5 problems

Zero-set conjecture.

Nonexistence conjecture. For certain kernels, there is no gradient-flow structure, even in an adapted nonlocal Hilbert space.

Let $f:\mathbb{R}\to[0,1]$ be a steep sigmoid-like firing-rate function; one example considered is … where $H$ is the unit step function. The paper establishes existence and linear…

Let $\omega$ be a connectivity function and consider the neural field model with firing-rate function $f$. A periodic stationary solution is a stationary solution that is periodic…

Optimal convergence-speed conjecture. The fastest possible convergence has speed $1/\sqrt{N}$, achieved when