In this paper we investigate power allocation and crosstalk cancellation for MIMO-DSL (a.k.a. bonded-DSL) systems. Exploiting a property of the DSL channel, namely columnwise diagonal dominance, allows us to simplify the power allocation and crosstalk cancellation problems. This leads to a significant reduction in initialisation and run-time complexity whilst maintaining near-optimal performanc...

We study the covariance of the cross-power spectrum of different tracers for the largescale structure. We develop the counts-in-cells framework for the multi-tracer approach, and use this to derive expressions for the full non-Gaussian covariance matrix. We show, that for the usual auto-power statistic, besides the off-diagonal covariance generated through gravitational mode-coupling, the discr...

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...

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...

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...

The jam phases in a two-dimensional cellular automata model of traffic flow are investigated by computer simulations. Two different types of the jam phases are found. The spatially diagonal long-range correlation obeys the power law at the low-density jam configurations. The diagonal correlation exponentially decays at the high-density jam. The exponent of the short-range correlation in the dia...