  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.
