On Conditions for Convergence to Consensus

A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE Transactions on Automatic Control, vol. 50, no. 2, 2005) about set-valued Lyapunov theory and convergence under switching communication topologies. We give examples that point out differences of approaches including examples where Moreau's theorem is not applicable but ours is. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.Comment: 5 pages, 2 columns, example adde

On the complexity of Hamel bases of infinite dimensional Banach spaces

We call a subset S of a topological vector space V linearly Borel, if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It will be shown that a Hamel base of an infinite dimensional Banach space can never be linearly Borel. This answers a question of Anatolij Plichko

Geschlechterunterschiede im Zentralabitur? Fairness von High-Stakes-Tests für Jungen und Mädchen im Fach Englisch in Nordrhein-Westfalen im Kontext der Educational Governance

The shift from decentralized to centralized A-level examinations (Abitur) was implemented in the German school system as a measure of Educational Governance in the last decade. This reform was mainly introduced with the intention of providing higher comparability of school examinations and student achievement as well as increasing fairness in school examinations. It is not known yet if these ambitious aims and functions of the new centralized examination format have been achieved and if fairer assessment can be guaranteed in terms of providing all students with the same opportunities to pass the examinations by allocating fair tests to different student subpopulations e.g., students of different background or gender. The research presented in this article deals with these questions and focuses on gender differences. It investigates gender-specific fairness of the test items in centralized Abitur examinations as high school exit examinations in Germany. The data are drawn from Abitur examinations in English (as a foreign language). Differential item functioning (DIF) analysis reveals that at least some parts of the examinations indicate gender inequality. (DIPF/Orig.)Die fast flächendeckende Implementation des Zentralabiturs in Deutschland als Maßnahme im Kontext der Neuen Steuerung im Bildungswesen ist eng mit dem Ziel verbunden, die Vergleichbarkeit von Schulabschlüssen und schulischen Leistungen insgesamt zu erhöhen und durch zentrale Prüfungen die Fairness von Leistungsfeststellungen im Sinne der Komparabilitätsfunktion zentraler Prüfungsformate zu sichern. Bisher ist jedoch nicht bekannt und untersucht, ob das Zentralabitur diesen Ansprüchen tatsächlich gerecht wird und die vorgenannten Funktionen so erfüllt, dass eine faire Leistungsmessung für unterschiedliche Schülersubgruppen gegeben ist. Auf der Grundlage von Daten zu differenzierten Schülerergebnissen zum Zentralabitur im Fach Englisch untersucht dieser Beitrag exemplarisch die geschlechtsspezifische Fairness von Abitur aufgaben. Eine Differential-Item-Functioning-Analyse (DIF-Analyse) zeigt, dass zumindest ein Teil der eingesetzten Aufgaben auf eine geschlechtsspezifische Ungleichbehandlung durch die Aufgabenstellung hinweist. (DIPF/Orig.

Community-based micro grids: a common property resource problem

This paper introduces a new methodological and theoretical foundation for studying the reasons for successes and failures of community-based micro grids (CBMGs). While technical and financial factors involved are very critical they are comparatively well researched. This analysis argues that further research into, in particular, the institutional design of CBMGs is required in order to improve long-term sustainability. The paper suggests that the electricity in an isolated micro grid can be treated as a common property resource (CPR), which then opens up the established academic literature regarding collective action in the presence of CPRs. More specifically this paper analyses how the rich set of enabling conditions for collective action, which has been established in the context of traditional CPR situations such as water for irrigation or pasture for grazing, can be applied to the context of CBMGs. The goal is to arrive at workable recommendations for policy-makers and practitioners to inform the design and improve the long-term sustainability of CBMGs. Ultimately this has the potential to contribute towards efforts to bring modern energy services to significant parts of rural populations without electricity access