We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2+ε moments outside the sphere of radius O( √ k). In the specific case...

This study presents the impact of carbon nanotubes (CNTs) on mitochondrial oxygen mass flux (Jm) under three experimental conditions. New experimental results and a new methodology are reported for the first time and they are based on CNT Raman spectra star graph transform (spectral moments) and perturbation theory. The experimental measures of Jm showed that no tested CNT family can inhibit th...

A formulation of the Green’s function method is presented in the n-pole approximation. Without referring to a specific model we give a general scheme of calculations that easily permits the computation of the “single-particle” Green’s function in terms of the energy matrix. A theorem is proved which states that the moments of the spectral density function are conserved up to the order 2(n−l+1),...

We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices : any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large N and fixed p the spectrum contains a large eigenvalue at Np and a semi-circle of “small” eigen...

In the pursuit of portable, efficient and effective sleep staging systems, researchers have been testing a massive number of combinations of EEG features and classifiers. State of the art sleep classification ensembles achieve accuracy in the order of 90%. However, there is presently no consensus regarding the best set of features for identifying sleep stages with a single EEG channel, leading ...

|Vub| is notoriously hard to measure model-independently. The first extraction of |Vub| from experimental data relied on a study of the lepton energy spectrum in inclusive charmless semileptonic B decay [ 1], a region in which (as will be discussed) the rate is highly model-dependent. |Vub| has also been measured from exclusive semileptonic B → ρlν̄ and B → πlν̄ decay [ 2]. These exclusive determ...

The radar Doppler spectrum contains a wealth of information on cloud microphysical properties. Typically, radar-based cloud retrievals use only the zeroth or first moments of the Doppler spectrum – reflectivity and mean Doppler velocity – to derive quantities such as cloud water content and particle characteristic size (e.g., Liou and Sassen 1994; Matrosov et al. 2002). When using only the mome...

Quantum effects in the teraherz dynamics of supercritical 4He have been studied as a function of both density rho and temperature T; they have been characterized through their effects on the second and third spectral moments of the dynamic structure factor S(Q, omega), measured by the inelastic x-ray scattering (IXS) technique. The IXS spectra were collected in the low-Q region below and around...