Q1. Grid cells are neurons in the medial entorhinal cortex (MEC) that fire at vertices of hexagonal lattices tessellating an environment.
Q2. Suppose that 4 stimuli (A, B, C and D) are presented to an animal with equal probabilities, while a fifth stimulus, E, is presented with twice the probability of the other 4. The table below shows the probability of different spike counts recorded in the experiment in response to each of these stimuli.
|stimulus/response||5 spikes||10 spikes||15 spikes||20 spikes|
|stimulus C||1/4||1/4||1/4||1 / 4|
|stimulus D||0||0||1/2||1 / 2|
|stimulus E||1/2||0||0||1 / 2|
Q3. (a) Describe what noise correlation (5 points) and signal correlation (5 points) mean. (b) Take a case of positive or negative noise and signal correlations between two cells. Discuss the consequence that these correlations will have on the stimulus-response mutual information. (10 points)
Q4. How does the balance between inhibition and excitation in a recurrent network lead to irregular firing? In addition to the irregular firing, describe another consequence of the inhibition-excitation balance. (10 points)
Q5. Consider the following 3 layer network. The input values shown in ellipses on top of the figure are propagated through the network. The numbers next to each line show the synaptic weights and each neuronal transfer function is shown in a circle. As shown in the figure, neurons in the second layer are all binary neurons with threshold 1 except for the right most neuron which has a threshold of 0. Neurons in the second layer are thresholdlinear neurons with threshold at 1 and a gain of 1.
Calculate input to and the firing rate of each of the 5 neurons. (2 points each)
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