Construction of dual modules using Martin's Axiom

AbstractSeveral authors considered abelian groups, which can be represented as dual groups, see [P.C. Eklof, A.H. Mekler, Almost Free Modules—Set-Theoretic Methods, rev. ed., North-Holland Math. Library, North-Holland, 2002; R. Göbel, J. Trlifaj, Approximation Theory and Endomorphism Algebras, Walter de Gruyter, Berlin, 2005] for references. Recall that dual modules are those of the form G∗=HomR(G,R). We will work in the category of R-modules, over countable PIDs with a multiplicatively closed subset S such that R is Hausdorff in its natural S-topology. Using Martin's Axiom (MA), we represent a large class of modules which are submodules of P=Rω as dual modules. Martin's Axiom is mainly used to reduce the problem of solving infinite systems of linear equations over R to the finite one (see Step Lemma 4.10). An analysis in Section 4 will show that being a dual module of a submodule H⊆P requires two necessary conditions (Definition 4.7); we will say that H is admissible in this case. Conversely we will show (Theorem 4.13) that under (MA) and negation of (CH) precisely these modules (of size <2ℵ0) are dual modules of pure modules G sandwiched between R(ω) and its S-adic closure in P. In the last section of the paper we strengthen this result by the additional demand that the endomorphism ring of G is ‘minimal,’ hence G becomes also essentially rigid

Dr. Karl König

Königs Idee von Camphill, wie man es ab Oktober 1940 mit dem Umzug in das Camphill-Haus nannte, lagen in drei heilenden Faktoren: den heilpädagogischen Übungen und Behandlungen, der Schule und dem sozialen Leben in der Gemeinschaft. Mit den ersten Kindern begann die heilpädagogische Arbeit mit Programmen, speziellen Übungen, Gymnastik, und der Schule. Die heilpädagogischen Programme und Methoden wurden für die Kinder speziell erarbeitet und angewandt, entwickelten sich aber erst nach und nach. Es entstanden neue und grundlegende Beiträge zur Musik-, Bewegungs-, Farbtherapie und der sogenannten Bobath-Therapie für cerebral gelähmte Kinder. Auch die heilpädagogischen Maßnahmen in der Schule waren neuartig. Die Unterrichtsform wurde maßgebend geprägt von Rudolf Steiners Waldorfpädagogik, deren Methoden sich, wie König meinte, in leicht abgeänderter Form hervorragend auf die Heilpädagogik übertragen ließ. Eine wichtige Innovation bedeutete in diesem Zusammenhang der integrative Unterricht, in dem König Kinder mit und ohne Behinderung bis zum elften Lebensjahr in gemeinsamen Klassen unterbrachte, was bis heute in fast allen Camphill-Schulen weitergeführt wird

БИБЛЕЙСКИЙ ИНТЕРТЕКСТ В РАННИХ СТИХОТВОРЕНИЯХ А. ДЕ ВИНЬИ («СУСАННА», «КУПАНИЕ ЗНАТНОЙ РИМЛЯНКИ», «ИЗМЕННИЦА)

Ранние стихотворения А. де Виньи исследуются как библейский интертекст и мифопоэтический дискурс в контексте современных идей о романтизме

Explanatory machine learning for justified trust in human-AI collaboration : Experiments on file deletion recommendations

In the digital age, saving and accumulating large amounts of digital data is a common phenomenon. However, saving does not only consume energy, but may also cause information overload and prevent people from staying focused and working effectively. We present and systematically examine an explanatory AI system (Dare2Del), which supports individuals to delete irrelevant digital objects. To give recommendations for the optimization of related human-computer interactions, we vary different design features (explanations, familiarity, verifiability) within and across three experiments (N1 = 61, N2 = 33, N3= 73). Moreover, building on the concept of distributed cognition, we check possible cross-connections between external (digital) and internal (human) memory. Specifically, we examine whether deleting external files also contributes to human forgetting of the related mental representations. Multilevel modeling results show the importance of presenting explanations for the acceptance of deleting suggestions in all three experiments, but also point to the need of their verifiability to generate trust in the system. However, we did not find clear evidence that deleting computer files contributes to human forgetting of the related memories. Based on our findings, we provide basic recommendations for the design of AI systems that can help to reduce the burden on people and the digital environment, and suggest directions for future research

A nationwide trend analysis on the usage of endomyocardial biopsy

Background Endomyocardial biopsy (EMB) is a safe procedure performed in diagnostic work-up of cardiac disease. Hypothesis Data regarding temporal trends of total numbers, characteristics, in-hospital outcomes, and complications of patients undergoing EMB are sparse. Methods The nationwide German inpatient sample (2005–2019) was used for this analysis. Patient cases of EBM during the 5-year cycles from 2005 to 2009, 2010 to 2014, and 2015 to 2019 were compared, and temporal trends regarding total numbers and presumable major and minor EMB-associated complications were investigated. Results Overall, 67 745 EMB were performed in Germany 2005–2019. Total number of EMB increased from 3083 in 2005 to 5646 in 2019 (β 0.40 [95% confidence interval [CI] 0.37–0.43], p < .001). Among these EMB, 19 083 (28.2%) were performed during the period 2005–2009, 22 867 (33.7%) 2010–2014, and 25 795 (38.1%) between 2015 and 2019. The proportion of patients aged ≥70 years was highest 2015–2019 (2005–2009: 9.3%; 2010–2014: 13.8%; 2015–2019: 16.1%, p < .001) and the most aggravated comorbidity profile (Charlson Comorbidity Index 2.25 ± 1.93; 2.67 ± 2.14; 3.01 ± 2.29, p < .001) was also detected 2015–2019. Major complications occurred less often in the period 2015–2019 compared to 2005–2009 (odds ratio [OR] 0.921 [95% CI 0.893–0.950], p < .001), whereas minor complications were more frequently observed between 2015 and 2019 (OR 1.067 [95% CI 1.042–1.093], p < .001). While a decrease in major complications was detected irrespective of age, an increase in minor complications was identified only in patients between 30–59 years. Conclusions Annual numbers of EMB increased significantly in Germany 2005–2019. Patients who underwent EMB in recent years were older and showed an aggravated comorbidity profile accompanied by fewer major complications, underscoring safety of the procedure

