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NEU 501: From Molecules to Systems

NEU 501: From Molecules to Systems. Module 6: Neural Coding Class 2: Receptive Field Models Michael J Berry II Monday, Dec. 2 , 2013. Day 2: Receptive Field Models. • Tuning Curves • The Linear-Nonlinear (LN) Model •  The Spike -Triggered Covariance Model.

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NEU 501: From Molecules to Systems

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  1. NEU 501:From Molecules to Systems Module 6: Neural Coding Class 2: Receptive Field Models Michael J Berry II Monday, Dec. 2, 2013

  2. Day 2: Receptive Field Models • Tuning Curves • The Linear-Nonlinear (LN) Model • The Spike-Triggered Covariance Model

  3. Receptive Fields and Tuning Curves • tuning curve: r = f(s)

  4. Receptive Fields and Tuning Curves II • tuning curve: r = f(s)

  5. Higher brain areas represent increasingly complex features • human epilepsy patients: awake, behaving • medial temporal lobe • present different pictures, measure spiking response

  6. Common Stimulus

  7. Another Cell

  8. Another Cell: Stimuli

  9. Common Stimuli

  10. Inadequacy of Tuning Curves • Provides insight into neuronal function, spatial maps • What if there is a stimulus outside of the test set? –want a model that can predict response to an arbitrary stimulus • What about the dynamics of the response? • What about spike times? • What about a stimulus with dynamics?

  11. Day 2: Receptive Field Models • Tuning Curves • The Linear-Nonlinear (LN) Model • The Spike-Triggered Covariance Model

  12. Neural Coding

  13. LNP Model of Neural Representation • Allows time-varying stimulus • Predicts time-varying firing rate • Converts time-varying firing rate into a spike train

  14. Linear Response: Example

  15. Linear Response: Example cont.

  16. Linear Response: Example cont.

  17. LN Model: Applying the Nonlinear Function

  18. Key Property of the LN Model • If the stimulus is white noise… then the linear filter is the spike-triggered stimulus average: • Arises from symmetry in the stimulus ensemble (Chichilnisky) • Implies that you measure all these parameters from data

  19. Measuring the Receptive Field • Reverse correlation to a flickering checkerboard

  20. The Receptive Field •Example from a retinal ganglion cell Temporal Profile Spatial Profile

  21. Finding the Nonlinear Function • Convolve the linear filter with the stimulus: • Find the distribution of effective stimulus values at spike times: • Invert using Bayes’ Rule:

  22. The LN Model 1) Find the spike-triggered stimulus average (STA): 2) Linear filter must be time-reversed STA: 3) Find the effective stimulus, s1(t): 4) Sample s1(t) at the times of spikes: 5) Use Bayes’ Rule to find the nonlinear function:

  23. The END

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