In the article "A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology" by Y. Dabaghian, F. Mémoli, L. Frank, G. Carlsson I read some sentences with huge confusion concerning the use of the termss firing and spiking. Do they mean the same thing? It seems to me that when they say a place cell is firing or a place cell is spiking they refer to exactly the same thing. The confusion comes from using both words in the same sentence as in the following sample sentences from the article (emphasis mine):
Indeed, a rat’s path through a small space can later be re-traced with a high degree of accuracy by recording hippocampal spiking activity during its explorations and then analyzing the location, size, and firing rates of a mere 40–50 place fields [...]
To understand what algorithms the brain might use to decode hippocampal place cell firing, then, we should rely solely on the information provided by place cell spiking activity [...]
It is, in fact, generally assumed that neurons downstream of the hippocampus interpret place cell spiking patterns based on co-firing [...]
It should thus be possible to trace the emergence of topological information as more and more spikes are fired [...]
There are biophysical variables (firing rates, spike amplitude, etc.) [...]