Related papers: The eigenspectra of Indian musical drums
This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is…
Creating a complex work of art like music necessitates profound creativity. With recent advancements in deep learning and powerful models such as transformers, there has been huge progress in automatic music generation. In an accompaniment…
Small-size acoustic arrays exploit spatial diversity to achieve capabilities beyond those of single-element devices, with applications ranging from teleconferencing to immersive multimedia. A key requirement for broadband array processing…
The noise of a device under test (DUT) is measured simultaneously with two instruments, each of which contributes its own background. The average cross power spectral density converges to the DUT power spectral density. This method enables…
We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of…
We generalize Weyl's law to inhomogeneous bodies in $d$ dimensions. Using a perturbation scheme recently obtained by us in Ref. \cite{Amore09}, we have derived an explicit formula, which describes the asymptotic behavior of the eigenvalues…
Scattering of obliquely incident electromagnetic waves from periodically space-time modulated slabs is investigated. It is shown that such structures operate as nonreciprocal harmonic generators and spatial-frequency filters. For oblique…
This work is about uniform, plane, singly connected, strictly regular Hall-plates with an arbitrary number of peripheral contacts exposed to a uniform magnetic field of arbitrary strength. The strictly regular symmetry is the highest…
We have investigated quasi-eigenmodes of a quadrupolar deformed microcavity by extensive numerical calculations. The spectral structure is found to be quite regular, which can be explained on the basis of the fact that the microcavity is an…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…
The magnetic field integral equation for axially symmetric cavities with perfectly conducting piecewise smooth surfaces is discretized according to a high-order convergent Fourier--Nystr\"om scheme. The resulting solver is used to…
We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…
Generative artificial intelligence models can be a valuable aid to music composition and live performance, both to aid the professional musician and to help democratize the music creation process for hobbyists. Here we present a novel…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few different techniques are employed: the most sophisticated, which relates the 1-skeleton of the polytope to a Cayley graph, is based on methods akin to…
(abbreviated) In this paper we develop a consistent WKBJ formalism, together with a formal first order perturbation theory for calculating the properties of the inertial modes of a uniformly rotating coreless body (modelled as a polytrope…
Eigenspectra that fill regions in the complex plane have been intriguing to many, inspiring research from random matrix theory to esoteric semi-infinite bounded non-Hermitian lattices. In this work, we propose a simple and robust ansatz for…
We propose a computationally feasible estimator for the needlet trispectrum, which develops earlier work on the bispectrum by Donzelli et al. (2012). Our proposal seems to enjoy a number of useful properties, in particular a) the…
To achieve a flexible recommendation and retrieval system, it is desirable to calculate music similarity by focusing on multiple partial elements of musical pieces and allowing the users to select the element they want to focus on. A…
We compute exact asymptotic of the statistical density of random matrices belonging to invariant random matrices ensemble (RMT) orthogonal, unitary and symplectic ensembles, where all its eigenvalues lie within the interval $[\sigma,…