Aspherical Word Labeled Oriented Graphs and Cyclically Presented Groups

A {\em word labeled oriented graph} (WLOG) is an oriented graph $\cal G$ on vertices $X=\{ x_1,\ldots ,x_k\}$, where each oriented edge is labeled by a word in $X^{\pm1}$. WLOGs give rise to presentations which generalize Wirtinger presentations of knots. WLOG presentations, where the underlying graph is a tree are of central importance in view of Whitehead's Asphericity Conjecture. We present a class of aspherical world labeled oriented graphs. This class can be used to produce highly non-injective aspherical labeled oriented trees and also aspherical cyclically presented groups.Comment: 7 pages, 3 figure

State Aid in the Enlarged European Union. An Overview

In the early phase of transition that started with the 1990s, Central and Eastern European Countries pursued economic restructuring of the enterprise sector that involved massive injections of state support. Also foreign investment from the West and facilitation of the development of a market economy involved massive injections of state support. With their accession to the European Union (EU), levels and forms of state aid came under critical review by the European Commission. This inquiry investigates whether the integration of the new member states operates on a level playing field with respect to state aid. Quantitative and qualitative analysis is relied upon to answer this key, as well as other, related questions. Findings suggest that in recent years a level playing field across the EU has indeed emerged. State aid in the new EU member countries is rather handled more strictly than laxer compared to the ‘old’ EU countries.competition policy, economic transition, EU enlargement, state aid

Outgassing, Temperature Gradients and the Radiometer Effect in LISA: A Torsion Pendulum Investigation

Thermal modeling of the LISA gravitational reference sensor (GRS) includes such effects as outgassing from the proof mass and its housing and the radiometer effect. Experimental data in conditions emulating the LISA GRS are required to confidently predict the GRS performance. Outgassing and the radiometer effect are similar in characteristics and are difficult to decouple experimentally. The design of our torsion balance allows us to investigate differential radiation pressure, the radiometer effect, and outgassing on closely separated conducting surfaces with high sensitivity. A thermally controlled split copper plate is brought near a freely hanging plate-torsion pendulum.We have varied the temperature on each half of the copper plate and have measured the resulting forces on the pendulum. We have determined that to first order the current GRS model for the radiometer effect, outgassing, and radiation pressure are mostly consistent with our torsion balance measurements and therefore these thermal effects do not appear to be a large hindrance to the LISA noise budget. However, there remain discrepancies between the predicted dependence of these effects on the temperature of our apparatus.Comment: 6th International LISA Symposiu

Dissipative Bose-Einstein condensation in contact with a thermal reservoir

We investigate the real-time dynamics of open quantum spin-$1/2$ or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work [Phys. Rev. A 93, 021602 (2016)] we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-$1/2$ particles into a totally symmetric superposition state, corresponding to a Bose-Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations. We establish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles $N$, we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit $N\rightarrow \infty$, the coupling to the thermal bath destroys any long-range order.Comment: 30 pages, 8 figures; Revised version: Minor changes and references adde

Dialects, Cultural Identity, and Economic Exchange

We investigate whether time-persistent cultural borders impede economic exchange across regions of the same country. To measure cultural differences we evaluate, for the first time in economics, linguistic micro-data about phonological and grammatical features of German dialects. These data are taken from a unique linguistic survey conducted between 1879 and 1888 in 45,000 schools. Matching this information to 439 current German regions, we construct a dialect similarity matrix. Using a gravity analysis, we show that current cross-regional migration is positively affected by historical dialect similarity. This suggests that cultural identities formed in the past still influence economic exchange today.gravity, internal migration, culture, language, dialects, Germany