Table 1.
Parameters and their values set in simulations for the spherical camera model, template model, and oscillatory interference model
| Description of parameter | Value |
|---|---|
| Pre-processing of Simulated trajectories a | |
| Adds points for rotations above (90 ° · 50 Hz) | 4,500 °/s |
| Removes points for linear velocities below (0.05 cm · 50 Hz) | 2.5 cm/s |
| Adds points for linear velocities above (1.2 cm · 50 Hz) | 60 cm/s |
| Environment of a ground plane | |
| Radius of the circular ground platform b | 100 cm |
| Number of triangles to represent the ground platform | 32 |
| Spherical camera model | |
| Horizontal field of view | 240 ° |
| Vertical field of view | 120 ° |
| Number of sample points in vertical dimension c | 40 |
| Number of sample points in horizontal dimension c | 20 |
| Minimum distance for a sample point | D min = 0 cm |
| Maximum distance for a sample point | D max = 1000 cm |
| Eye-height above ground | h = 3.5 cm |
| Tilt angle of the optical axis with respect to ground | γ = 0 ° |
| Template model | |
| Standard deviation of the objective function for the linear velocity v z | σ v = 10 °/s |
| Standard deviation of the objective function for the rotational velocity ω y | σ ω = 25 °/s |
| Interval of rotational velocities | ω y,k ∈ {±4,500 °/s} |
| Samples for rotational velocities | k = 1…451 |
| Interval for linear velocities | v z,j ∈ {2…60 cm/s} |
| Samples for linear velocities | j = 1…117 |
| Oscillatory interference model | |
| Frequency d | f = 7.38 Hz |
| Parameter e | β = 0.00385 s/cm |
| Angles for basis vectors | φ1 = 0 °, φ2 = 120 °, φ3 = 240 ° |
| Threshold value for spiking | Θ = 1.8 |
aFile names of the trajectories included in the simulation are ‘Hafting_Fig2c_Trial1’, ‘Hafting_Fig2c_Trial2’, and ‘rat_10925’ from the Moser lab: http://www.ntnu.no/cbm/gridcell. For the simulations we extracted the maximum subsequence without not-a-numbers
bIn the simulation the size of the circular ground platform was extended by 15 cm on each side with respect to the original size of a radius of 85 cm. This extension provides sample points at the outmost boundary of 85 cm and allows for picking up optic flow
cThis refers to an image resolution of 40 × 20 pixels or n = 800. Note that image flow may not be acquired for each pixel because of the tilt angle and simulating an open cage, see Figs. 2 and 3
dFrequency f has been fitted to subthreshold oscillations of entorhnial cells (Giocomo et al. 2007)
eParameter β has been fitted to the measured subthreshold oscillations for neurons and their simulated grid cell spacing (Giocomo et al. 2007)