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. 2013 Feb 28;9(2):e1002867. doi: 10.1371/journal.pcbi.1002867

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© 2013 Cazé et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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(A–B) The x-axis (Expected EPSP) is the arithmetic sum of two EPSPs induced by two distinct stimulations and y-axis (Measured EPSP) is the measured EPSP when the stimulations are made simultaneously. (A) Observations made on pyramidal neurons (redrawn from [13]). Summation is supra-linear and sub-linear due to the occurrence of a dendritic spike. (B) Â Observations made on cerebellar interneurons (redrawn from [10]). In this case summation is purely sub-linear due to a saturation caused by a reduced driving force. (C) Â The activation function modeling the dendritic spike type non-linear summation: both supra-linear and sub-linear on . (D) Â The activation function modeling the saturation type non-linear summation: strictly sub-linear on . (E) Structure and parameters of the neuron model: and are binary variables describing pre and post-synaptic neuronal activity; in circles are two independent sets of non-negative integer-valued synaptic weights respectively for the linear (black) and the non-linear integration (blue) sub-units; in the blue square, and are the non-negative integer-valued threshold and height that parameterize the dendritic activation function ; in the black square is a positive integer-valued threshold determining post-synaptic firing. (F) Â Truth tables of three Boolean functions for inputs: AND, NAND, and XOR. The first column gives the possible values of the input vector ; the other three columns give the binary outputs in response to each for the three functions considered.

Inline graphic — (A–B) The x-axis (Expected EPSP) is the arithmetic sum of two EPSPs induced by two distinct stimulations and y-axis (Measured EPSP) is the measured EPSP when the stimulations are made simultaneously. (A) Observations made on pyramidal neurons (redrawn from [13]). Summation is supra-linear and sub-linear due to the occurrence of a dendritic spike. (B) Â Observations made on cerebellar interneurons (redrawn from [10]). In this case summation is purely sub-linear due to a saturation caused by a reduced driving force. (C) Â The activation function modeling the dendritic spike type non-linear summation: both supra-linear and sub-linear on . (D) Â The activation function modeling the saturation type non-linear summation: strictly sub-linear on . (E) Structure and parameters of the neuron model: and are binary variables describing pre and post-synaptic neuronal activity; in circles are two independent sets of non-negative integer-valued synaptic weights respectively for the linear (black) and the non-linear integration (blue) sub-units; in the blue square, and are the non-negative integer-valued threshold and height that parameterize the dendritic activation function ; in the black square is a positive integer-valued threshold determining post-synaptic firing. (F) Â Truth tables of three Boolean functions for inputs: AND, NAND, and XOR. The first column gives the possible values of the input vector ; the other three columns give the binary outputs in response to each for the three functions considered.