From the 1 of 6 linked papers with an AI index.
6 papers
The Maxwell Conjecture is False
Philip Arathoon, Gavin Ball, Matthew D. Kvalheim
The authors present a configuration of five point charges that yields at least 24 non‑degenerate critical points of the electrostatic potential, disproving Maxwell's conjecture abo…
Stabilizability of first-order dynamics in second-order systems
Matthew D. Kvalheim
We study whether second-order systems can be made to behave like prescribed first-order dynamical systems through feedback control. More precisely, we study whether prescribed vect…
Linearizability of flows by embeddings
Matthew D. Kvalheim, Philip Arathoon
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on…
Autoencoding Dynamics: Topological Limitations and Capabilities
Matthew D. Kvalheim, Eduardo D. Sontag
Given a "data manifold" and "latent space" , an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\t…
Global linearization of asymptotically stable systems without hyperbolicity
Matthew D. Kvalheim, Eduardo D. Sontag
We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjuga…
Differential topology of the spaces of asymptotically stable vector fields and Lyapunov functions
Matthew D. Kvalheim
We study the topology of the space of all smooth asymptotically stable vector fields on , as well as the space of all proper smooth Lyapunov functions for such vector…