Testing for Measurement Equivalence in Surveys: Dimensions of Social Trust across Cultural Contexts

Our study evaluates the dimensionality and equivalence of social trust across cultural contexts, using new data from Switzerland and the World Values Survey 2005–2008. Whereas some scholars assert that trust should be regarded as a coherent concept, others claim that trust is better conceived of as a multidimensional concept. In contrast to the conventional dichotomy of the forms of social trust, we identify three distinct forms of trust, namely, particularized, generalized, and identity-based trust. Moreover, we dispute the view that respondents understand the wording of survey questions regarding social trust differently between different cultural contexts, which would imply that comparative research on trust is a pointless endeavor. Applying multiple-group confirmatory factor analysis to the various constructs of social trust, we conclude that one may study relationships among the three forms of trust and other theoretical constructs as well as compare latent means across cultural contexts. Our analyses therefore provide an optimistic outlook for future comparative analyses that investigate forms of social trust across cultural contexts.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Computed Ultrasound Tomography in Echo Mode for Imaging Speed of Sound Using Pulse-Echo Sonography: Proof of Principle

The limitations of diagnostic echo ultrasound have motivated research into novel modalities that complement ultrasound in a multimodal device. One promising candidate is speed of sound imaging, which has been found to reveal structural changes in diseased tissue. Transmission ultrasound tomography shows speed of sound spatially resolved, but is limited to the acoustically transparent breast. We present a novel method by which speed-of-sound imaging is possible using classic pulse-echo equipment, facilitating new clinical applications and the combination with state-of-the art diagnostic ultrasound. Pulse-echo images are reconstructed while scanning the tissue under various angles using transmit beam steering. Differences in average sound speed along different transmit directions are reflected in the local echo phase, which allows a 2-D reconstruction of the sound speed. In the present proof-of-principle study, we describe a contrast resolution of 0.6% of average sound speed and a spatial resolution of 1 mm (laterally) × 3 mm (axially), suitable for diagnostic applications.

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

A note on the stable equivalence problem

We provide counterexamples to the stable equivalence problem in every dimension d ≥ 2. That means that we construct hypersurfaces H₁ , H₂ ⊂ C d+1 whose cylinders H₁ × C and H₂ × C are equivalent hypersurfaces in C d+2 , although H₁ and H₂ themselves are not equivalent by an automorphism of C d+1 . We also give, for every d ≥ 2, examples of two non-isomorphic algebraic varieties of dimension d which are biholomorphic.

The Principle of Common Concern and Climate Change

Effective policies combating global warming and incentivising reduction of greenhouse gases face fundamental collective action problems. States defending short term interests avoid international commitments and seek to benefit from measures combating global warming taken elsewhere. The paper explores the potential of Common Concern as an emerging principle of international law, in particular international environmental law, in addressing collective action problems and the global commons. It expounds the contours of the principle, its relationship to common heritage of mankind, to shared and differentiated responsibility and to public goods. It explores its potential to provide the foundations not only for international cooperation, but also to justify, and delimitate at the same time, unilateral action at home and deploying extraterritorial effects in addressing the challenges of global warming and climate change mitigation. As unilateral measures mainly translate into measures of trade policy, the principle of Common Concern is inherently linked and limited by existing legal disciplines in particular of the law of the World Trade Organization.

Higher order elicitability and Osband’s principle

A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for multi-dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions. We cover the case of functionals with elicitable components, but we also show that one-dimensional functionals that are not elicitable can be a component of a higher order elicitable functional. In the case of the variance, this is a known result. However, an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the “correct” quantiles. A direct consequence of applied interest is that the pair (Value at Risk, Expected Shortfall) is jointly elicitable under mild conditions that are usually fulfilled in risk management applications.