Building an allocentric travelling direction signal via vector computation

The Drosophila central complex is shown to perform vector arithmetic related to navigation.

• A neural signal in the fan-shaped body tracks the allocentric travelling angle of a fly relative to external cues.
• This signal helps update the sense of space when the travelling and heading angles differ.
• A neuronal circuit has been characterized that transforms coordinates from a body-centred to a world-centred reference frame.
• Vector addition is computed by mapping two-dimensional vectors onto sinusoidal activity patterns in distinct neuronal populations.
• The amplitude of the sinusoid indicates vector length, while the phase represents vector angle.
• The principles of this circuit may apply to other brains and scenarios requiring vector operations.

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