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Normalization effects on shallow neural networks and related asymptotic expansions
Jiahui Yu, Konstantinos Spiliopoulos
We consider shallow (single hidden layer) neural networks and characterize their performance when trained with stochastic gradient descent as the number of hidden units and gra…
Large deviations for interacting multiscale particle systems
Zachary Bezemek, Konstantinos Spiliopoulos
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical dist…
How reaction-diffusion PDEs approximate the large-population limit of stochastic particle models
Samuel A Isaacson, Jingwei Ma, Konstantinos Spiliopoulos
Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion (PBSRD) models are commonly-used approaches for modeling the spatial dynamics of chemical and biological sy…
Discrete-time inference for slow-fast systems driven by fractional Brownian motion
Solesne Bourguin, Siragan Gailus, Konstantinos Spiliopoulos
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimato…
Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models
Samuel A. Isaacson, Jingwei Ma, Konstantinos Spiliopoulos
Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transp…