On the Complexity of Digraph Colourings and Vertex Arboricity

It has been shown by Bokal et al. that deciding 2-colourability of digraphs is an NP-complete problem. This result was later on extended by Feder et al. to prove that deciding whether a digraph has a circular $p$-colouring is NP-complete for all rational $p>1$. In this paper, we consider the complexity of corresponding decision problems for related notions of fractional colourings for digraphs and graphs, including the star dichromatic number, the fractional dichromatic number and the circular vertex arboricity. We prove the following results: Deciding if the star dichromatic number of a digraph is at most $p$ is NP-complete for every rational $p>1$. Deciding if the fractional dichromatic number of a digraph is at most $p$ is NP-complete for every $p>1, p \neq 2$. Deciding if the circular vertex arboricity of a graph is at most $p$ is NP-complete for every rational $p>1$. To show these results, different techniques are required in each case. In order to prove the first result, we relate the star dichromatic number to a new notion of homomorphisms between digraphs, called circular homomorphisms, which might be of independent interest. We provide a classification of the computational complexities of the corresponding homomorphism colouring problems similar to the one derived by Feder et al. for acyclic homomorphisms.Comment: 21 pages, 1 figur

DIE ANTICHRISTLICHEN TRAKTATE VON KELSOS, PORPHYRIOS UND JULIAN UND IHRE REZEPTION IN DER AUFKÄRUNG

Einer verbreiteten Ansicht zufolge sah sich das Christentum in der Aufklärung Einwänden ausgesetzt, die vom Standpunkt einer ihm fremden — neuzeitlichen — Rationalität aus entwickelt wurden und daher als anachronistisch und unangemessen zurückzuweisen sind. Tatsächlich jedoch griffen Religionskritiker der Aufklärung immer wieder auf Argumente zurück, mit denen bereits in der Spätantike Philosophen wie Kelsos, Porphyrios, Hierokles und Julian Apostata aus einer zeitgenössischen Perspektive dem Christentum entgegengetreten waren. Der Einfluss dieser spätantiken Philosophen auf die Religionskritik der Aufklärung wird exemplarisch anhand der Debatten über die Autorität der biblischen Offenbarung, der Wunderdiskussion und der Auseinandersetzung mit dem christlichen Moralverständnis dargestellt

Anophelinae (Diptera: Culicidae) in ausgewählten Marschgebieten Niedersachsens : Bestandserfassung, Habitatbindung und Interpolation

Nach HIRSCH (1883) war die Malariasituation im 19. Jahrhundert in Norddeutschland am schlimmsten in Schleswig-Holstein, an der Küste westlich der Elbe sowie in den Moorgebieten von Hannover und Oldenburg. Erst mit Beginn des 20. Jahrhunderts nahm dort die Zahl der Infektionen ab. Dieser Rückgang wurde vielfach auf die Trockenlegung von Marsch-, Sumpf- und Moorgebieten zurückgeführt (MAIER 2004). Aktuell wird deshalb in Teilen der Bevölkerung ein Wiederaufflackern der Malaria bzw. anderer Mückenassoziierter Krankheiten als indirekte Folge von Wiedervernässungsmaßnahmen befürchtet. Hinzu kommen Klima- und weitere Umweltveränderungen, welche nach MAIER et al. (2003) Ursache für neu auftretende oder wiederkehrende Krankheiten sein können. Mit dem Verschwinden der Malaria wurde in Deutschland kaum weitere Forschung zur Verbreitung und Ökologie der Culiciden betrieben. Das Fehlen von fundierten Daten zur Ökologie und Populationsentwicklung der präimaginalen Culicidenstadien in den heute vorhandenen Lebensräumen (z.B. Gräben, Polder, Wiedervernässungsflächen, Mooren) erschwert Aussagen und Prognosen zur Verbreitung potenzieller Vektoren. Die aktuellen Untersuchungen konzentrierten sich zunächst auf die Untersuchung der aquatischen Entwicklungsstadien von Anopheles-Arten (Diptera: Culicidae) in Entwässerungsgräben. Diese Biotope sind für die heutige Landschaftsstruktur der Marschengebiete im Nordwesten Niedersachsens typisch, stellen dort einen hohen Anteil der Wasserflächen dar und sind grundsätzlich als Brutgewässer geeignet (CRANSTON et al. 1987, MOHRIG 1969). Wesentliches Ziel der Untersuchung war zunächst die Darstellung historischer Fundgebiete, der abgesicherte Nachweis aktueller Brutgebiete verschiedener Anopheles-Arten und die Entwicklung einer standardisierten Methode zur Charakterisierung der betreffenden Biotope. Darauf aufbauend sollen mit GISTechniken, Classification and Regression Trees (CART) und Geostatistik zukünftig Möglichkeiten der Übertragung dieser Resultate auf ähnlich ausgestattete Landschaftsräume geprüft werden.The disappearance of malaria from Northern Germany in the middle of the 20th century was closely linked to a significant reduction of Anopheles breeding sites as a consequence of intense drainage of marshes, swamps and moors. Nature conservation activities and the reestablishment of swamps and wetland areas may nowadays lead to a converse effect and contribute to the multiplication and spread of culicid mosquitoes again. Therefore, the monitoring of their distribution and abundance is advisable. The presented investigation concentrates on typical Lower Saxony marshland ditches and on their suitability to provide breeding facilities for Culicidae in general, and for the former malaria vectors An. atroparvus and An. messeae in particular. The study area was fixed geographically with special reference to historical vector findings, former malaria regions and current archive data. To determine the habitat preferences of the mosquitoes, a structural mapping of single ditches was performed and essential abiotic factors were recorded. Anopheles specimens regularly were found in ditches with submerse and emerse macrophytes but never in ditches with a high degree of surface coverage by swimming plants. Conductivity, pHvalue and total phosphate in the water body appear to be further variables which correlate with the occurrence and abundance of Anopheles larvae and pupae and therefore can be used for predictions. By means of geographic information systems (GIS) and geostatistical procedures, a surface related assessment of the given Anopheles densities within the ditches should now be feasible. To this end, the multivariate correlations between the empirical data were analysed by Classification and Regression Trees. The relations detected serve to predict the empirical findings to biotopes similar to the sampling sites. Furthermore, recent climate predictions will be analysed with respect to possible effects climate change may have on the distribution of Anophilinae in Lower Saxon

