arXiv research

The paper extends hypothesis testing to non-diagonalizable matrices, improving network statistics inference.

In this paper we construct a family of complex analytic manifolds that generalize Inoue surfaces and Oeljeklaus-Toma manifolds. To a matrix $M$ in $SL(N,\mathbb{Z})$ satisfying some mild conditions on its characteristic polynomial we associate a manifold $T(M,\mathbf{D})$ (depending on an auxiliary parameter $\mathbf{D…

This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate transformation rules for integral order forms are also computed. Matrix order f…

We describe three-dimensional Lorentzian homogeneous Ricci solitons, showing that all types (i.e. shrinking, expanding and steady) exist. Moreover, all non-trivial examples have non-diagonalizable Ricci operator with one only eigenvalue.

In this paper, we study Lorentzian hypersurfaces in Minkowski 5-space with non-diagonalizable shape operator whose characteristic polinomial is $(t-k_1)^2(t-k_3)(t-k_4)$ or $(t-k_1)^3(t-k_4)$. We proved that in these cases, a hypersurface is biharmonic if and only if it is minimal.

Recent work of Ballas, Cooper, and Leitner identifies $(n+1)$ types of $n$-dimensional convex projective cusps, one of which is the standard hyperbolic cusp. Work of Ballas-Marquis, and Ballas-Danciger-Lee give examples of these exotic (non-hyperbolic) type cusps in dimension $3$. Here an extension of the techniques of…

In this paper, we obtain some properties of biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex eigen values. We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with at most five distinct prin…

In this paper, we determine the type numbers of the pseudo-hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non-diagonalizable shape operator in the $3$-dimensional anti-de Sitter space. Also, we investigate the behavior of type numbers of the pseudo-hyperbolic Gaus…

The paper studies quasi-umbilical timelike surfaces in a specific geometric setting.

Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of imag…

The paper explores polyharmonic hypersurfaces in pseudo-Riemannian space forms.

We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.

Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.

Study on random matrices in deep neural networks with IID entries.

Financial markets analyzed by reducing correlation matrix complexity.

Study isotropy groups for complex orthogonal and skew-symmetric matrices.

The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important difference is that the population covariance matrices, which are assumed to be non-random…

We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…

In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather …

Study of strictly accretive matrices using Finsler geometry.

We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of real matrices of a given size.

Minimal spectral radii found for specific matrix types.

Researchers develop geodesics for a new metric on correlation matrices.

We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.

New methods for sketching non-PSD matrices improve regression and optimization tasks.

Improved method for computing Fréchet means on SPD matrices.

Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.

We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…

Method estimates M-matrices in graphical models with improved accuracy.

Algorithm calculates Seifert matrices for colored links.

In this paper we extend DDVV-type inequalities involving the Frobenius norm of commutators from real symmetric and skew-symmetric matrices to Hermitian and skew-Hermitian matrices.

Proposes a new Sliced-Wasserstein distance for covariance matrices in M/EEG signals.

Study extends bounds on sample covariance matrices with general dependence.

New $k$-means method clusters radar image sequences using SPD matrices.

Kaleidoscope matrices improve model quality and inference speed.

Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes, little is known about their impact on statistical estimation. In this work, we …

A method learns matrix factorization from diverse matrices and applies the knowledge to unseen matrices.

The paper identifies and critiques problems with risk matrices using ordinal scales.

Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of activity that are reproducible with statistically significant frequency compared…

Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computation…

In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erdős-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system …

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to achieve robust sparse recovery with binary matrices. We establish sufficient conditi…

Study of J-Hermitian matrices and geometric mean definition.

Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.

We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries

This work compresses heavy-tailed weight matrices for tighter generalization bounds.

Simple bounds for covariance and Gram matrices across various settings.

Paper develops new method for detecting latent structure in large symmetric data matrices.