An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices

We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a particular component of the unique solution to a vector equilibrium problem. Moreover, we show that the other components describe the limiting behavior of certain generalized eigenvalues. In this way, we generalize the recent results of Duits and Kuijlaars for banded Toeplitz matrices.Comment: 20 pages, 2 figure

Heidegger And Metaphysical Aesthetics

The aim of this paper is to bring to light some of the fundamental differences between Heidegger’s approach to art and the traditional approach, and to do so within the context of Heidegger’s project of what he calls “overcoming metaphysics”

Convention And Difference

The claim that music is language may be oft repeated, but it remains wholly unenlightening unless a sufficient explanation of one of these terms has already been given. On the face of it, music is entirely dissimilar to natural language, at least when conceived functionally, the one being categorised primarily as an aesthetic object, the other first and foremost as a means of communication

Invertible Orientation Scores of 3D Images

The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical applications. To handle complex crossing structures in 2D images, 2D orientation scores were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores. First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake-wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. For efficient implementation of the different steps in the wavelet creation we use a spherical harmonic transform. Finally, we show some first results of practical applications of 3D orientation scores.Comment: ssvm 2015 published version in LNCS contains a mistake (a switch notation spherical angles) that is corrected in this arxiv versio