Figure 4.

Read-out in temporal interference models. Top. A 5-Hz baseline oscillation (black) and three active oscillators (colors) path integrating while receiving a constant velocity input. The oscillator outputs are (A) sinusoids or (B) exponentially decaying synaptic potentials (50 ms time constant). The simulated animal begins between grid fields at time t = 0 s and enters fields at times t = {1,3,5} s. The remaining rows show the output of various models in response to the input oscillations (some using fewer than three active oscillator inputs). The rules all aim to produce maximal activity when the oscillators are all closely aligned in phase. The activity would then be thresholded (grid field width in vivo is about one-half the field spacing). Most of these rules were not intended to work with synaptic potentials (right column), but we show them to illustrate the difficulty of performing coincidence detection with spiking inputs: with some rules there is no threshold that would produce realistic field widths. Abbreviations: b, baseline oscillation; a_i, active oscillations; H(x), the Heaviside step function (H(x) = 0 if x < 0 and H(x) = 1 if x ≥ 0), and R(x) the ramp function (R(x) = 0 if x < 0 and R(x) = x if x ≥ 0).