Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Testing for spatial autocorrelation: the regressors that make the power disappear

We show that for any sample size, any size of the test, and any weights matrix outside a small class of exceptions, there exists a positive measure set of regression spaces such that the power of the Cli-Ord test vanishes as the autocorrelation increases in a spatial error model. This result extends to the tests that dene the Gaussian power envelope of all invariant tests for residual spatial autocorrelation. In most cases, the regression spaces such that the problem occurs depend on the size of the test, but there also exist regression spaces such that the power vanishes regardless of the size. A characterization of such particularly hostile regression spaces is provided.

Cereal-based wholecrop silages: a potential conservation measure for farmland birds in pastoral landscapes

Declines of farmland birds have been pronounced in landscapes dominated by lowland livestock production and densities of seed-eating birds are particularly low in such areas. Modern livestock production often entails a simple cropping system dominated by ley grassland and maize grown for animal feed. These crops often lack invertebrate and seed resources for foraging birds and can be hostile nesting environments. Cereal-based wholecrop silages (CBWCS) offer potential benefits for farmland birds because they can be grown with minimal herbicide applications and can be spring-sown with following winter stubbles. We compared the biodiversity benefits and agronomic yields of winter-sown wheat and spring-sown barley as alternatives to grass and maize silage in intensive dairy livestock systems. Seed-eating birds foraged mainly in CBWCS fields during summer, and mainly on barley stubbles during winter and this reflected the higher densities of seed-bearing plants therein. Maize and grass fields lacked seed-bearing vegetation and were strongly avoided by most seed-eating birds. Production costs of CBWCS are similar to those of maize and lower than those of grass silage. Selective (rather than broad-spectrum) herbicide application on spring barley crops increased forb cover, reduced yields (by 11%) but caused only a small (<4%) increase in production costs. CBWCS grown with selective herbicide and with following winter stubbles offer a practical conservation measure for seed-eating farmland birds in landscapes dominated by intensively-managed grassland and maize. However, the relatively early harvesting of CBWCS could destroy a significant proportion of breeding attempts of late-nesting species like corn bunting (Emberiza calandra) or yellow wagtail (Motocilla flava). Where late-breeding species are likely to nest in CBWCS fields, harvesting should be delayed until most nesting attempts have been completed (e.g. until after 1st August in southern Britain). (C) 2010 Elsevier Ltd. All rights reserved.

Developing a brand performance measure for financial services brands

With no universal approach for measuring brand performance, we show how a consumer-based brand measure was developed for corporate financial services brands. Churchill's paradigm was adopted. A literature review and 20 depth interviews with experts suggested that brand loyalty, consumer satisfaction and reputation constitute the brand performance measure. Ten financial services organisations provided access to their consumers. Following a postal survey, 600 questionnaires were analysed through principal components analysis to identify the consumer-based measure. Further testing revealed this to be a valid and reliable brand performance measure.

The Huntington's Disease health-related Quality of Life questionnaire (HDQoL): a disease-specific measure of health-related quality of life

Hocaoglu MB, Gaffan EA, Ho AK. The Huntington's disease health-related quality of life questionnaire: a disease-specific measure of health-related quality of life. Huntington's disease (HD) is a genetic neurodegenerative disorder characterized by motor, cognitive and psychiatric disturbances, and yet there is no disease-specific patient-reported health-related quality of life outcome measure for patients. Our aim was to develop and validate such an instrument, i.e. the Huntington's Disease health-related Quality of Life questionnaire (HDQoL), to capture the true impact of living with this disease. Semi-structured interviews were conducted with the full spectrum of people living with HD, to form a pool of items, which were then examined in a larger sample prior to data-driven item reduction. We provide the statistical basis for the extraction of three different sets of scales from the HDQoL, and present validation and psychometric data on these scales using a sample of 152 participants living with HD. These new patient-derived scales provide promising patient-reported outcome measures for HD.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.

Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.

Spectrally invariant approximation within atmospheric radiative transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These ‘‘spectrally invariant relationships’’ are the consequence of wavelength independence of the extinction coefficient and scattering phase function in veg- etation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accu- rately describe the extinction and scattering properties of cloudy atmospheres. The validity of the as- sumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Can we measure terrestrial photosynthesis from space directly, using spectral reflectance and fluorescence?

Attempts to estimate photosynthetic rate or gross primary productivity from remotely sensed absorbed solar radiation depend on knowledge of the light use efficiency (LUE). Early models assumed LUE to be constant, but now most researchers try to adjust it for variations in temperature and moisture stress. However, more exact methods are now required. Hyperspectral remote sensing offers the possibility of sensing the changes in the xanthophyll cycle, which is closely coupled to photosynthesis. Several studies have shown that an index (the photochemical reflectance index) based on the reflectance at 531 nm is strongly correlated with the LUE over hours, days and months. A second hyperspectral approach relies on the remote detection of fluorescence, which is a directly related to the efficiency of photosynthesis. We discuss the state of the art of the two approaches. Both have been demonstrated to be effective, but we specify seven conditions required before the methods can become operational.

Validation of three new measure-correlate-predict models for the long-term prospection of the wind resource

The estimation of the long-term wind resource at a prospective site based on a relatively short on-site measurement campaign is an indispensable task in the development of a commercial wind farm. The typical industry approach is based on the measure-correlate-predict �MCP� method where a relational model between the site wind velocity data and the data obtained from a suitable reference site is built from concurrent records. In a subsequent step, a long-term prediction for the prospective site is obtained from a combination of the relational model and the historic reference data. In the present paper, a systematic study is presented where three new MCP models, together with two published reference models �a simple linear regression and the variance ratio method�, have been evaluated based on concurrent synthetic wind speed time series for two sites, simulating the prospective and the reference site. The synthetic method has the advantage of generating time series with the desired statistical properties, including Weibull scale and shape factors, required to evaluate the five methods under all plausible conditions. In this work, first a systematic discussion of the statistical fundamentals behind MCP methods is provided and three new models, one based on a nonlinear regression and two �termed kernel methods� derived from the use of conditional probability density functions, are proposed. All models are evaluated by using five metrics under a wide range of values of the correlation coefficient, the Weibull scale, and the Weibull shape factor. Only one of all models, a kernel method based on bivariate Weibull probability functions, is capable of accurately predicting all performance metrics studied.

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.