University of Heidelberg, **Applied Analysis Seminar**

Prof. Dr. Laurent Bétermin (ICJ, Université Claude Bernard Lyon 1)

Theta functions and optimal lattices for a grid cells model

*Seminar Room 2/414*

Theta functions and optimal lattices for a grid cells model

Certain types of neurons, called "grid cells", have been shown to fire on a triangular grid when an animal is navigating on a two-dimensional environment. The goal of this talk is to show new evidences of this phenomenon by considering an infinite set of independent neurons with Poisson statistics and periodic spread out Gaussian tuning curves. This question of the existence of an optimal grid is transformed into a maximization problem among all possible unit density lattices for a Fisher Information which measures the accuracy of grid-cells representations. Furthermore, this Fisher Information has translated lattice theta functions as building blocks, for which we know different results. After introducing the model, some analytic and numerical results will be presented and some open problem discussed.

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