The Swartz Program in Theoretical Neuroscience: "Hyperbolic geometry in olfaction”

Using the sense of smell as an example, I will describe both theoretical reasons and experimental evidence that natural stimuli and human perception can be mapped onto a three dimensional hyperbolic surface. The results are obtained using a combination of tools from algebraic topology and multi-dimensional scaling with a hyperbolic metric. Although the representation that we derive is obtained purely from the statistics of co-occurrence between mono-molecular odorants in the natural environment, it revealed topography in the organization of human perception of smell. I will conclude with arguments for why hyperbolic metric should be generally applicable elsewhere in the nervous system.