We scaled the denominator by k to ensure that the estimate of target speed has the correct amplitude, on average. Although it provides the best fit to our data, even Figure 4B does not mimic the data perfectly. It shows a tendency for smaller MT-pursuit correlations for model neurons with lower preferred speeds, a tendency that was weak
Selleckchem Panobinostat but visible in our data ( Figures 3F and 4A). We found somewhat worse agreement with the data when we decoded with “numerator-opponent vector averaging” (Equations 2, 3, and 4) using the same correlated neurons in the numerator and denominator (Churchland and Lisberger, 2001). In broad strokes, the predicted MT-pursuit correlations (Figure 4C) were positive versus negative for model neurons with preferred directions within 90 degrees of target direction versus within 90 degrees of the opposite direction. However, the model predicted small negative MT-pursuit correlations that were not seen in our data for neurons with preferred directions from 22 to 90 degrees different from target direction and preferred speeds below target speed. Numerator-opponent vector averaging is more successful than some of our other decoders, because the use of opponent motion signals only in the numerator partially de-correlates the numerator and denominator even though the same population
of model MT neurons contributes to both. The three decoding computations used in Figures 4D–4F failed qualitatively to predict the MT-pursuit correlations in our data. In each case, the predicted Metabolism inhibitor MT-pursuit correlations depended strongly on the difference between target speed and preferred speed when target direction was within 90 degrees of the preferred direction. Each graph has positive MT-pursuit correlations in the upper-left quadrant and negative MT-pursuit correlations in the lower-left quadrant. In our data, MT-pursuit correlations were positive in both of these quadrants. The decoding computation used in Figure 4D was standard vector averaging (Groh, 2001, Groh
et al., 1997, Lisberger and Ferrera, 1997, Priebe and Lisberger, 2004 and Salinas and Abbott, 1994): equation(Equation 5) sˆ=∑iRilog2(si)∑iRi,s=2sˆwhere s is the estimate of speed, and R i the response of the i th Dipeptidyl peptidase neuron. Standard vector averaging estimates only target speed, and not target direction. The decoding computation used in Figure 4E was fully opponent vector averaging using the same model populations in the numerator and denominator: equation(Equation 6) sh=∑icos(θi)Rilog2(si)Rh2+Rv2 equation(Equation 7) sv=∑isin(θi)Rilog2(si)Rh2+Rv2 equation(Equation 8) s=2sh2+sv2where Rh=i∑cos(θi)RiRh=∑icos(θi)Ri and Rv=i∑sin(θi)RiRv=∑isin(θi)Ri. The decoding computation used in Figure 4F was the maximum likelihood computation of Deneve et al.