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.

Negative Aspects of Close Relationships as a Predictor of Increased Body Mass Index and Waist Circumference: The Whitehall II Study

Objectives. We investigated whether exposure to negative aspects of close relationships was associated with subsequent increase in body mass index (BMI) and waist circumference.
Methods. Data came from a prospective cohort study (Whitehall II) of 9425 civil servants aged 35 to 55 years at baseline (phase 1: 1985-1988). We assessed negative aspects of close relationships with the Close Persons Questionnaire (range 0-12) at phases 1 and 2 (1989-1990). We measured BMI and waist circumference at phases 3 (1991-1994) and 5 (1997-1999). Covariates at phase 1 included gender, age, marital status, ethnicity, BMI, employment grade, smoking, physical activity, fruit and vegetable consumption, and common mental disorder.
Results. After adjustment for sociodemographic characteristics and health behaviors, participants with higher exposure to negative aspects of close relationships had a higher likelihood of a 10% or greater increase in BMI and waist circumference (odds ratios per 1-unit increase 1.08 [95% confidence interval (CI)=1.02, 1.14; P=.007] and 1.09 [CI=1.04, 1.14; P <= .001], respectively) as well as a transition from the overweight (25 <= BMI <30) to the obese (BMI >= 30) category.
Conclusions. Adverse social relationships may contribute to weight gain.