Scott Cole

6 May 2017

This notebook is to formalize the hypothesis that the neural response to a very fast movement in the preferred direction can be more similar to that of a movement in the opposite direction (perceptually: the wagon wheel effect).

The predicted neural response to a motion is computed by convolving the neural responses to static gratings



In [1]:

    
# Import libraries
import numpy as np

%config InlineBackend.figure_format = 'retina'
%matplotlib inline
import matplotlib.pyplot as plt

1. Define kernels of neuronal response to static gratings

The kernels plotted here represent the transient and sustained neural responses. (I believe these are firing rates in thalamic projection neurons in response to static gratings?)



In [24]:

    
kernel_fast = np.array([0, .5, 1, .8, .4, .2, .1, 0])
kernel_slow = np.hstack([np.arange(0,1,.2),np.arange(1,0,-.04)])

plt.figure(figsize=(5,6))
plt.subplot(2,1,1)
plt.plot(kernel_fast,'k')
plt.xlim((0,30))
plt.ylabel('Neural response\n(fast)',size=15)
plt.subplot(2,1,2)
plt.plot(kernel_slow,'k')
plt.xlim((0,30))
plt.xlabel('Time (a.u.)',size=20)
plt.ylabel('Neural response\n(slow)',size=15)









    Out[24]:





<matplotlib.text.Text at 0x11b264a58>

2. Estimate neural response to preferred and opposite directions

Preferred direction



In [26]:

    
# Define times of sustained-response-inducing (slow)
# and transient-response-inducing (fast) stimuli
slow_event_times = np.arange(0,100,20)
fast_event_times = np.arange(10,110,20)

# Compute rasters of events
N = 200
slow_event_raster = np.zeros(N)
slow_event_raster[slow_event_times] = 1
fast_event_raster = np.zeros(N)
fast_event_raster[fast_event_times] = 1

# Compute trace of neural activity
slow_neural = np.convolve(slow_event_times, kernel_slow, mode='same')
fast_neural = np.convolve(fast_event_times, kernel_fast, mode='same')
neural = slow_neural + fast_neural









    



---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-26-739597e8427e> in <module>()
     14 slow_neural = np.convolve(slow_event_times, kernel_slow, mode='same')
     15 fast_neural = np.convolve(fast_event_times, kernel_fast, mode='same')
---> 16 neural = slow_neural + fast_neural

ValueError: operands could not be broadcast together with shapes (30,) (8,)



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