Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems

We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in $L_2$ for small complex $L_\infty$ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator. We establish quadratic estimates for this Dirac operator, which implies that the associated Hardy projection operators are bounded and depend continuously on the coefficient matrix. We also prove that certain transmission problems for $k$-forms are well posed for small perturbations of block matrices.Comment: Some changes made in the introduction of the pape

Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments

In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.Comment: 57th IEEE Conference on Decision and Control 201

No longer gatekeeper: Why the European Commission provides access to justice for civil society organisations

Introduction: One of the characteristic features of European Union law is its emphasis on rights. Over time, the EU has steadily evolved to become a distinctly rights-based polity. The origin of this development was the founding members’ focus on the four ‘market freedoms’, which were interpreted as fundamental rights: a right to free movement of goods, persons, services and capital. More recently, additional rights have been particularly pronounced in the area of non-discrimination. The foundational principle, the prohibition of discrimination based on nationality (now art. 18 TFEU), was first extended to equality between men and women, and later to all discrimination based on sex, race, colour, ethnic or social origin, genetic features, language, religion or belief, political or any other opinion, membership of a national minority, property, birth, disability, age or sexual orientation racial or ethnic origin, religion or belief, disability, age or sexual orientation (art. 21 of the Charter of Fundamental Rights). Other rights have been formulated in areas like environmental or consumer protection. Increasingly, measures pertaining to social policy have been incorporated in this “rights revolution” (Mabbett 2011). ! 1 By virtue of its superiority and direct effect, EU law now vests its subjects with a wide array of rights that are directly enforceable – individual citizens can use EU law against their own national authorities. That rights are enforceable does of course not mean that they are self-enforcing. Rights have to be activated – claimed – in face of alleged infringements, and their nature is frequently in dispute. The EU provides a comprehensive system for rights vindication and dispute resolution, based on its own judicial bodies and the judicial systems of the member states. This enforcement mechanism has frequently been identified as the major source of the expansion of EU rights: private litigants claim rights derived from EU law against their national authorities before national courts who refer such questions to the Court of Justice of the European Union (CJEU). The CJEU, in turn, has again and again signaled its openness to such rights claims, interpreted EU statutes broadly and developed novel rights even were they had not been specifically mentioned in the legal texts

Macroeconomic fluctuations and bank lending: evidence for Germany and the euro area

This paper analyzes how bank lending to the private nonbank sector responds dynamically to aggregate supply, demand and monetary policy shocks in Germany and the euro area. The results suggest that the dynamic responses in the two areas are broadly similar, although there are some differences in the relative contribution of the three shocks to the development of output, prices, interest rates and bank loans over time. In order to assess the role of bank lending in the transmission of macroeconomic shocks, we perform counterfactual simulations and analyze the dynamic responses of German loan sub-aggregates in order to test the distributional implications of potential credit market frictions. The results suggest that there is no evidence that loans amplify the transmission of macroeconomic fluctuations or that a "financial accelerator" via bank lending exists. --Business cycle fluctuations,bank lending,SVAR model,sign restrictions