A European research agenda for somatic symptom disorders, bodily distress disorders, and functional disorders: Results of an estimate-talk-estimate delphi expert study

Background: Somatic Symptom Disorders (SSD), Bodily Distress Disorders (BDD) and functional disorders (FD) are associated with high medical and societal costs and pose a substantial challenge to the population and health policy of Europe. To meet this challenge, a specific research agenda is needed as one of the cornerstones of sustainable mental health research and health policy for SSD, BDD, and FD in Europe. Aim: To identify the main challenges and research priorities concerning SSD, BDD, and FD from a European perspective. Methods: Delphi study conducted from July 2016 until October 2017 in 3 rounds with 3 workshop meetings and 3 online surveys, involving 75 experts and 21 European countries. EURONET-SOMA and the European Association of Psychosomatic Medicine (EAPM) hosted the meetings. Results: Eight research priorities were identified: (1) Assessment of diagnostic profiles relevant to course and treatment outcome. (2) Development and evaluation of new, effective interventions. (3) Validation studies on questionnaires or semi-structured interviews that assess chronic medical conditions in this context. (4) Research into patients preferences for diagnosis and treatment. (5) Development of new methodologic designs to identify and explore mediators and moderators of clinical course and treatment outcomes (6). Translational research exploring how psychological and somatic symptoms develop from somatic conditions and biological and behavioral pathogenic factors. (7) Development of new, effective interventions to personalize treatment. (8) Implementation studies of treatment interventions in different settings, such as primary care, occupational care, general hospital and specialty mental health settings. The general public and policymakers will benefit from the development of new, effective, personalized interventions for SSD, BDD, and FD, that will be enhanced by translational research, as well as from the outcomes of research into patient involvement, GP-patient communication, consultation-liaison models and implementation. Conclusion: Funding for this research agenda, targeting these challenges in coordinated research networks such as EURONET-SOMA and EAPM, and systematically allocating resources by policymakers to this critical area in mental and physical well-being is urgently needed to improve efficacy and impact for diagnosis and treatment of SSD, BDD, and FD across Europe

Leave Me Alone With Your Symptoms! Social Exclusion at the Workplace Mediates the Relationship of Employee's Mental Illness and Sick Leave

Although a substantial part of employees suffers from a mental illness, the work situation of this population still is understudied. Previous research suggests that people with a mental illness experience discrimination in the workplace, which is known to have detrimental effects on health. Building on the stereotype content model and allostatic load theory, the present study investigated whether employees with a mental illness become socially excluded at the workplace and therefore show more days of sick leave. Overall, 86 employees diagnosed with a mental disorder were interviewed and completed online-surveys. Path analyses supported the hypotheses, yielding a serial mediation: The interview-rated severity of the mental disorder had an indirect effect on the days of sick leave, mediated by the symptomatic burden and the social exclusion at the workplace. In the light of the costs associated with absenteeism the present paper highlights the harmfulness of discrimination. Organizations and especially supervisors need to be attentive for signs of exclusion within their teams and try to counteract as early as possible

Spatially valid data of atmospheric deposition of heavy metals and nitrogen derived by moss surveys for pollution risk assessments of ecosystems

