Synchronization of spiking neuronal activity plays a role in many important processes in the human body. In 2011, Zhao, Beverlin, Netoff, and Nykamp explored the relationship between synchrony and network structure by developing the SONET model where one can modulate the microstructure of the network by adjusting frequencies of pairs of directed connections between nodes, which correspond to the second order statistics of the network. We extended the SONET framework to allow for the prescription of probabilities of neuronal connections based on location to modulate spatial macrostructure. We used this spatial SONET model to explore how both network microstructure (SONET motif frequencies) and macrostructure influence the emergence of synchrony. To enable a consistent analysis of synchrony across a wide range of networks, we developed a novel measure of synchrony based on the rate of synchronous events. We discovered that the microstructure played the dominant role in shaping synchrony. Moreover, we found that the influence of the microstructure can depend on the dynamics of the inputs to the network.
University of Minnesota Ph.D. dissertation. June 2019. Major: Mathematics. Advisor: Duane Nykamp. 1 computer file (PDF); viii, 63 pages.
How dynamical regime and neuronal network structure influence synchronous events.
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