Related papers: Spectrally arbitrary pattern extensions
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the…
We study a new random matrix ensemble $X$ which is constructed by an application of a two dimensional linear filter to a matrix of iid random variables with infinite fourth moments. Our result gives asymptotic lower and upper bounds for the…
Arbitrarily sparse sets A of integers are constructed with the property that every integer can be represented uniquely in the form n = a + a', where a and a' belong to the set A and a < a' or a = a'. Some related open problems are stated.
Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation E x' + A x = 0. Such an equation is invariant by changes of variables,…
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
This article focuses on a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, which are called irreducible triangulations. The structure has been introduced by Xin He under…
We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to…
Learning of matrix-valued data has recently surged in a range of scientific and business applications. Trace regression is a widely used method to model effects of matrix predictors and has shown great success in matrix learning. However,…
Hermitian linear matrix pencils are ubiquitous in control theory, operator systems, semidefinite optimization, and real algebraic geometry. This survey reviews the fundamental features of the matricial solution set of a linear matrix…
We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically…
A spectrahedron is a convex set defined by a linear matrix inequality, i.e., the set of all $x \in \mathbb{R}^g$ such that \[ L_A(x) = I + A_1 x_1 + A_2 x_2 + \dots + A_g x_g \succeq 0 \] for some symmetric matrices $A_1,\ldots,A_g$. This…
The main purpose of this article is to alert spectroscopists, particularly those involved in surveys, to the fact that rapidly pulsating sources induce periodic structures in spectra. This would allow the detection of new classes of objects…
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…
In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…
We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown positions and orientations that we aim…
We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect…
We define extension maps as maps that extend a system (through adding ancillary systems) without changing the state in the original system. We show, using extension maps, why a completely positive operation on an initially entangled system…