3D Organization of Eukaryotic and Prokaryotic Genomes

There is a complex mutual interplay between three-dimensional (3D) genome organization and cellular activities in bacteria and eukaryotes. The aim of this thesis is to investigate such structure-function relationships. A main part of this thesis deals with the study of the three-dimensional genome organization using novel techniques for detecting genome-wide contacts using next-generation sequencing. These so called chromatin conformation capture-based methods, such as 5C and Hi-C, give deep insights into the architecture of the genome inside the nucleus, even on a small scale. We shed light on the question how the vastly increasing Hi-C data can generate new insights about the way the genome is organized in 3D. To this end, we first present the typical Hi-C data processing workflow to obtain Hi-C contact maps and show potential pitfalls in the interpretation of such contact maps using our own data pipeline and publicly available Hi-C data sets. Subsequently, we focus on approaches to modeling 3D genome organization based on contact maps. In this context, a computational tool was developed which interactively visualizes contact maps alongside complementary genomic data tracks. Inspired by machine learning with the help of probabilistic graphical models, we developed a tool that detects the compartmentalization structure within contact maps on multiple scales. In a further project, we propose and test one possible mechanism for the observed compartmentalization within contact maps of genomes across multiple species: Dynamic formation of loops within domains. In the context of 3D organization of bacterial chromosomes, we present the first direct evidence for global restructuring by long-range interactions of a DNA binding protein. Using Hi-C and live cell imaging of DNA loci, we show that the DNA binding protein Rok forms insulator-like complexes looping the B. subtilis genome over large distances. This biological mechanism agrees with our model based on dynamic formation of loops affecting domain formation in eukaryotic genomes. We further investigate the spatial segregation of the E. coli chromosome during cell division. In particular, we are interested in the positioning of the chromosomal replication origin region based on its interaction with the protein complex MukBEF. We tackle the problem using a combined approach of stochastic and polymer simulations. Last but not least, we develop a completely new methodology to analyze single molecule localization microscopy images based on topological data analysis. By using this new approach in the analysis of irradiated cells, we are able to show that the topology of repair foci can be categorized depending the distance to heterochromatin

Strategies of the Repeat Player. The European Commission between Courtroom and Legislature

One of the startling empirical insights from the growing body of research on the workings of the EU judicial system is that the European Commission almost always wins. This finding is remarkably robust – the Court follows the Commission’s opinion in the vast majority of cases. Since the Court has been the author of many important decisions shaping the content of EU policies, being a frequent and frequently successful litigator provides the Commission with an alternative means of achieving policy objectives, at least when all else fails. This study systematically assesses how the Commission makes use of its access to both legislation and litigation in order to advance its policy interests. It proposes that the Commission is more likely to resort to litigation when the likelihood of initiating successful legislation is low. To test this proposition, the study proceeds in two steps. It starts with a quantitative analysis of the relationship between legislative obstacles and infringement proceedings across policy areas over time. In a second step, it undertakes two longitudinal case studies of Commission policy initiatives and judicial action in two policy areas: the free movement of goods, in particular with regard to the removal of barriers to trade in goods, and the free movement of persons, in particular with regard to the rights of European Union nationals to move and reside within the Union

Edge instabilities of topological superconductors

Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground-state degeneracy. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry-broken phases, which lift the ground-state degeneracy. We examine the instabilities of the flat-band edge states of d_{xy}-wave superconductors by performing a mean-field analysis in the Majorana basis of the edge states. The leading instabilities are Majorana mass terms, which correspond to coherent superpositions of particle-particle and particle-hole channels in the fermionic language. We find that attractive interactions induce three different mass terms. One is a coherent superposition of imaginary s-wave pairing and current order, and another combines a charge-density-wave and finite-momentum singlet pairing. Repulsive interactions, on the other hand, lead to ferromagnetism together with spin-triplet pairing at the edge. Our quantum Monte Carlo simulations confirm these findings and demonstrate that these instabilities occur even in the presence of strong quantum fluctuations. We discuss the implications of our results for experiments on cuprate high-temperature superconductors.Comment: 4 pages, 3 figure

Von der ›Sozialistischen Arbeiterpartei‹ zur ›Sozialdemokratischen Partei Deutschlands‹. Die Geschichte der politischen Arbeiterbewegung im Kaiserreich (1871 bis 1918)

Der Vortrag skizziert die historisch-politischen Grundlagen des 19. Jahrhunderts, die schließlich in der zweiten Hälfte zur Etablierung des Sozialismus als politischer Strömung und der Gründung sozialistischer Parteien führten. Er blickt ferner auf die Gense der Sozialdemokratischen Partei Deutschlands von Ihrer Vereinigung 1875 bis hin zur Revolution von 1918/19