2 citations · 2 across the 3 of their papers we have counts for
5 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…
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…
Multilevel Hybrid Chernoff Tau-leap
Alvaro Moraes, Raul Tempone, Pedro Vilanova
In this work, we extend the hybrid Chernoff tau-leap method to the multilevel Monte Carlo (MLMC) setting. Inspired by the work of Anderson and Higham on the tau-leap MLMC method wi…