Mapping neural representations of topologically non-trivial spaces

We consider a biologically realistic artificial model of neurons, simulating place cells (PCs) found in the hippocampus of living brains, that are known to encode the physical space. We make our model encode such spaces of distinct topological structure (namely, 2D arenas with 1, 2, 3 holes in them), in which an artificial agent is moving, with its simulated PCs firing when the agent visits the receptive fields of the corresponding PCs. We analyze -- with persistent homology and Isomap -- such signals (artificial PCs' spike trains), showing that their topological properties reflect those of the physical space (encoded by the PCs as the agent explores the arenas), thus demonstrating that said properties can be successfully recovered from such signal alone.