower bounds); lower panel: summary bar charts on logarithmic scale. (B) Venn diagram for the sets of Boolean functions for . The set border color depends on the type of integration, as per panel A (relative size of sets not to scale). Stars are examples of Boolean functions within each set.

doi: https://doi.org/10.1371/journal.pcbi.1002867.g002