Related papers: On the breakdown point of transport-based quantile…
Numerous unconventional superconductors such as cuprates, heavy-fermions, and twisted-bilayer graphene exhibit incoherent metallic transport above the superconducting critical temperature. This phenomenon cannot be described with…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
We prove that, for general cost functions on $\mathbb{R}^n$, or for the cost $d^2/2$ on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.
We have evaluated the transport coefficients of quark and hadronic matter in the frame work of Polyakov-Quark-Meson model. The thermal widths of quarks and mesons, which inversely control the strength of these transport coefficients, are…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
We introduce folded optimal transport, as a method to extend a cost or distance defined on the extreme boundary of a convex to the whole convex, related to convex extension. This construction broadens the framework of standard optimal…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
The study explores perpendicular transport through macroscopically inhomogeneous three-dimensional disordered conductors using mesoscopic methods (real-space Green function technique in a two-probe measuring geometry). The nanoscale samples…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…
Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points. Under projective duality, this can be interpreted…
We theoretically study transport in two-dimensional semimetals. Typically, electron and hole puddles emerge in the transport layer of these systems due to smooth fluctuations in the potential. We calculate the electric response of the…
We prove reducibility of a transport equation on the $d$-dimensional torus $T^d$ with a time quasi-periodic unbounded perturbation. As far as we know this is the first example of a reducibility result for an equation in more than one…
Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is optimal in a certain sense. In the general model, the optimality…
In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant…
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are…
We review two models of optimal transport, where congestion effects during the transport can be possibly taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given…
The optimal transportation problem, first suggested by Gaspard Monge in the 18th century and later revived in the 1940s by Leonid Kantorovich, deals with the question of transporting a certain measure to another, using transport maps or…
The quadratically regularized optimal transport problem has recently been considered in various applications where the coupling needs to be \emph{sparse}, i.e., the density of the coupling needs to be zero for a large subset of the product…
In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the…
In [3], the authors used the Legendre transform to give a tractable method for studying Topological Data Analysis (TDA) in terms of sums of Gaussian kernels. In this paper, we prove a variant for sums of cosine similarity-based kernel…