We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced res...

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combin...

In this paper, we prove a conjecture, which was proposed by Frank Stenger in 1997, concerning the localization of eigenvalues of the Sinc matrix I(−1), a problem that is important in both the theory and the practice of Sinc methods. In 2003, Iyad Abu-Jeib and Thomas Shores established a partial answer to this unsolved problem. The techniques they have developed, however, turn out to be the key ...

In this paper we present a new measure for corner detection based on the eigenvalues of the covariance matrix of boundary points over a small region of support. It avoids false alarms for superfluous corners on circular arcs. Experimental results have shown that the proposed corner detection methods using curvature measures. It has good detection and localization for curved objects in different...

wireless sensor networks attracting a great deal of research interest. accurate localization of sensor nodes is a strong requirement in a wide area of applications. in recent years, several techniques have been proposed for localization in wireless sensor networks. in this paper we present a localization scheme with using only one mobile anchor station and received signal strength indicator tec...

We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schrödinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment bound to obtain a new n-level Wegner-type estimate that measures eigenvalue correlations through an upper bound on the probability that a local Hamiltonian ha...

We examine the stability domains of a 1D discrete Schr\"{o}dinger equation in simultaneous presence parity-time ($\cal{PT}$) symmetry and fractionality. Direct numerical examination eigenvalues system reveals that, as fractional exponent is decreased away from unity (the standard case), instability gain increases abruptly past critical value. Also, length increases, stable fraction decreases we...

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...