Related papers: Transmission eigenvalue-free regions
This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common…
Model-free reinforcement learning algorithms have exhibited great potential in solving single-task sequential decision-making problems with high-dimensional observations and long horizons, but are known to be hard to generalize across…
This paper investigates degenerate nonlocal free boundary problems arising in the context of superconductivity, extending the nonlocal counterpart to the work of Caffarelli, Salazar, and Shahgholian \cite{CS02, CSS04} in the local setting.…
This paper contains a lower bound of the Weyl type on the counting function of the positive eigenvalues of the interior transmission eigenvalue problem which justifies the existence of an infinite set of positive interior transmission…
We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…
We study the optimal diffusive transmission and absorption of broadband or polychromatic light in a disordered medium. By introducing matrices describing broadband transmission and reflection, we formulate an extremal eigenvalue problem…
We consider a single hop wireless X network with $K$ transmitters and $J$ receivers, all with single antenna. Each transmitter conveys for each receiver an independent message. The channel is assumed to have constant coefficients. We…
In this work we investigate a specific transfer learning approach for deep reinforcement learning in the context where the internal dynamics between two tasks are the same but the visual representations differ. We learn a low-dimensional…
Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector…
This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm-Liouville problem together with two supplementary transmission…
We develop a novel frequency-based H-infinity control method for a large class of infinite-dimensional Linear-Time-Invariant systems in transfer function form. Major benefits of our approach is that reduction or identification techniques…
Using the transfer-matrix approach and solving time-domain differential equations, we analyze the loss compensation mechanism in multilayer systems composed of an absorbing transparent conductive oxide and dielectric doped with an active…
Recently, contour integral-based methods have been actively studied for solving interior eigenvalue problems that find all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we reconsider the…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
For geometric systems of real principal type, we define a subprincipal symbol and derive a transport equation for polarizations which, in the scalar case, is a well-known equation of Duistermaat and H\"ormander. We apply the transport…
The eigenvalue spectrum of the sum of large random matrices that are mutually "free", i.e., randomly rotated, can be obtained using the formalism of R-transforms, with many applications in different fields. We provide a direct…
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…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from…
Resonance frequencies are complex eigenvalues at which the homogeneous transmission problems have non-trivial solutions. These frequencies are of interest because they affect the behavior of the solutions even when the frequency is real.…