25 citations · 103 across the 19 of their papers we have counts for
4 papers · 1 filter
Manifold learning with bi-stochastic kernels
Nicholas F. Marshall, Ronald R. Coifman
In this paper we answer the following question: what is the infinitesimal generator of the diffusion process defined by a kernel that is normalized such that it is bi-stochastic wi…
Stretching convex domains to capture many lattice points
Nicholas F. Marshall
We consider an optimal stretching problem for strictly convex domains in that are symmetric with respect to each coordinate hyperplane, where stretching refers to tr…
Triangles capturing many lattice points
Nicholas F. Marshall, Stefan Steinerberger
We study a combinatorial problem that recently arose in the context of shape optimization: among all triangles with vertices , , and and fixed area, which one…
The Stability of the First Neumann Laplacian Eigenfunction Under Domain Deformations and Applications
Nicholas F. Marshall
The robustness of manifold learning methods is often predicated on the stability of the Neumann Laplacian eigenfunctions under deformations of the assumed underlying domain. Indeed…