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We present first-order perturbation analysis of a simple eigenvalue and the corresponding right and left eigenvectors of a general square matrix, not assumed to be Hermitian or normal. The eigenvalue result is well known to a broad…
The robust Chinese remainder theorem (CRT) has been recently proposed for robustly reconstructing a large nonnegative integer from erroneous remainders. It has found many applications in signal processing, including phase unwrapping and…
The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…
Recently learned image compression (LIC) has achieved great progress and even outperformed the traditional approach using DCT or discrete wavelet transform (DWT). However, LIC mainly reduces spatial redundancy in the autoencoder networks…
We verify that persistent observers in causally invariant hypergraph substrates satisfy the conditions of the Conant-Ashby Good Regulator Theorem. Building on Wolfram's hypergraph physics and Vanchurin's neural network cosmology, we…
We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show that their…
We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well. More…
The benefits of the wavelet approach for density estimation are well established in the literature, especially when the density to estimate is irregular or heterogeneous in smoothness. However, wavelet density estimates are typically not…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…
To construct dispersion relations for diffusion or oscillation processes on random networks, it is necessary to obtain effective length scales for the eigenvectors of a graph Laplacian matrix, whose eigenvalues represent inverse time…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
We consider skew-products with concave interval fiber maps over a certain subshift obtained as the projection of orbits staying in a given region. It generates a new type of (essentially) coded shift. The fiber maps have expanding and…
Recently, autoencoders (AEs) have gained interest for creating parametric and invertible projections of multidimensional data. Parametric projections make it possible to embed new, unseen samples without recalculating the entire projection,…
In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs…
We present a method to reconstruct the initial linear-regime matter density field from the late-time non-linearly evolved density field in which we channel the output of standard first-order reconstruction to a convolutional neural network…
We propose a variation on wavefield reconstruction inversion for seismic inversion, which takes advantage of randomized linear algebra as a way to overcome the typical limitations of conventional inversion techniques. Consequently, we can…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…