A computational model of the integration of landmarks and motion in the insect central complex
Fig 6
The model can learn to map landmarks to positions on the ring attractor with slow consolidation (β = 0.5) of the plastic weights. In addition the evolved offsets when the ring attractor is seeded to one position are shown.
A The model performance (see E for comparison with the results from Experiment 2) in terms of mean and circular standard deviation (calculated using the Matlab Circular Statistics Toolbox [38]) of the ring attractor direction from the world direction (corresponding to the location of the single stimulus, and remapped from 270° to 360°) is shown at the top, and shows that the model is able to track the motion of the world well in all cases, with an offset to the position of the stimulus on the visual field. Additionally, a polar plot contains an example of the evolution of the weights over the course of the simulation (with time increasing from the centre to the outside) for a single stimulus. In the polar plot each receptive field (RF) is given a colour, with the key around the outside of the ring, and the angular position of each line denotes the position on the ring attractor that each RF maps to. An ordered mapping, with no offset, should therefore be shown by each line lying in the circular segment under the corresponding key item. Instead, we see that the weights remap the 260° world onto approximately 360° of the ring attractor, and the learning is established early in the simulation, although the weights do show changes in the mapping over the course of the simulation. A second Cartesian plot shows the clustering of the RFs into retinotopic maps (see Methods for details), with the size of the marker denoting the number of RFs in a cluster. For the single stimulus it can be seen that a single map evolves, but changes offset over time. B As A, but with the panorama. The polar plots are not helpful for the panorama as there are multiple retinotopic mappings developed. Here there is once again a good performance in tracking the world in most cases, albeit with one run where tracking performance is poor. The example showing the weight clustering shows that multiple retinotopic mappings are developed, however these mappings change over the course of the simulation. C As A, but with dual stimuli. In this case the model exhibits poor performance tracking the world, and the weights remain largely changeable throughout the simulation. D This panel shows the correlations between the changes in azimuthal position and the changes in the offset between the actual azimuth and the azimuth represented on the ring attractor. The single and panorama simulations show a similar correlation to that found with fixed RFs, however the dual stimuli simulations show a negative correlation between the change in position and the change in error.