The world is very noisy but a stimulus that triggers a response must have structure. A stimulus is a dynamical system in itself. This is opposed to the practice of using white noise as a stimulus model. So we have a dynamical system, the neuron, encoding the output of another dynamical system. In the cricket cercal system this is an encoding of wind pulses, specifically those of the air turbulence preceding the attack of a predator. What are the parameters of these movements which are encoded from pulses of air? They are direction, intensity, and timing.
Direction is encoded by a bidirectional hinge at the base of each hair which, taken over the whole array, encodes a circle relative to the axis of the cricket.
Intensity comes from the length of the hairs. They can be divided into three sizes, less stiff as they get longer.
Timing, which includes the duration of the puff, the timing between puffs, and the timing as the puff moves across the array. This could give more information: a third dimension to adjust the jump and a recognition frequency to trigger a jump. Likewise intensity would be a trigger. So the response would be a trigger and a 2d or 3d direction, I’m not sure if a cricket can control the steepness of a jump. Timing would be controlled by the spacing between hairs on the array and maybe by the length of the sensory dendrite.
I am assuming that cercal sensory neurons are similar to insect olfactory sensory neurons, a single dendrite and no action potential. I have not found out for sure. This is simpler than the olfactory neuron as it doesn’t seem to have the chemical receptors although a male cricket might have these.
The axon arbors of the various sensory neurons map to a helical neural map. The various directions form the circular part of the helix. Why a helix and not a circle? This could be the third dimension and the trigger timing.
The 2d circular tuning curve has been calculated using a cosine model. The stiffness trigger map might be possible by looking at the same data but using the hair length parameters rather than direction. The tuning curve would necessarily be sigmoidal. The timing coding would be much harder. I have to know more about the air structure of a prey attack.