arXiv research

The paper extends decay estimates to graphs with positive spectrum.

We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local $X$-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …

Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.

Paper bounds the lowest spectrum of manifolds with curvature constraints.

Sharp spectral estimates for negatively curved foliations.

Study shows discrete spectra on base spaces for certain Riemannian submersions.

This work improves density estimation by characterizing pdf complexity using NL-spectrum.

Estimates area and spectrum of stable minimal surfaces in Euclidean and hyperbolic spaces.

Study estimates hypersurface areas in curved spaces, with applications to spectrum bounds.

Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.

Sharp gradient estimate for harmonic functions on Kähler manifolds.

Paper sharpens inequality linking curvature and spectrum on manifolds.

We obtain upper estimates for the bottom (that is, greatest lower bound) of the essential spectrum of weighted Laplacian operator of a weighted manifold under assumptions of the volume growth of their geodesic balls and spheres. Furthermore, we find examples where the equality occurs in the estimates obtained. As a con…

In all dimensions, we prove that the marked length spectrum of a Riemannian manifold $(M,g)$ with Anosov geodesic flow and non-positive curvature locally determines the metric in the sense that two close enough metrics with the same marked length spectrum are isometric. In addition, we provide a completely new stabilit…

Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to analyze a particular case of the correlations in financial series and to show that…

Researchers improve spectrum reconstruction formula with proof.

New invariant extends curvature estimates to noncompact manifolds.

Study on spectral properties of Riemannian submersions with special fibers.

We consider a complete noncompact smooth Riemannian manifold $M$ with a weighted measure and the associated drifting Laplacian. We demonstrate that whenever the $q$-Bakry-Émery Ricci tensor on $M$ is bounded below, then we can obtain an upper bound estimate for the heat kernel of the drifting Laplacian from the upper b…

Study on Kohn Laplacian spectrum on sphere quotients.

In this paper, we study the spectral problem on a compact Finsler manifold with or without boundary. More precisely, given a certain collection of sets in Sobolev space $H^{1,2}(M)$ and a dimension-like function, we can define a corresponding spectrum. Such a spectrum satisfies nice properties. In particular, the eigen…

This paper concerns the $L^2$ essential spectrum of the Laplacian $Δ$ and the drift Laplacian $Δ_f$ on complete Riemannian manifolds endowed with a weighted measure $e^{-f}d\;vol_g$. We prove that the essential spectrum of the drift Laplacian $Δ_f$ is $[0,+\infty)$ provided the Bakry-Émery curvature tensor $Ric_f$ is …

In this paper, we study the spectrums of faithful dimension pairs on a closed Finsler manifold and obtain a Gromov type and a Buser type lower bounds for eigenvalues. Furthermore, for the Lusternik-Schnirelmann spectrum, we not only obtain a better lower bound, but also estimate the multiplicity of each eigenvalue.

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O'Neill tensor and the first eigenvalue of the Dirac op…

New stability estimate for metric rigidity in hyperbolic dynamics.

Researchers refine local rigidity for marked length spectrum and introduce a new pressure metric.

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an a…

Liquid chromatography coupled with tandem mass spectrometry, also known as shotgun proteomics, is a widely-used high-throughput technology for identifying proteins in complex biological samples. Analysis of the tens of thousands of fragmentation spectra produced by a typical shotgun proteomics experiment begins by assi…

We establish an upper estimate for the small eigenvalues of the twisted Dirac operator on Kahler submanifolds in Kahler manifolds carrying Kahlerian Killing spinors. We then compute the spectrum of the twisted Dirac operator of the canonical embedding \CP^d \rightarrow \CP^n in order to test the sharpness of the upper …

Closed hyperbolic manifolds and manifolds with nonpositive sectional curvature are geometrically rigid under certain curvature conditions.

A neural network improves DOA estimation from a single snapshot.

Algorithm optimizes spectrum access for dynamic multi-user environments.

Study on multiplicities in length spectrum of Salem numbers.

A neural network learns to estimate spectra from few noisy samples.

In this paper, we prove that Euclidean hypersurfaces with almost extremal extrinsic radius or $λ_1$ have a spectrum that asymptotically contains the spectrum of the extremal sphere in the Reilly or Hasanis-Koutroufiotis Inequalities. We also consider almost extremal hypersurfaces which satisfy a supplementary bound on …

Paper excludes the lowest energy level as an accumulation point for harmonic maps into analytic manifolds.

The article studies eigenvalues and spectrum of magnetic Dirac operators.

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the total space is discrete if and only if the base is di…

Paper proves ellipticity of certain Reeb orbits and estimates ECH spectrum on lens spaces.

Study improves Hayashi-Yoshida estimator for high-dimensional stock covolatility.

Estimates the first eigenvalue of a Laplacian on self-shrinkers in Ricci shrinkers.

Study the Bochner-Schrödinger operator on symplectic manifolds, proving gap existence and asymptotic kernel behavior.

Study on variance estimation for dynamic regression with finite sample guarantees.

We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.

We consider the Dirac operator on compact quaternionic Kaehler manifolds and prove a lower bound for the spectrum. This estimate is sharp since it is the first eigenvalue of the Dirac operator on the quaternionic projective space.

A new debiasing method for high-dimensional regression with applications to PCR.

The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically slowly. The key general properties of the covariance matrices are the following…

Proposes a new sparse spectrum method for Bayesian optimization.