Nelken’s Tutorial on Neurophysiology and Information

Assignments:

The assignment phrasing

1. First assignment: simple decoding
   1. Make simulation of a binary stimulus and a probablistic response such that if stimuli 1 is presented the values are x = 1,2,3 with p = 0.25, 0.5, 0.25 respectivly and x = 3,4,5 with p = 0.25, 0.5, 0.25.
   2. Try to decode a single cell. What will be the error probability?
   3. Now say there is an additional recorded cell (y). What will be the optimal decoder and it’s performance in case that y is:
      1. independent of x
      2. perfectly correlated (rho =1) and anti correlated (rho=-1)
      3. (x,y) are correlated such that rho moves from -1 to 1. How can you generate such a distribution?
2. Now the conditional stimuli is P(x=1,2,3|s=1) = (0.25, 0.5, 0.25) and P(x=2,3,4|s=2) = (0.25, 0.5, 0.25).
   1. What is the theoretical mutual information between the stimuli and the response?
   2. Try to measure the mutual information empirically from simulated data and compare it to the theoretical result.

Proposed Assignments Solutions:

1. Solution to first assignment (by Hanan Shteingart). Remarks: the t = (x+y)/2 <>3 is optimal just by chance because the cell (3,3) is the only on that is shared (symmetrically) by stimuli = 1 & 2 and that the line y = 3-x seperates between the conditional distributions of (x,y)
   link to solution (not a doc file change extension to .zip – WORDPRESS limitation)

Papers to read:

1. About the non linearity of audiotory coding in A1 (birds chirps were decomposed into background noise, the natural waveform, a clean version of it (main) and a simplified version (artificial). These produced very different spike counts with very low correlations between them. However, substituting the envelope of the artificial and main signals revealed a strong correlation in responses  which might indicate the importance of envelope in a single neuron coding.
   • Bar-Yosef O and Nelken I.
     The effects of background noise on the neural responses to natural sounds in cat primary auditory cortex. Front. Comput. Neurosci. (2007) 1:3. doi:10.3389/neuro.10.003.2007
     frontiersin.org
   • Bar-Yosef O, Rotman Y and Nelken I.
     Responses of Neurons in Cat Primary Auditory Cortex to Bird Chirps: Effects of Temporal and Spectral Context. J. Neurosci. 22:8619-3220, 2002.
     JNS| pdf file
     presentation on the article by Hanan Shteingart
2. Information theory in the auditory cortex – the measurement of mutual information between stimuli and response and its importance in decoding.
   • Nelken I and Chechik G.
     Information theory in auditory research. Hear. Res. 229:94-105, 2007
     sciencedirect.com