Center for Integrative

Abstract:  Topological maps from signals We discuss the task of reconstructing the topological map of an environment based on the sequences of locations visited by a mobile agent. This problem statement naturally appears in certain practical contexts. In systems neuroscience, one runs into the task of reconstructing the global topological map of the environment based on activation patterns of the place coding cells in hippocampus area of the brain. A similar task appears in the context of establishing wifi connectivity maps and wireless network optimization problems. We show how both cases can be naturally analyzed using notions from mereotopology (specifically the Region Connection Calculus) and graph theoretic notions. The specifics of the algorithms may vary depending on the nature and the quality (completeness) or the character of the available signals (e.g. the signal be selectively sensitive to a particular regional characteristic, such as the direction and the speed of motion). We discuss some problems appearing in this map reconstructing task and outline more general situations and directions of future developments. 1.