arXiv research

Edge augmentation connects disconnected graphs by elevating eigenvalues.

Elevating houses to flood risk increases uncertainty, leading to higher optimal elevations.

Mathematical problems of digital terrain analysis include interpolation of digital elevation models (DEMs), DEM generalization and denoising, and computation of morphometric variables by calculation of partial derivatives of elevation. Traditionally, these procedures are based on numerical treatments of two-variable di…

In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or minutes up to two days, we compare magnitude of the largest eigenvalue of the corre…

Algorithm identifies interpretable subgroups with elevated treatment effects.

Deep learning extracts terrain texture covariates for geostatistical modeling.

Generative Adversarial Networks simulate elevator group control without extensive data.

In this paper, mm-Pose, a novel approach to detect and track human skeletons in real-time using an mmWave radar, is proposed. To the best of the authors' knowledge, this is the first method to detect >15 distinct skeletal joints using mmWave radar reflection signals. The proposed method would find several applications …

The paper analyzes how quantization affects the Fisher Information Matrix's dominant eigenvalue.

Framework for applying GPs to real-world data with scalability guidelines.

In recent years, advances in machine learning algorithms, cheap computational resources, and the availability of big data have spurred the deep learning revolution in various application domains. In particular, supervised learning techniques in image analysis have led to superhuman performance in various tasks, such as…

When the residents of Flint learned that lead had contaminated their water system, the local government made water-testing kits available to them free of charge. The city government published the results of these tests, creating a valuable dataset that is key to understanding the causes and extent of the lead contamina…

In compressed sensing problems, $\ell_1$ minimization or Basis Pursuit was known to have the best provable phase transition performance of recoverable sparsity among polynomial-time algorithms. It is of great theoretical and practical interest to find alternative polynomial-time algorithms which perform better than $\e…

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…

The paper compares Steklov and Laplacian eigenvalues on graphs.

Paper presents a new method for better financial market forecasting.

The principal submatrix localization problem deals with recovering a $K\times K$ principal submatrix of elevated mean $μ$ in a large $n\times n$ symmetric matrix subject to additive standard Gaussian noise. This problem serves as a prototypical example for community detection, in which the community corresponds to the …

In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted La…

The paper explores inequalities between eigenvalues on Riemannian manifolds.

Eigenvalues of Steklov eigenproblems change predictably with boundary tweaks.

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

We report the first, to the best of our knowledge, hand-in-hand collaboration between human rights activists and machine learners, leveraging crowd-sourcing to study online abuse against women on Twitter. On a technical front, we carefully curate an unbiased yet low-variance dataset of labeled tweets, analyze it to acc…

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

Paper finds how Steklov eigenvalues change on graphs and trees.

Bayesian methods reduce variance in subspace identification for small data sets.

Eigenvalue estimate for shrinkers in mean curvature flow.

Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the signal may not available, we examine here a simple procedure for estimating the…

In this paper we study eigenvalues of the closed eigenvalue problem of the Witten-Laplacian on an $n$-dimensional compact Riemannian manifold. Estimates for eigenvalues are given. As applications, we give a sharp upper bound for the $k^{\text{th}}$ eigenvalue and for isoparametric minimal hypersurfaces in the unit sphe…

For a bounded domain $Ω$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Lap…

The paper provides estimates for eigenvalues of elliptic differential problems.

The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.

The paper characterizes isomorphic covers of surfaces and applies it to distinguish representations.

Sharp bounds derived for the first two Steklov eigenvalues of exterior domains.

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &Δ{\mathbf u}+ α{\rm grad}(\text{div}{\mathbf u})=-σ{\mathbf u}, \ \text{in $Ω$}, &{\mathbf u}|_{\partial Ω}={\mathbf 0}. \aligned . $$ Estimate…

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.

We study the eigenvalue problem for the Riemannian Pucci operator on geodesic balls. We establish upper and lower bounds for the principal Pucci eigenvalues depending on the curvature, extending Cheng's eigenvalue comparison theorem for the Laplace-Beltrami operator. For manifolds with bounded sectional curvature, we p…

The paper studies eigenvalues of Xin-Laplacian on Riemannian manifolds.

The paper finds new inequalities for Laplacian and biharmonic eigenvalues on manifolds.

In this paper, we mainly study eigenvalue problems of p-Laplacian on domains with an interior hole. Firstly we prove Faber-Krahn-type inequalities, and Cheng-type eigenvalue comparison theorems on manifolds. Secondly, we prove a comparison theorem for eigenvalues with inner Dirichlet and outer Neumann boundary in minim…

Study on eigenvalues of complex Hessian operator on pseudoconvex manifolds.

Study on second Robin eigenvalue for Laplacian on manifolds.

Paper finds principal eigenvalue for infinity Laplacian in metric spaces.

Estimates for eigenvalues on Riemannian manifolds using classical inequalities.

Lower bounds for eigenvalues on Bakry-Emery manifolds proven.

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization. We propose a tensor block model, develop a unified least-square estimation, and obtain the t…

Study proves inequalities for eigenvalues of fourth-order elliptic operators on Riemannian manifolds.

In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.