Biomathematics seminar – Yasser Roudi-Rashtabadi, King’s College London
Topological Data Analysis, oscillations and grid cells’ toroidal topology
Abstract:
Topological Data Analysis (TDA) has emerged as a powerful tool for analyzing complex biological data. With advances in neural recording technologies capturing increasingly large numbers of neurons, topological techniques offer insight into the structure of high-dimensional neural activity. In this talk, we will first discuss how the degree to which various topological features are present in high-dimensional data can be quantified. We will then focus on topological features of the activity of populations of grid cells in mammalian Medial Entorhinal Cortex. Grid cells are specialized neurons that exhibit spatially periodic firing patterns across hexagonally arranged fields. Application of TDA to data from grid cells shows that the activity of the population of grid cells lives on a toroidal manifold. We show that in combination with the regular grid like activity of these neurons, oscillatory components in the neural activity play a critical role in the emergence of such toroidal topology.