Title: Learning on manifolds without manifold learning Abstract: Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about […]

Title: Randomly pivoted Cholesky: Fast, accurate matrix approximation for scientific machine learning Abstract: Low-rank approximation of positive semidefinite matrices is a basic problem in computational mathematics, with many applications to machine learning and scientific computing. Existing approaches for this problem largely fall into two categories: simple, fast, but sometimes inaccurate methods and sophisticated, slower methods […]

Title: Erlang-Distributed SEIR Epidemical Models Abstract: We examine the effects of different dynamics in epidemiological models, focusing on two key approaches. The first model incorporates reaction-diffusion dynamics, where susceptible individuals avoid areas with high concentrations of infected individuals. The second model divides exposed and infectious individuals into symptomatic and asymptomatic subclasses. Our findings emphasize the […]