Singular values of the Dirac operator in dense QCD-like theories

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

Impact-based integrated real-time control for improvement of the Dommel River water quality

The KALLISTO project aims at finding cost-efficient sets of measures to meet the Water Framework Directive (WFD) derived goals for the river Dommel. Within the project, both acute and long term impacts of the urban wastewater system on the chemical and ecological quality of the river are studied with an integral monitoring campaign in the urban wastewater system (WWTP and sewers) and in the river. Based on this monitoring campaign, detailed models were calibrated. These models are partly simplified and integrated in a single model, which is validated using the detailed submodels. The integrated model was used to study the potential for impact-based real-time control (RTC). Impact based RTC proved to be able to improve the quality of the receiving waters significantly, although additional measures remain necessary to be able to meet the WFD requirements

Conviction Statistics as an Indicator of Crime Trends in Europe from 1990 to 2006

Convictions statistics were the first criminal statistics available in Europe during the nineteenth century. Their main weaknesses as crime measures and for comparative purposes were identified by Alphonse de Candolle in the 1830s. Currently, they are seldom used by comparative criminologists, although they provide a less valid but more reliable measure of crime and formal social control than police statistics. This article uses conviction statistics, compiled from the four editions of the European Sourcebook of Crime and Criminal Justice Statistics, to study the evolution of persons convicted in European countries from 1990 to 2006. Trends in persons convicted for six offences -intentional homicide, assault, rape, robbery, theft, and drug offences- and up to 26 European countries are analysed. These trends are established for the whole of Europe as well as for a cluster of Western European countries and a cluster of Central and Eastern European countries. The analyses show similarities between both regions of Europe at the beginning and at the end of the period under study. After a general increase of the rate of persons convicted in the early 1990s in the whole of Europe, trends followed different directions in Western and in Central and Eastern Europe. However, during the 2000s, it can be observed, throughout Europe, a certain stability of the rates of persons convicted for intentional homicides, accompanied by a general decrease of the rate of persons convicted for property offences, and an increase of the rate of those convicted for drug offences. The latter goes together with an increase of the rate of persons convicted for non lethal violent offences, which only reached some stability at the end of the time series. These trends show that there is no general crime drop in Europe. After a discussion of possible theoretical explanations, a multifactor model, inspired by opportunity-based theories, is proposed to explain the trends observed