Topology of cognitive maps

In present paper we test different approaches to reconstructing the topology of the physical space from neural activity data in A1 fields of mice brains, in particular, having a Cognitome-focused approach in mind. Animals were placed in different new environments and discovered them while their physical and neural activity was recorded. We discuss possible approaches to identifying the place cells and make assumptions on how Cognitome theory might help with that. We also test and discuss various methods of dimension reduction and topology reconstruction. In particular, two main strategies we focus on are the Nerve theorem and point cloud-based methods. Conclusions on the results of reconstruction are supported with illustrations and mathematical background which is also briefly discussed.