sbe ii hw 4 soln

sbe ii hw 4 soln - SBE II Solutions HW4(60 pts 1(5 pts for...

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SBE II Solutions- HW4 (60 pts) 1. (5 pts for each plot) 0 20 40 0 0.02 0.04 0.06 p1 Time (msec) p1(tau) 0 20 40 0 0.02 0.04 0.06 p2 Time (msec) p2(tau) 0 20 40 0 0.5 1 F1 Time (msec) F1(t) 0 20 40 0 0.5 1 F2 Time (msec) F2(t) F1(t) = 1 - exp(-1ambda*t) F2(t) = 1 - exp(-1ambda*(t – t0)) Note the lag time in the plots for p2 and F2. 2. Spike trains: 0 50 100 150 200 250 300 0 0.5 1 1.5 2 Time (msec ) Spike amplitude Homogenous poisson 0 50 100 150 200 250 300 350 400 0 0.5 1 1.5 2 Time (msec ) modified poisson (The figure above is not required)
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(5 pts for the 2 plots showing the estimated densities and 5 points for the explanation) 0 20 40 0 0.05 0.1 0.15 0.2 Tau(msec) est p(tau) Estimated density 0 20 40 0 0.05 0.1 0.15 0.2 Tau(msec) Estimated density 0 20 40 0 0.05 0.1 p1 Time (msec) p1(tau) 0 20 40 0 0.05 0.1 p2 Time (msec) p2(tau) The estimated densities (top row) are generated using a limited set of numbers drawn from the corresponding distribution. Our estimation will more closely match the true densities if we increase the number of sampled point for each distribution. 3. -5 points for the combined distribution histogram -5 points for the simulated spike train (blue stem plots) 0 100 200 300 400 500 600 700 800 0 0.5 1 1.5 2 Time (msec ) Spike amplitude Part (a) -10 0 10 20 30 40 0 0.05 0.1 ISI (msec) Estimated density combined modified poisson gamma
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In this case the combined distribution is more dictated by the modified poisson. b) -5 points for the combined distribution histogram -5 points for the simulated spike train (blue stem plots) -5 points for the explanation 0 100 200 300 400 500 600 0 0.5 1 1.5 2 Time (msec ) Spike amplitude Part b -10 0 10 20 30 40 0 0.05 0.1 ISI (msec) Estimated density combined modified poisson gamma Note in part (b) the gamma distribution has more of an effect compared to (a). From the distributions we see that there exist ISIs that violate the refractoriness present in
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This note was uploaded on 03/30/2009 for the course BME 580 taught by Professor Winslow during the Spring '09 term at Johns Hopkins.

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sbe ii hw 4 soln - SBE II Solutions HW4(60 pts 1(5 pts for...

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