# [Problem Set 3 Spike trains] Problem 2: Analysis of spike trains

Link of the iPython notebook for the code

# PROBLEM 2: Analysis of spike train

One records and analyses several spike trains from a single neuron in the primary somatosensory cortex of a monkey experiencing a vibratory stimulus on the fingertip, for different vibration frequencies $f_1 ∈ \lbrace 8.4, 12, 15.7, 19.6, 23.6, 25.9, 27.7, 35\rbrace \text{ Hz}$. The simulation is conducted between $200$ and $700$ msec.

As shown in Figure a. and Figure b., the spikes within the simulation period (between $200$ and $700$ msec):

• seem to be periodically spaced for a given frequency $f_1$
• are more and more numerous as the frequency increases

and even more: the number of spikes seem to depend linearly on the vibration frequency.

The latter observation is backed up by the shape of the average spike count, plotted as a function of the vibration frequency:

A linear regression of the average spike counts (as a function of the vibration frequency) can me made:

• Linear equation: $y = 1.39 x + 3.08$
• Correlation coefficient: $0.997$
• Standard error of the estimate: $0.04$

The very high correlation coefficient and very low standard error of the estimate highlight an almost perfect match!

We have similar results for the average firing rate as a function of the vibration frequency:

The linear regression yields:

• Linear equation: $y = 2.78 x + 6.15$
• Correlation coefficient: $0.997$
• Standard error of the estimate: $0.08$

As a result: the firing rate of the neuron can be regarded as a non-decreasing linear function of the vibration frequency.

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