The University of Pittsburgh received a $299,792 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program. The grant will fund a research project to study the spread of activity in networks of neurons, particularly those involved in critical, rhythmic behaviors like breathing. The project will develop new mathematical methods for analyzing activity patterns in multi-state, directed graphs that represent neuronal networks. The research aims to generate insights and predictions about the function of neuronal circuits, with a focus on the key networks driving essential behaviors. The project will also provide training for students, generate openly available software code, and conduct public outreach through online videos and a summer math program for girls. Overall, the award supports an interdisciplinary collaboration to advance knowledge about neuronal dynamics and interactions using novel mathematical approaches.