Figure 1
Spatial maps. (A) A simulated place field map of a small (\(1m\times 1m\)) environment \({\mathcal {E}}\), similar to the arenas used in typical electrophysiological experiments66,67. Dots represent spikes produced by the individual cells (color-coded); their locations mark the rat’s position at the time of spiking. The pool of place cell coactivities is schematically represented by a coactivity complex \({\mathcal {T}}_{PC}\) (top right). The navigated trajectory r(t) induces a sequence of activated simplexes—a simplicial path \(\Gamma \in {\mathcal {T}}_{PC}\). (B) The head direction cell combinations ignited during navigation induce a coactivity complex \({\mathcal {T}}_{HD}\) (top). The corresponding head direction fields cover a unit circle—the space of directions (bottom). (C) Spatial view cells activate when the primate gazes at their respective preferred domains in the visual field (left). The curves \(r_1(t)\) and \(r_2(t)\) traced by the monkey’s gaze induce simplicial paths \(\Gamma _1\) and \(\Gamma _2\) running through the corresponding coactivity complex \({\mathcal {T}}_{VC}\) (right).
