A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved… Expand

This work is the first to demonstrate that well-designed quantum neural networks offer an advantage over classical neural networks through a higher effective dimension and faster training ability, which is verified on real quantum hardware.Expand

We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform with respect to s bounded away from 0. This allows us to address local and global minimality properties of… Expand

Given two densities f and g, we consider the problem of transporting a fraction $${m \in [0,\min\{\|f\|_{L^1},\|g\|_{L^1}\}]}$$ of the mass of f onto g minimizing a transportation cost. If the cost… Expand

In this paper we provide a well-posedness theory for weak measure solutions of the Cauchy problem for a family of nonlocal interaction equations. These equations are continuum models for interacting… Expand

Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c(x, y).… Expand