, 2010), such as might arise if naive animals experienced greater fluctuations in arousal during the session. Signal correlation (rsignal) was computed as the Pearson correlation coefficient (ranging between −1 and 1) between the tuning curves from two simultaneously recorded neurons. Tuning curves for each stimulus condition were constructed by computing the mean response (average firing rate during the middle 1 s of the stimulus Selleck BKM120 duration) across trials for each heading direction. Permutation tests were applied to test for significant differences between trained and naive animals with
respect to: the difference in time courses of noise correlation (Figure 2C), mean response (Figures 3A and 3C), and Fano factor (Figures 3B and 3D). We first computed the sum of squared differences between two time courses: equation(1) x2=∑i=1n(Ttrained,i−Tnaive,i)2using a 500 ms sliding window moved in 50 ms steps, for a total of 31 data points. We then created permuted naive and trained groups by randomly drawing data from the original groups, pooled together. Within each cell, all of the responses were preserved (no shuffling across trials). We computed a new x2 value for each permutation (x2permuted), and this process was repeated 10,000 times. A p
value was computed as the proportion of x2permuted > x2. A difference between the two groups of animals was considered significant if p < 0.05. Fano factor, http://www.selleckchem.com/products/BI6727-Volasertib.html or the variance/mean ratio, was computed from log-log scatter plots of the variance of the spike count against the mean spike count, and this was done for each 500 ms time window used to compute time
courses. The data were fit by minimizing the orthogonal distance to the fitted line (type II regression). The slope was generally close to 1 and was thus forced to be 1 for convenience, such that variance scaled linearly with mean spike count. The Fano factor was then computed as 10∧intercept (see Figure S3). Fisher information (IF) provides an upper limit on the precision with which an unbiased estimator can discriminate between small variations in a variable (x) around a reference value (xref) (Pouget et al., 1998 and Seung and Sompolinsky, 1993). before We computed the smallest deviation in heading around straight ahead (threshold, Δx) that could be reliably discriminated (at 84% correct) by an ideal observer: equation(2) Δx=2Ifwhere IF was computed according to (Abbott and Dayan, 1999): equation(3) IF(xref)=f′T(xref)Q−1(xref)f′(xref)+0.5Tr[Q′(xref)Q−1(xref)Q′(xref)Q−1(xref)]IF(xref)=f′(xref)TQ−1(xref)f′(xref)+0.5Tr[Q′(xref)Q−1(xref)Q′(xref)Q−1(xref)]Here, f′ denotes the derivative of a matrix of tuning curves; superscript T denotes the matrix transpose, Tr represents the trace operation, and superscript −1 indicates the matrix inverse. The reference heading was straight ahead in our simulations (xref = 0°).
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