Date of Award

Spring 1-1-2017

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computer Science

First Advisor

Juan G. Restrepo

Second Advisor

Elizabeth Bradley

Third Advisor

Rafael Frongillo

Fourth Advisor

Aaron Clauset


Networks of excitable units are found in varied disciplines such as social science, neuroscience, genetics, epidemiology, etc. Previous studies have shown that some aspects of network function can be optimized when the network operates in the 'critical regime', i.e., at the boundary between order and disorder where the statistics of node excitations correspond to those of a classical branching process. In this thesis, we introduce and study a mathematical model of a neural network with the goal of understanding the long-standing problem of determining the mechanisms by which a neural network regulates its activity so as to operate in the critical regime. In particular, we study the dynamics of a two-layered network model consisting of an excitable node network and a complementary network that supplies resources required for node firing. More specifically, we study the dynamics of an excitable neural network consisting of neurons (nodes) connected via synapses (edges). Synaptic strengths are mediated by resources supplied by the complementary glial cell network. Resources from the bloodstream are supplied to the glial network at some fixed rate, resources transport diffusively within the glial cell network and ultimately to the synapses, and each time a presynaptic neuron fires the resources for all outgoing synapses get consumed at some fixed rate. We show that this natural and very compelling mechanism for feedback control can stabilize the critical state. Additionally, the neural network can learn, remember and recover the critical state after learning. The critical state is characterized by power-law distributed avalanche sizes that are robust to changes in the supply, consumption and diffusion rates. Finally, we show that our findings are fairly robust to heterogeneity in model parameters or network structure.