Mitgliedschaft in Gewerkschaften: Inklusions- und Exklusionstendenzen in der Organisation von Arbeitnehmerinteressen in Europa

"Die Gewerkschaften stehen heute in vielen europäischen Ländern vor beträchtlichen Mitgliederproblemen. Jedoch variiert der gewerkschaftliche Organisationsgrad zwischen einem eher niedrigen Niveau in Süd- und Osteuropa und einem höheren Niveau in Nordeuropa. Außerdem zeigen sich im internationalen Vergleich erhebliche Unterschiede zwischen sozialen Gruppen. Zu welchem Grad gelingt es den Gewerkschaften noch, ihre Klientel einzubinden und zumindest als Mitglieder zu mobilisieren? Dieser Frage wird mit Hilfe von deskriptiven Analysen des European Social Surveys von 2002/03 für West- und Ost-Deutschland sowie weiteren 18 europäischen Ländern nachgegangen. Es werden zentrale Muster der Inklusion bzw. Exklusion von Arbeitnehmerinteressen aufgezeigt und mögliche Erklärungen der (Nicht-)Mitgliedschaft in Gewerkschaften erörtert. Neben den sozialstrukturellen Ursachen für geringere Organisationsgrade von Frauen, Arbeitslosen und atypisch Beschäftigten, werden zentrale institutionelle Faktoren herausgearbeitet, die selektive Anreize für eine Gewerkschaftsmitgliedschaft schaffen und den betrieblichen Zugang für Gewerkschaften erleichtern. Die theoretische Fruchtbarkeit eines In-/ Exklusionsansatzes zeigt sich besonders in der mangelnden Repräsentation der Interessen von atypisch Beschäftigten und Arbeitslosen sowie solchen in peripheren (unorganisierten) Arbeitsplätzen." (Autorenreferat)"In many European countries trade unions face considerable membership problems. Union density varies between a mostly low level in Southern and Eastern European societies and high levels in Nordic countries. Moreover, there are considerable cross-national differences between social groups. To what degree do trade unions integrate their clientele and are they capable of mobilizing members? We study this question by using descriptive statistics from the European Social Survey of 2002/03 for (Western and Eastern) Germany and for 18 other European countries. We discuss crucial patterns of inclusion and exclusion in the organization of labour interests and possible explanatory factors for (non-)membership. In addition to social structural causes for low union density of women, the unemployed and atypical employed, we review several institutional factors that provide selective incentives for membership and foster union access to workplaces. The inclusion/exclusion perspective proves particularly valuable for the analysis of low representation of the unemployed and atypical employed as well for those working in peripheral (unorganized) workplaces." (author's abstract

Filifactor alocis - involvement in periodontal biofilms

<p>Abstract</p> <p>Background</p> <p>Bacteria in periodontal pockets develop complex sessile communities that attach to the tooth surface. These highly dynamic microfloral environments challenge both clinicians and researchers alike. The exploration of structural organisation and bacterial interactions within these biofilms is critically important for a thorough understanding of periodontal disease. In recent years, <it>Filifactor alocis</it>, a fastidious, Gram-positive, obligately anaerobic rod was repeatedly identified in periodontal lesions using DNA-based methods. It has been suggested to be a marker for periodontal deterioration. The present study investigated the epidemiology of <it>F. alocis </it>in periodontal pockets and analysed the spatial arrangement and architectural role of the organism in <it>in vivo </it>grown subgingival biofilms.</p> <p>Results</p> <p>A species-specific oligonucleotide probe, FIAL, was designed and evaluated. A total of 490 subgingival plaque samples were submitted to PCR and subsequent dot blot hybridization to compare the prevalence of <it>F. alocis </it>in patients suffering from generalized aggressive periodontitis (GAP), chronic periodontitis (CP), and control subjects resistant to periodontitis. Moreover, a specially designed carrier system was used to collect <it>in vivo </it>grown subgingival biofilms from GAP patients. Subsequent topographic analysis was performed using fluorescence in situ hybridization.</p> <p>While the majority of patients suffering from GAP or CP harboured <it>F. alocis</it>, it was rarely detected in the control group. In the examined carrier-borne biofilms the organism predominantly colonized apical parts of the pocket in close proximity to the soft tissues and was involved in numerous structures that constitute characteristic architectural features of subgingival periodontal biofilms.</p> <p>Conclusions</p> <p><it>F. alocis </it>is likely to make a relevant contribution to the pathogenetic structure of biofilms accounting for periodontal inflammation and can be considered an excellent marker organism for periodontal disease.</p