hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

A Global Trend towards Democratic Convergence? A Lijphartian Analysis of Advanced Democracies.

The article offers a systematic analysis of the comparative trajectory of international democratic change. In particular, it focuses on the resulting convergence or divergence of political systems, borrowing from the literatures on institutional change and policy convergence. To this end, political-institutional data in line with Arend Lijphart’s (1999, 2012) empirical theory of democracy for 24 developed democracies between 1945 and 2010 are analyzed. Heteroscedastic multilevel models allow for directly modeling the development of the variance of types of democracy over time, revealing information about convergence, and adding substantial explanations. The findings indicate that there has been a trend away from extreme types of democracy in single cases, but no unconditional trend of convergence can be observed. However, there are conditional processes of convergence. In particular, economic globalization and the domestic veto structure interactively influence democratic convergence.

Balancing the mind: vestibular induced facilitation of egocentric mental transformations

The body schema is a key component in accomplishing egocentric mental transformations, which rely on bodily reference frames. These reference frames are based on a plurality of different cognitive and sensory cues among which the vestibular system plays a prominent role. We investigated whether a bottom-up influence of vestibular stimulation modulates the ability to perform egocentric mental transformations. Participants were significantly faster to make correct spatial judgments during vestibular stimulation as compared to sham stimulation. Interestingly, no such effects were found for mental transformation of hand stimuli or during mental transformations of letters, thus showing a selective influence of vestibular stimulation on the rotation of whole-body reference frames. Furthermore, we found an interaction with the angle of rotation and vestibular stimulation demonstrating an increase in facilitation during mental body rotations in a direction congruent with rightward vestibular afferents. We propose that facilitation reflects a convergence in shared brain areas that process bottom-up vestibular signals and top-down imagined whole-body rotations, including the precuneus and tempero-parietal junction. Ultimately, our results show that vestibular information can influence higher-order cognitive processes, such as the body schema and mental imagery.

Remarks on the convergence of pseudospectra

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant resolvent norm on an open set. We extend the class of operators for which it is known that the latter cannot happen by showing that if the resolvent norm is constant on an open set, then this constant is the global minimum. We present a number of examples exhibiting various resolvent norm behaviours and illustrating the applicability of this characterisation compared to known results.

Towards Faster Method Search Through Static Ecosystem Analysis

Software developers are often unsure of the exact name of the method they need to use to invoke the desired behavior in a given context. This results in a process of searching for the correct method name in documentation, which can be lengthy and distracting to the developer. We can decrease the method search time by enhancing the documentation of a class with the most frequently used methods. Usage frequency data for methods is gathered by analyzing other projects from the same ecosystem - written in the same language and sharing dependencies. We implemented a proof of concept of the approach for Pharo Smalltalk and Java. In Pharo Smalltalk, methods are commonly searched for using a code browser tool called "Nautilus", and in Java using a web browser displaying HTML based documentation - Javadoc. We developed plugins for both browsers and gathered method usage data from open source projects, in order to increase developer productivity by reducing method search time. A small initial evaluation has been conducted showing promising results in improving developer productivity.

Disparate Wages in a Globalized World

This study uses wage data from the UBS Prices and Earnings survey to highlight Disparate Wages in a Globalized World from di↵erent perspectives. This wage data is characterised by remarkable consistency over the last 40 years, as well as unusual global comparability. In the first chapter we analyse the convergence hypothesis for purchasing power adjusted wages across the world for 1970 to 2009. The results provide solid evidence for the hypotheses of absolute and conditional convergence in real wages, with the key driver being faster overall growing wage levels in lower wage countries compared to higher wage countries. At the same time, the highest skilled professions have experienced the highest wage growth, while low skilled workers’ wages have lagged, thus no convergence in this sense is found between skill groups. In the second chapter we examine deviations in international wages from Factor Price Equalisation theory (FPE). Following an approach analogous to Engel (1993) we find that deviations from FPE are more likely driven by the higher variability of wages between countries than by the variability of di↵erent wages within countries. With regard to the traditional analysis of the real exchange rate and the Balassa-Samuelson assumptions our analysis points to a larger impact on the real exchange rate likely stemming from the movements in the real exchange rate of tradables, and only to a lesser extent from the lack of equalisation of wages within countries. In the third chapter our results show that India’s economic and trade liberalisation, starting in the early 1990s, had very di↵erential impacts on skill premia, both over time and over skill levels. The most striking result is the large increase in wage inequality of high-skilled versus low-skilled professions. Both the synthetic control group method and the di↵erence-in-di↵erences (DID) approach suggest that a significant part of this increase in wage inequality can be attributed to India’s liberalisation.

New perioperative fluid and pharmacologic management protocol results in reduced blood loss, faster return of bowel function, and overall recovery.

Cystectomy and urinary diversion have high morbidity, and strategies to reduce complications are of utmost importance. Epidural analgesia and optimized fluid management are considered key factors contributing to successful enhanced recovery after surgery. In colorectal surgery, there is strong evidence that an intraoperative fluid management aiming for a postoperative zero fluid balance results in lower morbidity including a faster return of bowel function. Recently, a randomized clinical trial focusing on radical cystectomy demonstrated that a restrictive intraoperative hydration combined with a concomitant administration of norepinephrine reduced intraoperative blood loss, the need for blood transfusion and morbidity. The purpose of this review is to highlight specific anesthesiological aspects which have been shown to improve outcome after RC with urinary diversion.

Quick divergence but slow convergence during ecotype formation in lake and stream stickleback pairs of variable age

When genetic constraints restrict phenotypic evolution, diversification can be predicted to evolve along so-called lines of least resistance. To address the importance of such constraints and their resolution, studies of parallel phenotypic divergence that differ in their age are valuable. Here, we investigate the parapatric evolution of six lake and stream threespine stickleback systems from Iceland and Switzerland, ranging in age from a few decades to several millennia. Using phenotypic data, we test for parallelism in ecotypic divergence between parapatric lake and stream populations and compare the observed patterns to an ancestral-like marine population. We find strong and consistent phenotypic divergence, both among lake and stream populations and between our freshwater populations and the marine population. Interestingly, ecotypic divergence in low-dimensional phenotype space (i.e. single traits) is rapid and seems to be often completed within 100 years. Yet, the dimensionality of ecotypic divergence was highest in our oldest systems and only there parallel evolution of unrelated ecotypes was strong enough to overwrite phylogenetic contingency. Moreover, the dimensionality of divergence in different systems varies between trait complexes, suggesting different constraints and evolutionary pathways to their resolution among freshwater systems.

Topology of the ambient boundary and the convergence of causal curves

We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric topology but with the Zeeman fine topology. This then places severe constraints to the convergence of a sequence of causal curves and the extraction of a limit curve, and also to our ability to formulate conditions for singularity formation.