3 papers
math.AP2026
Nodal Deficiency of Neumann Eigenfunctions on a Symmetric Dumbbell Domain
Thomas Beck, Andrew Lyons
We study the nodal deficiency of pairs of Neumann eigenfunctions defined over symmetric dumbbell domains. As the width of the connecting neck shrinks, these eigenfunctions converge…
math.AP2025
Towards Spectral Convergence of Locally Linear Embedding on Manifolds with Boundary
Andrew Lyons
We study the eigenvalues and eigenfunctions of a differential operator that governs the asymptotic behavior of the unsupervised learning algorithm known as Locally Linear Embedding…
math.AP2025
Nodal Sets of Laplacian Eigenfunctions with an Eigenvalue of Multiplicity 2
Andrew Lyons
We study the effects of a domain deformation to the nodal set of Laplacian eigenfunctions when the eigenvalue is degenerate. In particular, we study deformations of a rectangle tha…