THEORETICAL NEUROSCIENCE CAAM 415
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This 2 page Class Notes was uploaded by Walker Witting on Monday October 19, 2015. The Class Notes belongs to CAAM 415 at Rice University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/225003/caam-415-rice-university in Applied Mathematics at Rice University.
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Date Created: 10/19/15
CAAM415 Gabbiani 1 Instructions Solve the following exercise Return both the code written for MATLAB and gures7 properly labeled Answer the questions and justify your claims with clear and logical explanations H 3 9 7 Properties of poisson and gamma distribu tions Plot on a single gure 10 spike trains7 each 1 sec long7 drawn from a Poisson process with mean rate 40 spksec Use a temporal resolution of 1 ms for the spike timing Compute the variance in the spike count7 VT as a function of the mean spike count NT for a gamma renewal process of order 2 with a mean rate of 40 spksec Simulate 1000 random spike trains one second long Then compute NT and VT on intervals going from 0 to 50 ms7 0 to 100 ms7 up to 0 to 1 s7 in steps of 50 ms Compare the curve obtained in this manner with the theoretical formula7 T VT T 31 N T i 2mm 8 where mm is the mean inter spike interval 7 77 7 eiTmAtL mm Compute the interspike interval correlation coef cient at lag 1 for a Poisson process of mean rate 40 spksec and an absolute refractory period of 2 msec Use 1000 random interspike intervals Use the same interspike interval sequence Ati of the previous exercise to generate a new sequence of interspike intervals At as follows Alt1 Atl 5 Atl and At for 239 gt 1 and where mm is the mean interspike interval of the original sequence Compute the correlation coeff cient at lag 1 Explain the results obtained here and in the previous exercise A1271 lt 77 1At7 if A1221 2 mAt7 Hints Use the matlab functions exprnd gamrnd cumsum to generate ran dom intervals and their corresponding spike times For problem 17 use the CAAM415 Gabbiani function linetspk t5ka 7 O 1 7 to plot a tick mark for each spike at time tst on your plot Read the MATLAB help to see how the call to line can be generalized to a 71st X 2 array of 71st spikes
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