representation of the environment and in forming spatial memories.
However, the exact structure of this spatial representation remains
unknown. Questions such as whether the experimentally observed patterns of activity of the
hippocampal cells may even be
considered as a single ?map? or whether the information contained in this map is reliable, given
the high variability of neuronal activity in the hippocampus, do not
yet have clear answers.
Possible ways of addressing these questions depend on the exact nature
of the spatial information contained in the hippocampus.
Several experiments suggest that the information contained in
electrode recordings from cells in the hippocampus of rats, together with the knowledge of the location of the centers of the place fields of each of these cells can be used to predict the instantaneous
position of a rat in a given environment. In our work, we study what type of information about the arena is retained by considering just
the electrode recordings without assuming knowledge of any spatial or geometric cues. Given that in a precise sense topology is more
parsimonious than geometry, the topology of the environment, which is reflected for example in the number of obstacles that are placed in
the arena, is our choice for the type of information that we study.
From the computational perspective, the hypothesis that the hippocampus encodes topological memory maps suggests a direct approach to studying their properties. It implies, first, that the information is mainly
contained in the relative temporal order of firing activity, e.g. in the patterns of temporal overlap
between the spike trains produced by
the hippocampal neurons.
Second, that such mechanism of global topological information encoding
must be robust with respect biological variability of the population
activity in the
hippocampus, i.e. it must persist within the biologically observed
range of parameters that characterize
place cell firing.
To address these questions, we investigate the robustness of the
topological map with
respect to independent variations of various place cell activity
parameters, such as the firing
rates, the distribution of sizes of the firing fields, the number of active cell, etc., using the persistent homology method applied to
simulated data. Using the
simulated data is essential in our approach because it allows scanning
the full range for each
parameter independently from one another and hence establishing the
theoretical boundaries of topological stability regime for the hippocampal map.