Figure 5. A linear-nonlinear decoder can detect the flash onset.

A. Stimulus detection error rates using single cell (red stars) and network (blue dots) responses. Stimulus onset was estimated from the response of every single cell, using the linear-nonlinear method algorithm. The stimulus detection ability of every cell is plotted as a star in the plane of false positive and false negative error rates. Note that the false negative rate decreases with an increasing false positive rate. For every cell, the discrimination threshold was set to minimise the sum of false positive and false negative errors. False negatives were normalised by the total number of events to be detected; false positives were normalised by the total number of detected events. B. The linear-nonlinear stimulus onset readout mechanism. The stimulus (red line) is represented as alternating values of zero (black) and one (coloured flash). The best linear filter (blue) for estimating the stimulus from the retinal response was found (see Materials and Methods and Warland et al. [38] for details). The linear estimation was transferred through a threshold (non-linearity) to determine when the flash occurred. C. Comparison between the stimulus (red) and the final estimation (blue) based on the full linear non-linear estimation. D. Comparison between the stimulus (red) and an estimation based on a naïve average over all cells (blue). The estimation fails to reflect the stimulus properly (∼80% increase in false negatives). E. Comparison between the stimulus (red) and an estimation based on a weighted average over all cells (blue). While this readout outperforms the naïve average, still it is less successful then the full linear-nonlinear readout. F. Stimulus detection error rates as a function of the number of cells used in the linear nonlinear readout mechanism (solid line with dots) and naïve mechanism (dashed line with dots). For every population size, error rates were averaged over 50 randomly selected subgroups. Approximately 100 cells were needed to reduce both false negatives and false positives to less than 5%. G. Onset time estimation error, as a function of population size. Error was divided into bias and RMS error for the linear nonlinear readout (sold lines with dots) and naïve readout (dashed line with dots). In the linear nonlinear model, the bias is of order 10 ms, and it decays with the population size such that it is expected to approach zero as more cells are added. Note the decay of the RMS estimation error of the onset time to less than 30 ms. In the naïve readout, the error does not improve significantly when we add more cells. H. Estimated onset times histogram for a network with 85 cells. I and J. The same as in linear nonlinear readout of F and G but with 125 ms filters.