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.