The responses of a cat LGN cell to two-dimensional visual images are contained in the file c2p3.mat, data are described in Kara et al., Neuron 30:803-817 (2000). In the file, counts is a vector containing the number of spikes in each 15.6 ms bin, and stim contains the 32767, 16x16 images that were presented at the corresponding times. Specifically, stim(x,y,t) is the stimulus presented at the coordinate (x,y) at time step t. Answer the questions below and provide Matlab codes for each question. (Note that stim is provided in integer format.) a) Calculate the STA images for each of the 10 time steps before each spike and show them all. For display, use imagesc with a grayscale colormap and identical display windowing for all STA images. Based on the STA derived filter, describe what type of spatio-temporal stimulus this LGN cell is selective for. b) Describe the changes in STA images across time. Sum the STA images over one of the spatial dimensions. You should obtain a matrix of 16 pixels by 10 time steps as a result of this process. Show this matrix (using imagesc). Based on the computed matrix, describe the temporal selectivity of the LGN cell. Is the matrix space-time separable?

c) Project the stimulus onto the STA image at a single time step prior to the spike. Obtain the projection for each time sample by computing the Frobenius inner product between the stimulus image and the STA image. Create a histogram from all stimulus projections, and another histogram from stimulus projections at time bins where a non-zero spike count was observed. Use identical binning for the two histograms, and normalize each histogram to a maximum of 1. Compare the histograms with a bar plot. Comment on whether STA significantly discriminates spike-eliciting stimuli.