We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Besides the technical advantages of the computational feasibility for data sets with large volume and complex geometry, the DWT scale-by-scale decomposition provides a physical insight into the covariance matrix of the cosmic mass field. Since the DWT repres...

We determine the asymptotic behaviour (as k →∞, up to multiplicative constants not depending on k) of the entropy numbers ek (Dσ : lp → lq), 1 ≤ p ≤ q ≤ ∞, of diagonal operators generated by logarithmically decreasing sequences σ = (σn). This complements earlier results by Carl [2] who investigated the case of power-like decay of the diagonal. 2000 Mathematics Subject Classification: 47B06, 46B...

The easiest matrices to compute with are the diagonal ones. The sum and product of diagonal matrices can be computed componentwise along the main diagonal, and taking powers of a diagonal matrix is simple too. All the complications of matrix operations are gone when working only with diagonal matrices. If a matrix A is not diagonal but can be conjugated to a diagonal matrix, say D := PAP−1 is d...

In this paper a framework for the analysis of a family of high order interpolative sigma-delta modulators is introduced. It is shown that a large number of high order architectures can be reduced to a diagonal form which facilitates the stability analysis of the system. In addition, the diagonal form is a canonical form which illustrates the equivalence of a variety of sigma-delta architectures...

The Capon-MVDR (Minimum Variance Distortionless Response) method of frequency-wavenumber spectral estimation requires an invertible spatial covariance estimate. Increasingly, however, one must deal with a singular covariance matrix. The ubiquity of inexpensive sensors implies that the dimension of the covariance matrix is ever-increasing, but coherence times have not changed, so the number of v...

This paper aims to show the power and versatility of exponential models by focusing on exponential model representations of Gaussian Mixture Models (GMMs). In a recent series of papers by several authors, GMMs of varying structure and complexity have been considered. These GMMs can all be readily represented as exponential models and oftentimes favorably so. This paper shows how the exponential...

In addition to the double-dimensional reduction procedure that employs world-volume Killing symmetries of p-brane supergravity solutions and acts diagonally on a plot of p versus spacetime dimension D, there exists a second procedure of “vertical” reduction. This reduces the transverse-space dimension via an integral that superposes solutions to the underlying Laplace equation. We show that ver...

On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form. Abstract In this paper, we will compare the convergence properties of three basic reduction methods, by placing them in a general framework. It covers the reduction to tridiagonal, semiseparable and semiseparable plus diagonal form. These reductions are often used as...

How can one justify the secession of a territory from a liberal-democratic state of the kind currently prevalent in North America and Western Europe? The question does not primarily concern a mutually agreed secession, such as that of Norway from the United Kingdoms of Norway and Sweden in 1905. If the government and legislature of the ‘parent state’ freely agree to a secession of a part of its...