arXiv research

Double-well transitions are stiffer than minimal surfaces.

We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.

We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $Ω\subset\mathds R^N$. The number of solutions is estimated in terms of topological …

Study confirms complex crypto market dynamics via non-linear potentials.

Assume that $f(s) = F'(s)$ where $F$ is a double-well potential. Under certain conditions on the Lipschitz constant of $f$ on $[-1,1]$, we prove that arbitrary bounded global solutions of the semilinear equation $Δu = f(u)$ on hyperbolic space $\HH^n$ must reduce to functions of one variable provided they admit asympto…

We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we employ posterior distributions over models, thus taking into account in a princi…

BNEM improves Boltzmann sampler efficiency.

We investigate the equation $(-Δ_{\mathbb H^n})^γ w=f(w)\quad in \mathbb H^{n},$ where $(-Δ_{\mathbb H^n})^γ$ corresponds to the fractional Laplacian on hyperbolic space for $γ\in (0,1)$ and $f$ is a smooth nonlinearity that typically comes from a double well potential. We prove the existence of heteroclinic connecti…

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the fun…

ECD algorithm speeds up non-convex optimization, offering quantum and stochastic enhancements.

iEFM trains CNF models from unnormalized densities efficiently.

A new training method for normalizing flows without samples.

Noise can stabilize systemic risk models with uncertain robustness.

kTULA improves sampling from distributions with super-linear log-gradients.

Algorithm learns stochastic system dynamics from data.

We study global monotone solutions of the free boundary problem that arises from minimizing the energy functional $I(u) = \int |\nabla u|^2 + V(u)$, where $V(u)$ is the characteristic function of the interval $(-1,1)$. This functional is a close relative of the scalar Ginzburg-Landau functional $J(u) = \int |\nabla u|^…

This work improves SGMs' convergence guarantees for semiconvex distributions with discontinuous gradients.

Framework for analyzing dynamic topological changes in point clouds using persistent homology and dynamic optimal transport.

ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.

New gauge fields modify Fokker-Planck dynamics without changing the stationary state.

The paper analyzes the score field of diffusion models using Burgers dynamics.

New method uses weighted SDEs to improve sampling from complex distributions.

Tractable model explains market dynamics using Langevin and SUSY QM.

Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations