Description

This exercise is based on a set of artificial “experiments” that we’ve run on four simulated neurons that emulate the behavior found in the cercal organs of a cricket. Please note that all the supplied data is synthetic. Any resemblance to a real cricket is purely coincidental.
In the first set of experiments, we probed each neuron with a range of air velocity stimuli of uniform intensity and differing direction. We recorded the firing rate of each of the neurons in response to each of the stimulus values. Each of these recordings lasted 10 seconds and we repeated this process 100 times for each neuron-stimulus combination.
We’ve supplied you with a .mat file for each of the neurons that contains the recorded firing rates (in Hz). These are named neuron1, neuron2, neuron3, and neuron4. The stimulus, that is, the direction of the air velocity, is in the vector named stim. Download the file:
tuning.mat
and save it into your MATLAB/Octave directory. To load the data, use the following command:
load(‘tuning.mat’)
The equivalent data files for Python 2.7 and Python 3.4 are:
tuning_2.7.pickle
tuning_3.4.pickle
To load the data, make sure you are in the same directory you saved it and add the following (shown for 2.7) to your script:

This will load everything into a dict called data, and you’ll be able to access the stim and neuron responses using data[‘stim’], data[‘neuron1’], etc. (In general, data.keys() will show you all the keys available in the dict.)
The matrices contain the results of running a set of experiments in which we probed the synthetic neuron with the stimuli in stim. Each column of a neuron matrix contains the firing rate of that neuron (in Hz) in response to the corresponding stimulus value in stim. That is, nth column of neuron1 contains the 100 trials in which we applied the stimulus of value stim(n) to neuron1.

Part A
Plot the tuning curve– the mean firing rate of the neuron as a function of the stimulus– for each of the neurons.
Part B
We have reason to suspect that one of the neurons is not like the others. Three of the neurons are Poisson neurons (they are accurately modeling using a Poisson process), but we believe that the remaining one might not be.
Which of the neurons (if any) is NOT Poisson?
In order to realize why this might be helpful, consider the fact that, for a constant a and a random variable X, E[aX]=aE[X] but Var(aX)=a2Var(X). What might this imply about the Poisson statistics (like the Fano factor) when we convert the spike counts (the raw output of the Poisson spike generator) into a firing rate (what we gave you)?
Part C
Finally, we ran an additional set of experiments in which we exposed each of the neurons to a
single stimulus of unknown direction for 10 trials of 10 seconds each. We have placed the results of this experiment in the following file:
pop_coding.mat
You should save the file into your MATLAB/Octave directory and import the data using the following command: load(‘pop_coding.mat’)
The equivalent python files are:
pop_coding_2.7.pickle
pop_coding_3.4.pickle
These can be loaded in the same way as described in question 7 above.
pop_coding contains four vectors named r1, r2, r3, and r4 that contain the responses (firing rate in Hz) of the four neurons to this mystery stimulus. It also contains four vectors named c1, c2, c3, and c4. These are the basis vectors corresponding to neuron 1, neuron 2, neuron 3, and neuron 4.
Decode the neural responses and recover the mystery stimulus vector by computing the population vector for these neurons. You should use the maximum average firing rate (over any of the stimulus values in ‘tuning.mat’) for a neuron as the value of rmax for that neuron. That is, rmax should be the maximum value in the tuning curve for that neuron.