3 papers
math.PR2025
The Kinetic Limit of Balanced Neural Networks
James MacLaurin, Pedro Vilanova
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that…
math-ph2024
The Hydrodynamic Limit of Neural Networks with Balanced Excitation and Inhibition
James MacLaurin, Pedro Vilanova
The theory of `Balanced Neural Networks' is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. We determine equations for the…
math.PR2024
Large Deviations of Mean-Field Jump-Markov Processes on Structured Sparse Disordered Graphs
James MacLaurin
We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometr…