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In contrast to the cross-correlation method, our method for measuring shifts works well for cells with all heading preferences, and is robust to variations in the gain, offset and shape of tuning curves.
It is also critical to distinguish between changes in response gain and changes in the shape of tuning curves, which our analysis allows because we sample the entire heading tuning curve (Mullette-Gillman et al., 2009; Chang and Snyder, 2010; Rosenberg and Angelaki, 2014).
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The results do not depend in detail on the shapes of tuning curves etc. (please see our response to comment 1).
The main advantages of the present method are: 1) capturing the basic physics of the problem surprisingly well, even at very coarse resolutions, 2) high-order accuracy without the need of tuning a shape parameter, and 3) the inclusion of polynomials eliminates stagnation (saturation) errors.
While most studies have focused on improving the uniformity and size control, few have addressed the potential of tuning the shape of the synthesized nanomaterials.
The building floor plan may place restrictions on the shape of a tuned liquid damper (TLD) tank, forcing a tank of complex geometry to be used.
For cells preferring forward or backward motion, rotations cause opposite directions of shifts in the peak and trough of the tuning curve, thus changing the shape of the tuning curve.
We should note that, in addition to the pre-adaptation tuning curve, the tuning widths of the presynaptic neurons affect the specific time-course and shape of adapted tuning curves.
The basic shape of the tuning curve was a single-parameter rounded-exponential Roex(p) filter <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0000909.e002.PNG" class= inline-graphic"/> where p is the steepness of the filter and g the relative width of the frequency notch.
A shift of 0° implies that the neuronal representation of translation is invariant to rotation (i.e., the shape of heading tuning curves are highly similar, as in Figure 3A).
For the same neuron, leftward eye rotation would cause the peak to shift to the left and the trough to shift to the right, thus having an opposite effect on the shape of the tuning curve.
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