Network Topology: Sensors & Systems
Networks arise in innumerable contexts from mobile communications devices, to environmental sensors nets, to biological systems at all scales. This talk explores the relationships between what happens on the network nodes (signals, sensing, dynamics) and the underlying spatial distribution of the nodes --- an especially delicate interplay in the context of coordinate-free, non-localized systems. The key tools are an adaptation of homology theory. Algebraic topology yields an enrichment of network topology that integrates cleanly with statistics and dynamics of networks, and which allows for solutions to problems of coverage, communication, and control.
Robert Ghrist, University of Pennsylvania