Fig. 4: Method for fitting spatial models to neural response fields.
From: Integration of landmark and saccade target signals in macaque frontal cortex visual responses
a Summary of the main models studied in this paper [TF(e), TL(e), LF(e)] for an example T-L-F configuration (see key for details). b Schematic of the logic behind the response field analysis, using simulated data. The x-axes represent the spatial coordinate. The y-axes show neural activity. Neural responses from individual trials are represented by the red dots. The black curving lines show the non-parametric fits, which in practice did not restrain the response field to a specific (e.g., gaussian) shape. Above and below these plots are the residuals of fit, i.e., the difference between individual responses and the fit. In the left column, data and fits are plotted in the TF(e) coordinate system, whereas the right column plots data and fits in the TL(e) coordinate system. The upper row shows hypothetical activity from a neuronal response field when the target is coded relative to fixation, TF(e). In this case, low residuals result when the data are plotted and fit in the same coordinate, i.e., TF(e) (left), and high residuals result when the data are plotted relative to the landmark, i.e., TL(e) (right). The opposite pattern occurs in the panels in the bottom row for a neuron that encodes targets relative to the landmark [TL(e)]. c–e Example analysis of a visual neuron with lowest residuals for the TF(e) model. c Raster and spike density plot of the neuron’s activity. The blue vertical line indicates the target onset, and the gray shaded area represents the time window (80–180 ms after the target onset) used to quantify the visual response to the target. The raster shows the action potentials for trials with the top 10% activity (corresponding to the ‘hot spot’ of the response field) in the analysis window. The gray line shows the spike density for these same top 10% trials whereas the black line shows the spike density for all the trials. The confidence intervals show the standard error. d The non-parametric fit of the neuron’s response field in the coordinates of its best model fit, TF(e) (with 0,0 origin at the intersection of the white cross, i.e., the fovea). Shown to the right is the color scale for the fit, ranging from low (blue) to high (red) activation. e Actual data (black circles placed at the stimulus location and scaled to the response in the sampling window—see key on right) plotted over the fit in the best fit coordinate system, with the difference between them (residuals) shown on the right.
