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.

Derivation and validation of multimarker prognostication for normotensive patients with acute symptomatic pulmonary embolism.

RATIONALE Not all patients with acute pulmonary embolism (PE) have a high risk of an adverse short-term outcome. OBJECTIVES This prospective cohort study aimed to develop a multimarker prognostic model that accurately classifies normotensive patients with PE into low and high categories of risk of adverse medical outcomes. METHODS The study enrolled 848 outpatients from the PROTECT (PROgnosTic valuE of Computed Tomography) study (derivation cohort) and 529 patients from the Prognostic Factors for Pulmonary Embolism (PREP) study (validation cohort). Investigators assessed study participants for a 30-day complicated course, defined as death from any cause, hemodynamic collapse, and/or adjudicated recurrent PE. MEASUREMENTS AND MAIN RESULTS A complicated course occurred in 63 (7.4%) of the 848 normotensive patients with acute symptomatic PE in the derivation cohort and in 24 patients (4.5%) in the validation cohort. The final model included the simplified Pulmonary Embolism Severity Index, cardiac troponin I, brain natriuretic peptide, and lower limb ultrasound testing. The model performed similarly in the derivation (c-index of 0.75) and validation (c-index of 0.85) cohorts. The combination of the simplified Pulmonary Embolism Severity Index and brain natriuretic peptide testing showed a negative predictive value for a complicated course of 99.1 and 100% in the derivation and validation cohorts, respectively. The combination of all modalities had a positive predictive value for the prediction of a complicated course of 25.8% in the derivation cohort and 21.2% in the validation cohort. CONCLUSIONS For normotensive patients who have acute PE, we derived and validated a multimarker model that predicts all-cause mortality, hemodynamic collapse, and/or recurrent PE within the following 30 days.

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.

Testing the Weak Equivalence Principle with an antimatter beam at CERN

The goal of the AEgIS experiment is to measure the gravitational acceleration of antihydrogen – the simplest atom consisting entirely of antimatter – with the ultimate precision of 1%. We plan to verify the Weak Equivalence Principle (WEP), one of the fundamental laws of nature, with an antimatter beam. The experiment consists of a positron accumulator, an antiproton trap and a Stark accelerator in a solenoidal magnetic field to form and accelerate a pulsed beam of antihydrogen atoms towards a free-fall detector. The antihydrogen beam passes through a moir ́e deflectometer to measure the vertical displacement due to the gravitational force. A position and time sensitive hybrid detector registers the annihilation points of the antihydrogen atoms and their time-of-flight. The detection principle has been successfully tested with antiprotons and a miniature moir ́e deflectometer coupled to a nuclear emulsion detector.

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.

The Principle of Proportionality in International Law

Whilst the principle of proportionality indisputably plays a crucial role in the protection of fundamental rights, it is still unclear to what extent it applies to other fields in international law. The paper therefore explores the role it plays in selected fields of public international law, beyond human rights. The examination begins in the classical domain of reprisals and in maritime boundary delimitation and continues to analyse the role played in the law of multilateral trade regulation of the World Trade Organization and in bilateral investment protection. In an attempt to explain differences in recourse to proportionality in the various fields, we develop in our conclusions a distinction between horizontal and vertical constellations of legal protection.