Spatial representability of neuronal activity

Abstract

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.

Estimation of animal location from grid cell population activity using persistent cohomology

“…In previous studies, persistent cohomology has found a ring-shaped data structure of H 0 = 1, H 1 = 1, H 2 = 0 in the population activity of place cells and head orientation cells [10] [11] [12] [13] [14]. In particular, in the case of head direction cells, the animal’s head direction can be estimated from 0 to the 360-degree phase of the ring-shaped data structure.…”