Related papers: Certified Real Eigenvalue Location
We give an $O(n)$ time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and $x\in \mathbb{R}$. Applications include determining the number of eigenvalues of a cograph's…
Cardiac Magnetic Resonance (CMR) images are widely used for cardiac diagnosis and ventricular assessment. Extracting specific landmarks like the right ventricular insertion points is of importance for spatial alignment and 3D modeling. The…
Indoor position technology has become one of the research highlights in the Internet of Things (IoT), but there is still a lack of universal, low-cost, and high-precision solutions. This paper conducts research on indoor position technology…
Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and…
In explainable artificial intelligence, discriminative feature localization is critical to reveal a blackbox model's decision-making process from raw data to prediction. In this article, we use two real datasets, the MNIST handwritten…
Three numerical coverage metrics for the symbolic simulation of dense-time systems and their estimation methods are presented. Special techniques to derive numerical estimations of dense-time state-spaces have also been developed.…
We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition…
We present a rational filter for computing all eigenvalues of a symmetric definite eigenvalue problem lying in an interval on the real axis. The linear systems arising from the filter embedded in the subspace iteration framework, are solved…
The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalisations in the subspace…
Recently, it has been suggested that the Many-Body Localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert space preserving renormalization scheme that iteratively finds such integrals of motion…
We show that the author of a recent paper [arXiv:2008.04929] put forward some false statements about the eigenstates of Hermitian and non-Hermitian systems. We conjecture that one of the non-Hermitian Hamiltonians for a one-dimensional…
The demands of automated shipping address recognition and verification have increased to handle a large number of packages and to save costs associated with misdelivery. A previous study proposed a deep learning system where the shipping…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based…
Signature verification has been one of the major researched areas in the field of computer vision. Many financial and legal organizations use signature verification as access control and authentication. Signature images are not rich in…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
Gradient estimation is a central challenge in training parameterized quantum circuits (PQCs) for hybrid quantum-classical optimization and learning problems. This difficulty arises from several factors, including the exponential…
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a…
We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main…
Recently a novel family of eigensolvers, called spectral indicator methods (SIMs), was proposed. Given a region on the complex plane, SIMs first compute an indicator by the spectral projection. The indicator is used to test if the region…