8 papers
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…
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…
The Hydrodynamic Limit of Hawkes Processes on Adaptive Stochastic Networks
James MacLaurin
We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the…
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…
Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks
Daniele Avitabile, James MacLaurin
We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on cou…
Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves
Gaetan Barbet, James MacLaurin, Moshe Silverstein
We prove a Large Deviation Principle for Piecewise Deterministic Markov Processes (PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size limi…
Population Level Activity in Large Random Neural Networks
James MacLaurin, Moshe Silverstein, Pedro Vilanova
We determine limiting equations for large asymmetric `spin glass' networks. The initial conditions are not assumed to be independent of the disordered connectivity: one of the main…
Extreme first passage times for populations of identical rare events
James MacLaurin, Jay M. Newby
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of such events to occur is called an extreme firs…