Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

Efficient Evaluation of Multidimensional Time-Varying Density Forecasts

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.

Genetic Algorithm Search for Predictive Patterns in Multidimensional Time Series

Based on an algorithm for pattern matching in character strings, we implement a pattern matching machine that searches for occurrences of patterns in multidimensional time series. Before the search process takes place, time series are encoded in user-designed alphabets. The patterns, on the other hand, are formulated as regular expressions that are composed of letters from these alphabets and operators. Furthermore, we develop a genetic algorithm to breed patterns that maximize a user-defined fitness function. In an application to financial data, we show that patterns bred to predict high exchange rates volatility in training samples retain statistically significant predictive power in validation samples.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.

Is Human Development Multidimensional?

Stiglitz's Commission on the Measurement of Economic Performance and Social Progress (CMEPSP) argued that well-being is multidimensional and identified eight distinct dimensions. Conventional linear techniques confirm that a large number of dimensions are needed to describe development. In contrast, a new non-linear technique that we introduce from chaos theory shows that a smaller number of dimensions are needed to span the development space. From the analysis, variables representing the Health, Education, Inequality and Individual Rights areas of life quality would provide a broad picture of development, whereas income per capita adds little extra information.

Multidimensional rehabilitation programmes for adult cancer survivors

This is the protocol for a review and there is no abstract. The objectives are as follows:

To assess the effectiveness of multidimensional rehabilitation programs in terms of maintaining or improving the physical and psychosocial well-being of adult cancer survivors.

The review will evaluate the extent to which:

Professionally led multidimensional rehabilitation programs achieve better outcomes than standard services for patients with cancer and their caregivers
Rehabilitation programmes exert a different impact on different domains (e.g. psychological health, physical functioning)
Different modes of delivery and different settings influence outcomes
There is relationship between the number, duration and intensity of rehabilitation sessions and degree of change in measured outcomes.

Economic vulnerability, multidimensional deprivation and social cohesion in an enlarged European community

In this article we have sought to combine regional and social exclusion perspectives on economic exclusion in the enlarged European Community. Our analysis, based on the European Quality of Life Survey, confirms that while the economically vulnerable, identified through latent class analysis, constitute substantially larger groups in the poorer economic clusters, they are much more sharply differentiated from others in the richer clusters. While the economically vulnerable are also disadvantaged in relation to measures of multidimensional deprivation and social cohesion, between economic clusters differences on these dimensions cannot be accounted for by corresponding variations in levels and intensity of economic vulnerability. In fact, the impact of such vulnerability on social cohesion is greater in the more affluent clusters. Copyright © 2005 SAGE Publications.

Multidimensional modelling of X-ray spectra for AGN accretion disc outflows - III. Application to a hydrodynamical simulation

We perform multidimensional radiative transfer simulations to compute spectra for a hydrodynamical simulation of a line-driven accretion disc wind from an active galactic nucleus. The synthetic spectra confirm expectations from parametrized models that a disc wind can imprint a wide variety of spectroscopic signatures including narrow absorption lines, broad emission lines and a Compton hump. The formation of these features is complex with contributions originating from many of the different structures present in the hydrodynamical simulation. In particular, spectral features are shaped both by gas in a successfully launched outflow and in complex flows where material is lifted out of the disc plane but ultimately falls back. We also confirm that the strong Fe Ka line can develop a weak, red-skewed line wing as a result of Compton scattering in the outflow. In addition, we demonstrate that X-ray radiation scattered and reprocessed in the flow has a pivotal part in both the spectrum formation and determining the ionization conditions in the wind. We find that scattered radiation is rather effective in ionizing gas which is shielded from direct irradiation from the central source. This effect likely makes the successful launching of a massive disc wind somewhat more challenging and should be considered in future wind simulations. © 2010 The Authors. Journal compilation © 2010 RAS.

Multidimensional modelling of X-ray spectra for AGN accretion disc outflows

We use a multidimensional Monte Carlo code to compute X-ray spectra for a variety of active galactic nucleus (AGN) disc-wind outflow geometries. We focus on the formation of blueshifted absorption features in the Fe K band and show that line features similar to those which have been reported in observations are often produced for lines of sight through disc-wind geometries. We also discuss the formation of other spectral features in highly ionized outflows. In particular, we show that, for sufficiently high wind densities, moderately strong Fe K emission lines can form and that electron scattering in the flow may cause these lines to develop extended red wings. We illustrate the potential relevance of such models to the interpretation of real X-ray data by comparison with observations of a well-known AGN, Mrk 766. Journal compilation © 2008 RAS.

Multidimensional simulations of radiative transfer in Type Ia supernovae

A three-dimensional Monte Carlo code for modelling radiation transport in Type Ia supernovae is described. In addition to tracking Monte Carlo quanta to follow the emission, scattering and deposition of radiative energy, a scheme involving volume-based Monte Carlo estimators is used to allow properties of the emergent radiation field to be extracted for specific viewing angles in a multidimensional structure. This eliminates the need to compute spectra or light curves by angular binning of emergent quanta. The code is applied to two test problems to illustrate consequences of multidimensional structure on the modelling of light curves. First, elliptical models are used to quantify how large-scale asphericity can introduce angular dependence to light curves. Secondly, a model which incorporates complex structural inhomogeneity, as predicted by modern explosion models, is used to investigate how such structure may affect light-curve properties. © 2006 RAS.