For analysing element input into ecosystems and associated risks due to atmospheric deposition, element concentrations in moss provide complementary and time-integrated data at high spatial resolution every 5 years since 1990. The paper reviews (1) minimum sample sizes needed for reliable, statistical estimation of mean values at four different spatial scales (European and national level as well as landscape-specific level covering Europe and single countries); (2) trends of heavy metal (HM) and nitrogen (N) concentrations in moss in Europe (1990–2010); (3) correlations between concentrations of HM in moss and soil specimens collected across Norway (1990–2010); and (4) canopy drip-induced site-specific variation of N concentration in moss sampled in seven European countries (1990–2013). While the minimum sample sizes on the European and national level were achieved without exception, for some ecological land classes and elements, the coverage with sampling sites should be improved. The decline in emission and subsequent atmospheric deposition of HM across Europe has resulted in decreasing HM concentrations in moss between 1990 and 2010. In contrast, hardly any changes were observed for N in moss between 2005, when N was included into the survey for the first time, and 2010. In Norway, both, the moss and the soil survey data sets, were correlated, indicating a decrease of HM concentrations in moss and soil. At the site level, the average N deposition inside of forests was almost three times higher than the average N deposition outside of forests

Modelling spatial patterns of correlations between concentrations of heavy metals in mosses and atmospheric deposition in 2010 across Europe

Background: This paper aims to investigate the correlations between the concentrations of nine heavy metals in moss and atmospheric deposition within ecological land classes covering Europe. Additionally, it is examined to what extent the statistical relations are affected by the land use around the moss sampling sites. Based on moss data collected in 2010/2011 throughout Europe and data on total atmospheric deposition modelled by two chemical transport models (EMEP MSC-E, LOTOS-EUROS), correlation coefficients between concentrations of heavy metals in moss and in modelled atmospheric deposition were specified for spatial subsamples defined by ecological land classes of Europe (ELCE) as a spatial reference system. Linear discriminant analysis (LDA) and logistic regression (LR) were then used to separate moss sampling sites regarding their contribution to the strength of correlation considering the areal percentage of urban, agricultural and forestry land use around the sampling location. After verification LDA models by LR, LDA models were used to transform spatial information on the land use to maps of potential correlation levels, applicable for future network planning in the European Moss Survey. Results: Correlations between concentrations of heavy metals in moss and in modelled atmospheric deposition were found to be specific for elements and ELCE units. Land use around the sampling sites mainly influences the correlation level. Small radiuses around the sampling sites examined (5 km) are more relevant for Cd, Cu, Ni, and Zn, while the areal percentage of urban and agricultural land use within large radiuses (75–100 km) is more relevant for As, Cr, Hg, Pb, and V. Most valid LDA models pattern with error rates of < 40% were found for As, Cr, Cu, Hg, Pb, and V. Land use-dependent predictions of spatial patterns split up Europe into investigation areas revealing potentially high (= above-average) or low (= below-average) correlation coefficients. Conclusions: LDA is an eligible method identifying and ranking boundary conditions of correlations between atmospheric deposition and respective concentrations of heavy metals in moss and related mapping considering the influence of the land use around moss sampling sites

Modelling and mapping heavy metal and nitrogen concentrations in moss in 2010 throughout Europe by applying Random Forests models

Objective: This study explores the statistical relations between the concentration of nine heavy metals(HM) (arsenic (As), cadmium (Cd), chromium (Cr), copper (Cu), mercury (Hg), nickel (Ni), lead (Pb),vanadium (V), zinc (Zn)), and nitrogen (N) in moss and potential explanatory variables (predictors)which were then used for mapping spatial patterns across Europe. Based on moss specimens collected in 2010 throughout Europe, the statistical relation between a set of potential predictors (such as the atmospheric deposition calculated by use of two chemical transport models (CTM), distance from emission sources, density of different land uses, population density, elevation, precipitation, clay content of soils) and concentrations of HMs and nitrogen (N) in moss (response variables) were evaluated by the use of Random Forests (RF) and Classification and Regression Trees (CART). Four spatial scales were regarded: Europe as a whole, ecological land classes covering Europe, single countries participating in the European Moss Survey (EMS), and moss species at sampling sites. Spatial patterns were estimated by applying a series of RF models on data on potential predictors covering Europe. Statistical values and resulting maps were used to investigate to what extent the models are specific for countries, units of the Ecological Land Classification of Europe (ELCE), and moss species. Results: Land use, atmospheric deposition and distance to technical emission sources mainly influence the element concentration in moss. The explanatory power of calculated RF models varies according to elements measured in moss specimens, country, ecological land class, and moss species. Measured and predicted medians of element concentrations agree fairly well while minima and maxima show considerable differences. The European maps derived from the RF models provide smoothed surfaces of element concentrations (As, Cd, Cr, Cu, N, Ni, Pb, Hg, V, Zn), each explained by a multivariate RF model and verified by CART, and thereby more information than the dot maps depicting the spatial patterns of measured values. Conclusions: RF is an eligible method identifying and ranking boundary conditions of element concentrations in moss and related mapping including the influence of the environmental factors