Network architecture, traveling waves and planning time.

<p>(a) Planning and readout network. For each neuron in the planning layer, 4 actions can be assigned. Actions neurons associated to planning neuron (<i>i</i>, <i>j</i>) are <i>W</i>_<i>ij</i>, <i>E</i>_<i>ij</i>, <i>N</i>_<i>ij</i> and <i>S</i>_<i>ij</i> which receive synaptic input respectively from the left, right, north, and south neighbor of the neuron (<i>i</i>, <i>j</i>) and evoke a motion in the same directions (just one synaptic input is shown). Action neurons corresponding to the current place of the agent (here again (<i>i</i>, <i>j</i>)) are driven by an additional input (</p><p></p><p></p><p></p><p><mi>I</mi></p><p><mi>e</mi><mi>x</mi><mi>t</mi></p><p><mi>a</mi></p><p><mi>i</mi><mi>j</mi></p><p></p><p></p><p></p><p></p><p></p>). The first of the 4 action neurons that is fired by the passing traveling wave inhibits the other 3 action neurons. (b) Synaptically propagating waves of activity from the goal neuron at (1,1) across a planning layer of 20 × 20 neurons, for four different obstacle configurations. Colors code for firing phases at steady state relative to the goal neuron. (c) Time courses of the local phase difference for two sample neurons at positions (10,10) and (20,20), indicated by □ and ○ in the top left panel of b, with their local west-positioned neighbors. The time to reach the maximal local phase difference represents the planning time for these two start positions towards the goal (here 600 and 1050 ms, vertical lines), and subsequently the full path towards the goal can be read out.<p>