Related papers: The Analysis of Matched Layers
Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
We consider the problem of recovering a distribution function on the real line from observations additively contaminated with errors following the standard Laplace distribution. Assuming that the latent distribution is completely unknown…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
In this paper, we study the convergence of Alternating Projection (AP) algorithm for the matrix completion and compressed sensing problems. We also present computational evidence for the excellent performance of the algorithm. Also, in the…
We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix Fuchs--Garnier pairs for the third and fifth Painleve' equations, together with the…
Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In…
A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
This is a contribution to the number theory of the dimer problem. The number of dimer coverings (i.e., perfect matchings) of a square lattice graph is discussed modulo powers of 2.
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane wave component (plane wave limit), separately. For gain media, we…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
Attribution methods aim to explain a neural network's prediction by highlighting the most relevant image areas. A popular approach is to backpropagate (BP) a custom relevance score using modified rules, rather than the gradient. We analyze…
Starting from a remark about the computation of Kashiwara-Schapira's enhanced Laplace transform by using the Dolbeault complex of enhanced distributions, we explain how to obtain explicit holomorphic Paley-Wiener-type theorems. As an…
The elusive nature of gradient-based optimization in neural networks is tied to their loss landscape geometry, which is poorly understood. However recent work has brought solid evidence that there is essentially no loss barrier between the…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…