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However, these studies only measured neural responses to three headings (forward, 30° leftward, and 30° rightward), and defined rotation-tolerance based on a rank-ordering of heading responses across the different eye movement conditions.
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Rightward rotation causes a rightward shift of the tuning curve for forward headings (around 90°), and a leftward shift for backward headings (around 270°).
DOI: http://dx.doi.org/10.7554/eLife.04693.008 10.7554/eLiFigure93 figuregure 3—figure supplement 2. Heading tuning curves from two example VIP neurons that preferred forward headings.
For cells preferring all other headings (close to forward or backward translations), the skew parameter was manipulated to yield a 20° shift in the peaks of the rotation-added tuning curves.
Step 2: because the predicted effects of rotation are opposite for forward and backward headings, RP and SP tuning curves were split into heading ranges of 0 180° and 180 360°.
We also made a prospective search of patients with a clinical picture from March 2008, which would be comprised under the headings or epicrania fugax with forward radiation, as was described by Pareja at al [1].
But, since opposite shifts are expected for forward and backward headings, the resulting tuning curve may exhibit substantial bandwidth changes.
To account for the expected changes in bandwidth and skew, partial shifts of the tuning curve were measured separately for forward (0°:180°) and backward (180°:360°) headings.
(C, D ) To account for bandwidth changes in the shift calculations, the RP/SP tuning curves are split into halves corresponding to forward (0 180°) and backward (180 360°) headings.
We used a maximum likelihood decoder (Sanger, 1996; Dayan and Abbott, 2001; Jazayeri and Movshon, 2006; Gu et al., 2010; Fetsch et al., 2011) to estimate heading from simulated population activity, and we required the population activity to discriminate between headings that were slightly leftward or rightward relative to a straight-forward reference heading.
As a result of the opposite shifts expected for forward (expansionary flow field) and backward translations (contractionary flow field), the heading tuning curve of a neuron preferring forward headings would have a peak that shifts to the right and a trough that shifts to the left during rightward eye rotation; together, these effects cause a skewing of the tuning curve.
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