Related papers: The eigenspectra of Indian musical drums
We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
The eigenvalues and eigenfunctions of a linear {\alpha}^{2}-dynamo have been computed for different spatial distributions of an isotropic \alpha-effect. Oscillatory solutions are obtained when \alpha exhibits a sign change in the radial…
We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of…
We examine resonantly damped kink modes in straight coronal slabs, paying special attention to the effects of the formulation for the transverse density distribution ("profile"). We work in the framework of pressure-less, gravity-free,…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
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We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…
We show that the fundamental eigenmode of a shallow optical bottle microresonator (also called a SNAP microresonator) can be made exceptionally uniform along its axial length. The introduced microresonator has the effective radius variation…
We investigate internal localized eigenmodes of the linearized equation around spin discrete breathers in 1D antiferromagnets with on-site easy axis anisotropy. The threshold of occurrence of the internal localized eigenmodes has a typical…
When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…
We consider the empirical eigenvalue distribution of an $m\times m$ principle submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. Earlier work of Petz and R\'effy identified the limiting spectral measure…
The statistical behavior of the eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the approximate…
Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential.…
Electromagnetic stimulation of the human brain is a key tool for the neurophysiological characterization and diagnosis of several neurological disorders. Transcranial magnetic stimulation (TMS) is one procedure that is commonly used…
We introduce the new concept of D-geometry (or "drum geometry"), which has been recently discovered by the author in \cite{KT-DRUMS} when constructing and classifying isospectral and length equivalent drums under certain constraints. We…
Modern digital music production typically involves combining numerous acoustic elements to compile a piece of music. Important types of such elements are drum samples, which determine the characteristics of the percussive components of the…
We study self-attention dynamics on the unit sphere as an interacting particle system arising from an idealized Transformer-type update. Under a symmetry assumption on weight matrices given by $Q^\top K=V=V^\top$, the flow admits a…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
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