Zobrazeno 1 - 10
of 173
pro vyhledávání: '"Maclaurin, James"'
Autor:
MacLaurin, James, Vilanova, Pedro
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 hydrodynamic limit of a balanced all-to-all network of 2n neurons for
Externí odkaz:
http://arxiv.org/abs/2412.17273
Autor:
MacLaurin, James
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 mean-field of the afferent edges and nodes. The flipping of the edge
Externí odkaz:
http://arxiv.org/abs/2411.09260
Autor:
Avitabile, Daniele, MacLaurin, James
We prove a Large Deviation Principle for Hawkes Processes on sparse large disordered networks with a graphon structure. We apply our results to a stochastic SIS epidemiological model on a disordered networks, and determine Euler-Lagrange equations th
Externí odkaz:
http://arxiv.org/abs/2410.13682
Autor:
Avitabile, Daniele, MacLaurin, James
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 coupling and nodal dynamics, we prove that the network admits a rigorous
Externí odkaz:
http://arxiv.org/abs/2408.12540
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 limit. Explicit Euler-Lagrange equations are determined for computing opti
Externí odkaz:
http://arxiv.org/abs/2406.12493
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 motivations for this is that allows one to understand how the structu
Externí odkaz:
http://arxiv.org/abs/2401.15272
Autor:
MacLaurin, James, Newby, Jay M.
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit to infinit
Externí odkaz:
http://arxiv.org/abs/2309.01827
Autor:
Adams, Zachary P., MacLaurin, James
We study the dynamics of waves, oscillations, and other spatio-temporal patterns in stochastic evolution systems, including SPDE and stochastic integral equations. Representing a given pattern as a smooth, stable invariant manifold of the determinist
Externí odkaz:
http://arxiv.org/abs/2210.10681
Autor:
Adams, Zachary P. a, ⁎, MacLaurin, James b, ⁎
Publikováno v:
In Journal of Differential Equations 5 January 2025 414:773-816
