Related papers: Symmetrized semi-discrete optimal transport
A power constrained sensor network that consists of multiple sensor nodes and a fusion center (FC) is considered, where the goal is to estimate a random parameter of interest. In contrast to the distributed framework, the sensor nodes may…
We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates this problem into a non-local Monge-Amp\`ere type equation.…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
One abstract method for the study of network transportation is proposed in this paper. By interpolating the properties of the edges that constitute network into the two leading parameters of the nodes, this method can abstract the…
This study presents a framework for optimizing the two-dimensional (2D) placement of electric motorcycle powertrain elements, accounting for the position, the orientation and geometric irregularities. Specifically, we construct a 2D…
In this work we consider the problem of semi-active damping optimization of mechanical systems with fixed damper positions. Our goal is to compute a damping that is locally optimal with respect to the $\mathcal{H}_\infty$-norm of the…
We consider certain matricial analogues of optimal mass transport of positive definite matrices of equal trace. The framework is motivated by the need to devise a suitable geometry for interpolating positive definite matrices in ways that…
In this paper, a joint transmitter and receiver design for pattern division multiple access (PDMA) is proposed. At the transmitter, pattern mapping utilizes power allocation to improve the overall sum rate, and beam allocation to enhance…
The Sinkhorn algorithm has emerged as a powerful tool for solving optimal transport problems, finding applications in various domains such as machine learning, image processing, and computational biology. Despite its widespread use, the…
In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying…
We develop criteria based on a calibration argument via discrete PDE and semidiscrete optimal transport, for finding sharp isoperimetric inequalities of the form $(\sharp \Omega)^{d-1} \le C (\sharp \overrightarrow{\partial\Omega})^d$ where…
This paper introduces new approaches for combining non-orthogonal multiple access with distributed antenna systems. The study targets a minimization of the total transmit power in each cell, under user rate and power multiplexing…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
Signals with single peak and symmetry property are very common in various fields, such as probability density function of normal distribution. Among the information contained in such signals, peak position is the most important, sometimes…
We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…
Many problems in dynamic data driven modeling deals with distributed rather than lumped observations. In this paper, we show that the Monge-Kantorovich optimal transport theory provides a unifying framework to tackle such problems in the…
In this work, we introduce an optimal transport framework for inferring power distributions over both spatial location and temporal frequency. Recently, it has been shown that optimal transport is a powerful tool for estimating spatial…