The locally-linked neuronal network model and external asynchronous stimulus currents.

<p>(a) The locally-linked neuronal network model on two-dimensional square having neurons and layers. Here, we take , and label neural number (1 – 1000) from left to right layers. (b) To train the network, the input pulse current with duration is injected alternately into each pair of layers with the left-right sequence having the same inter-stimulus interval , respectively. After each training trial, there is a long enough time to let network activity recover to the rest state for the next training. We perform training for all the pair of layers with the same number of trials. (c) To test the resulting feedforward structure and its propagative capacity, a steady current is injected into a certain layer (here, we choose the 3rd layer, i.e., L3).</p

Distribution of synaptic weights after the different training stimulus intervals.

<p>Distribution of synaptic weights for different connection types: feedforward (left), feedback (middle) and recurrent (right) after the 20 training trials with different stimulus intervals ms (a), ms (b), ms (c), ms (d). The other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>.</p

Distribution of synaptic weights after the different training trials.

<p>Distribution of synaptic weights for three different connection types: feedforward (left), feedback (middle) and recurrent (right) at the beginning of training (a) and after the training with different number of trials 10 (b), 20 (c), 30 (d). The same parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>, except for ms.</p

Average synaptic weights as a function of the stimulus interval for STDP with temporal asymmetry.

<p>The same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g006" target="_blank">Fig. 6</a>, but for the temporally asymmetric form of STDP. Here, the parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>, except for , ms, ms.</p

Dependance of exponents for the resulting structure on exponents of STDP after 20 training trials.

<p>(a) vs. for different (b) vs. for different . For comparison, and are shown as solid lines in (a) and (b), respectively. The other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>.</p

Average synaptic weights as a function of the number of training trials.

<p>Average synaptic weights for three different connection types: feedforward (squares), feedback (circles) and recurrent (upward triangles) as a function of the trial number for temporally symmetric form of STDP ( and ms) (a) and for temporally asymmetric form of STDP ( and ms) (b). The other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a> except for ms. Also, we show the average synaptic weights for the connections including both feedforward and feedback types (downward triangles) in (a) and (b).</p

Evolution of the network and dynamical propagation.

<p>The weights of synaptic strengths on the model before (a) and after (b) training trials. (c) The spatiotemporal pattern of neuron spikes by injecting steady current for testing feedforward network. The system parameters are , and ms. The parameters for training (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g001" target="_blank">Fig. 1(b)</a>) and testing (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g001" target="_blank">Fig. 1(c)</a>) are given by , ms, s, ms, and .</p

Average synaptic weights as a function of the stimulus interval for STDP with temporal symmetry.

<p>Average synaptic weights for three different connection types: feedforward (squares), feedback (circles) and recurrent (upward triangles) as a function of the stimulus interval after the 20 training trials (a). The amounts of average synaptic modification relative to its initial value 0.5, (b) and (c) for feedforward (b) and feedback (c) connections exhibit exponential falloffs as the stimulus interval increases with exponents (b) and (c), respectively in linear-log scales. we also show the average synaptic weights for the connections including both feedforward and feedback types (downward triangles) in (a). The parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>.</p

(Color online) The property of dynamical propagation in the resulting network.

<p>(a) The total number of spikes of propagated layers as a function of inter-stimulus interval in the feedforward network obtained after 20 trials of training when keeping all the connections, indicating the exponential behavior of propagation dynamics with exponent in the linear-log scales. For comparison, the are also plotted in (a) when feedback and recurrent connections are cut (i.e., without feedback and without recurrent), respectively. (b) The exponent as a function of exponent in STDP for different . (c) The exponent as a function of the corresponding exponent in the feedforward network structure for different . In (b) and (c), the linear fit lines of data are also given with slope . (d) The coefficient as a function of stimulation strength . The other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084644#pone-0084644-g002" target="_blank">Fig. 2</a>. Data of are compiled for ms, and averaged over independent runs with error bar in (a).</p