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Explore a case study on using dynamics to constrain neuronal population connectivity in the respiratory brainstem. Delve into the synchronized bursting activity of brainstem neurons driving diaphragm movement during mammalian respiration. Examine experimental observations of "pre-inspiratory" tonic spiking and its potential to trigger widespread, synchronized activations manifesting as small-scale burstlets or full-blown bursts. Analyze two models related to this process, with a focus on a multi-state bootstrap percolation model that may provide insights into the unknown connection architecture of this network. Gain valuable knowledge from Jonathan Rubin of the University of Pittsburgh in this 53-minute lecture recorded on February 13, 2024, as part of IPAM's Mathematical Approaches for Connectome Analysis Workshop.