Related papers: Inside-outside duality with artificial backgrounds
We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…
A ring with an Auslander dualizing complex is a generalization of an Auslander-Gorenstein ring. We show that many results which hold for Auslander-Gorenstein rings also hold in the more general setting. On the other hand we give criteria…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We continue the study of the Hermitian random matrix ensemble with external source $\frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM$ where $A$ has two distinct eigenvalues $\pm a$ of equal multiplicity. This model exhibits a phase transition for…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a…
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical setting, an abstract convex function is the upper envelope…
Adversarial examples reveal the blind spots of deep neural networks (DNNs) and represent a major concern for security-critical applications. The transferability of adversarial examples makes real-world attacks possible in black-box…
Foreground-conditioned inpainting aims to seamlessly fill the background region of an image by utilizing the provided foreground subject and a text description. While existing T2I-based image inpainting methods can be applied to this task,…
A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach…
We introduce an algorithm to piecewise dualise linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the $S$-wall which can all be derived by iterative applications of Seiberg-like…
Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…
We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the…
A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem…
We develop a novel method of virtual sources to formulate boundary integral equations for exterior wave propagation problems. However, by contrast to classical boundary integral formulations, we displace the singularity of the Green's…
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically…
We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…