Related papers: Planar Earthmover is not in $L_1$
We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the…
The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography…
Let $\omega$ be a closed, non-degenerate differential form of arbitrary degree. Associated to it there are an $L_{\infty}$-algebra of observables, and an $L_{\infty}$-algebra of sections of the higher Courant algebroid twisted by $\omega$.…
Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…
Under which conditions and with which distortions can we preserve the pairwise-distances of low-complexity vectors, e.g., for structured sets such as the set of sparse vectors or the one of low-rank matrices, when these are mapped in a…
We show that there is a sharp threshold in dimension one for the transport cost between the Lebesgue measure $\lambda$ and an invariant random measure $\mu$ of unit intensity to be finite. We show that for \emph{any} such random measure the…
Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not…
The ordered weighted $\ell_1$ (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform…
A forward model of matter and biased tracers at arbitrary order in Lagrangian perturbation theory (LPT) is presented. The forward model contains the complete LPT displacement field at any given order in perturbations, as well as all…
This paper presents a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric.The use of this equation is exemplified on the group of rigid body motions SE(3), using…
We demonstrate the effectiveness of one of the many multi-tracer analyses enabled by Optimal Transport (OT) reconstruction. Leveraging a semi-discrete OT algorithm, we determine the displacements between initial and observed positions of…
Autonomous navigation in off-road environments remains a significant challenge in field robotics, particularly for Unmanned Ground Vehicles (UGVs) tasked with search and rescue, exploration, and surveillance. Effective long-range planning…
Let $G$ be a countable discrete group with an orthogonal representation $\alpha$ on a real Hilbert space $H$. We prove $L_p$ Poincar\'e inequalities for the group measure space $L_\infty(\Omega_H,\gamma)\rtimes G$, where both the group…
Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds the space of distributions into an $L^2$-space. The…
General properties of charge carrier transport in disordered organic materials are discussed. Spatial correlation between energies of transport sites determines the form of the drift mobility field dependence. Particular kind of spatial…
The Planar Graph Metric Compression Problem is to compactly encode the distances among $k$ nodes in a planar graph of size $n$. Two na\"ive solutions are to store the graph using $O(n)$ bits, or to explicitly store the distance matrix with…
In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated optimal…
The spatial non-locality (dispersion) of the transport equations results in a nonlinear dependence of the voltage drop $U$ on the distance between the points of measuring. Therefore the results of the usual two-probe measurements of the…
It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it…