title: Can rodents conceive hyperbolic spaces?
abstract: The grid cells discovered in the rodent medial entorhinal cortex have been proposed to provide a metric for Euclidean space, possibly even hardwired in the embryo. Yet, one class of models describing the formation of grid unit selectivity is entirely based on developmental self-organization, and as such it predicts that the metric it expresses should reflect the environment to which the animal has adapted. We show that, according to self-organizing models, if raised in a non-Euclidean hyperbolic cage rats should be able to form hyperbolic grids. For a given range of grid spacing relative to the radius of negative curvature of the hyperbolic surface, such grids are predicted to appear as multi-peaked firing maps, in which each peak has seven neighbours instead of the Euclidean six, a prediction that can be tested in experiments. We thus demonstrate that a useful universal neuronal metric, in the sense of a multi-scale ruler and compass that remain unaltered when changing environments, can be extended to other than the standard Euclidean plane.
authors.affiliation: Cognitive Neuroscience, SISSA, via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Eugenio
authors.initials: E
authors.lastname: Urdapilleta
authors.affiliation: Cognitive Neuroscience, SISSA, via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Francesca
authors.initials: F
authors.lastname: Troiani
authors.affiliation: Cognitive Neuroscience, SISSA, via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Federico
authors.initials: F
authors.lastname: Stella
authors.affiliation: Cognitive Neuroscience, SISSA, via Bonomea 265, 34136 Trieste, Italy ale@sissa.it.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Treves
mesh_terms: D000818:Animals; D018728:Entorhinal Cortex / Q000502:physiology*; D008959:Models, Neurological; D051381:Rats; D013028:Space Perception / Q000502:physiology*
keywords: grid cells; hyperbolic geometry; self-organizing process; space representation