Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

How do multilateral institutions influence individual perceptions of international affairs? Evidence from Europe and Asia

To date there has been no systematic study of the relationship between individuals’ opinions of different institutions and their perceptions of world affairs. This article tries to fill this gap by using a large cross-country data set comprising nine EU members and seven Asian nations and instrumental variable bivariate probit regression analysis. Controlling for a host of factors, the article shows that individuals’ confidence in multilateral institutions affects their perceptions of whether or not their country is being treated fairly in international affairs. This finding expands upon both theoretical work on multilateral institutions that has focused on state actors’ rationale for engaging in multilateral cooperation and empirical work that has treated confidence in multilateral institutions as a dependent variable. The article also shows that individuals’ confidence in different international organizations has undifferentiated effects on their perceptions of whether or not their country is being treated fairly in international affairs, though individuals more knowledgeable about international affairs exhibit slightly different attitudes. Finally, the article demonstrates significant differences in opinion across Europe and Asia.

Plasma free fatty acids do not provide the link between obesity and insulin resistance or β-cell dysfunction: results of the Reading, Imperial, Surrey, Cambridge, Kings (RISCK) study

Aims To investigate the relationship between adiposity and plasma free fatty acid levels and the influence of total plasma free fatty acid level on insulin sensitivity and β-cell function. Methods An insulin sensitivity index, acute insulin response to glucose and a disposition index, derived from i.v. glucose tolerance minimal model analysis and total fasting plasma free fatty acid levels were available for 533 participants in the Reading, Imperial, Surrey, Cambridge, Kings study. Bivariate correlations were made between insulin sensitivity index, acute insulin response to glucose and disposition index and both adiposity measures (BMI, waist circumference and body fat mass) and total plasma free fatty acid levels. Multivariate linear regression analysis was performed, controlling for age, sex, ethnicity and adiposity. Results After adjustment, all adiposity measures were inversely associated with insulin sensitivity index (BMI: β = −0.357; waist circumference: β = −0.380; body fat mass: β = −0.375) and disposition index (BMI: β = −0.215; waist circumference: β = −0.248; body fat mass: β = −0.221) and positively associated with acute insulin response to glucose [BMI: β = 0.200; waist circumference: β = 0.195; body fat mass β = 0.209 (P values <0.001)]. Adiposity explained 13, 4 and 5% of the variation in insulin sensitivity index, acute insulin response to glucose and disposition index, respectively. After adjustment, no adiposity measure was associated with free fatty acid level, but total plasma free fatty acid level was inversely associated with insulin sensitivity index (β = −0.133), acute insulin response to glucose (β = −0.148) and disposition index [β = −0.218 (P values <0.01)]. Plasma free fatty acid concentration accounted for 1.5, 2 and 4% of the variation in insulin sensitivity index, acute insulin response to glucose and disposition index, respectively. Conclusions Plasma free fatty acid levels have a modest negative association with insulin sensitivity, β-cell secretion and disposition index but no association with adiposity measures. It is unlikely that plasma free fatty acids are the primary mediators of obesity-related insulin resistance or β-cell dysfunction.

Firms’ exporting and importing activities: is there a two-way relationship?

The literature on firm heterogeneity and trade has highlighted that most trading firms tend to engage in both importing and exporting activities. This paper provides some evidence that helps understanding to what extent this is the result of a two-way relationship. Using firm-level data for a group of 27 Eastern European and Central Asian countries from the World Bank Business Environment and Enterprise Performance Survey (BEEPS) over the period 2002–2008, we estimate a bivariate probit model of exporting and importing. After controlling for size (and other firm-level characteristics) we find that firms’ exporting activity does not increase the probability of importing, while the latter has a positive effect on foreign sales. This effect is mainly channeled through an increase in firm productivity and product innovation.

Communicating thematic data quality with web map services

Geospatial information of many kinds, from topographic maps to scientific data, is increasingly being made available through web mapping services. These allow georeferenced map images to be served from data stores and displayed in websites and geographic information systems, where they can be integrated with other geographic information. The Open Geospatial Consortium’s Web Map Service (WMS) standard has been widely adopted in diverse communities for sharing data in this way. However, current services typically provide little or no information about the quality or accuracy of the data they serve. In this paper we will describe the design and implementation of a new “quality-enabled” profile of WMS, which we call “WMS-Q”. This describes how information about data quality can be transmitted to the user through WMS. Such information can exist at many levels, from entire datasets to individual measurements, and includes the many different ways in which data uncertainty can be expressed. We also describe proposed extensions to the Symbology Encoding specification, which include provision for visualizing uncertainty in raster data in a number of different ways, including contours, shading and bivariate colour maps. We shall also describe new open-source implementations of the new specifications, which include both clients and servers.

An empirical model comparison for valuing crack spread options

In this paper, we investigate the pricing of crack spread options. Particular emphasis is placed on the question of whether univariate modeling of the crack spread or explicit modeling of the two underlyings is preferable. Therefore, we contrast a bivariate GARCH volatility model for cointegrated underlyings with the alternative of modeling the crack spread directly. Conducting an empirical analysis of crude oil/heating oil and crude oil/gasoline crack spread options traded on the New York Mercantile Exchange, the more simplistic univariate approach is found to be superior with respect to option pricing performance.