The Universal Critical Dynamics of Noisy Neurons
Date
2019-05-02
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Abstract
The criticality hypothesis posits that the brain operates near a critical point. Typically, critical neurons are assumed to spread activity like a simple branching process and thus fall into the universality class of directed percolation. The branching process describes activity spreading from a single initiation site, an assumption that can be violated in real neurons where external drivers and noise can initiate multiple concurrent and independent cascades. In this thesis, I use the network structure of neurons to disentangle independent cascades of activity. Using a combination of numerical simulations and mathematical modelling, I show that criticality can exist in noisy neurons but that the presence of noise changes the underlying universality class from directed to undirected percolation. Directed percolation describes only small scale distributions of activity, on larger scales cascades can merge together and undirected percolation is the appropriate description.
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Keywords
Percolation, Branching process, Noise, Spontaneous Activity, Neurons, Criticality, Critical phenomena, critical phenomenon, Criticality hypothesis, Brain, Phase transition, Directed percolation, Scaling, Finite size, Networks
Citation
Korchinski, D. J. (2019). The Universal Critical Dynamics of Noisy Neurons (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.