相关论文: Metasurfaces and Optimal transport
Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
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 consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic…
This paper develops a comprehensive theory of optimal transport for signed (real) measures on Rd. Extending the classical Brenier theorem, we consider Jordan decompositions of measures with possibly fractal singular parts. Under suitable…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
We introduce Neural Radiosity, an algorithm to solve the rendering equation by minimizing the norm of its residual similar as in traditional radiosity techniques. Traditional basis functions used in radiosity techniques, such as piecewise…
Metasurfaces are generally designed by placing scatterers in a periodic grid. We propose and discuss design rules for efficient random and functional metasurfaces with anisotropic elements. We investigate the impact of the elements density…
Multiport network theory (MNT) is a powerful analytical tool for modeling and optimizing complex systems based on circuit models. We present an overview of current research on the application of MNT to the development of electromagnetically…
We analyze single and multilayered metamaterials by modeling each layer as a metasurface with effective surface electric and magnetic susceptibility derived through a thin film approximation. Employing a transfer matrix method, these…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
Optimal transport has been used to define bijective nonlinear transforms and different transport-related metrics for discriminating data and signals. Here we briefly describe the advances in this topic with the main applications and…
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information…
We present a registration method for model reduction of parametric partial differential equations with dominating advection effects and moving features. Registration refers to the use of a parameter-dependent mapping to make the set of…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Metasurfaces have been proposed as a new paradigm to manipulate light and improve light-matter interactions. Conventional metasurfaces are restricted to the loss of materials, limiting their performance ceiling. Here, the loss of metallic…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…
In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing…