Interferon β-1a in relapsing multiple sclerosis: four-year extension of the European IFNβ-1a Dose-C omparison Study

Background: Multiple sclerosis (MS) is a chronic disease requiring long-term monitoring of treatment. Objective: To assess the four-year clinical efficacy of intramuscular (IM) IFNb-1a in patients with relapsing MS from the European IFNb-1a Dose-C omparison Study. Methods: Patients who completed 36 months of treatment (Part 1) of the European IFNb-1a Dose-C omparison Study were given the option to continue double-blind treatment with IFNb-1a 30 mcg or 60 mcg IM once weekly (Part 2). Analyses of 48-month data were performed on sustained disability progression, relapses, and neutralizing antibody (NA b) formation. Results: O f 608/802 subjects who completed 36 months of treatment, 493 subjects continued treatment and 446 completed 48 months of treatment and follow-up. IFNb-1a 30 mcg and 60 mcg IM once weekly were equally effective for up to 48 months. There were no significant differences between doses over 48 months on any of the clinical endpoints, including rate of disability progression, cumulative percentage of patients who progressed (48 and 43, respectively), and annual relapse rates; relapses tended to decrease over 48 months. The incidence of patients who were positive for NAbs at any time during the study was low in both treatment groups. Conclusion: C ompared with 60-mcg IM IFNb-1a once weekly, a dose of 30 mcg IM IFNb-1a once weekly maintains the same clinical efficacy over four years

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

Non-affirmative Theory of Education as a Foundation for Curriculum Studies, Didaktik and Educational Leadership

This chapter presents non-affirmative theory of education as the foundation for a new research program in education, allowing us to bridge educational leadership, curriculum studies and Didaktik. We demonstrate the strengths of this framework by analyzing literature from educational leadership and curriculum theory/didaktik. In contrast to both socialization-oriented explanations locating curriculum and leadership within existing society, and transformation-oriented models viewing education as revolutionary or super-ordinate to society, non-affirmative theory explains the relation between education and politics, economy and culture, respectively, as non-hierarchical. Here critical deliberation and discursive practices mediate between politics, culture, economy and education, driven by individual agency in historically developed cultural and societal institutions. While transformative and socialization models typically result in instrumental notions of leadership and teaching, non-affirmative education theory, previously developed within German and Nordic education, instead views leadership and teaching as relational and hermeneutic, drawing on ontological core concepts of modern education: recognition; summoning to self-activity and Bildsamkeit. Understanding educational leadership, school development and teaching then requires a comparative multi-level approach informed by discursive institutionalism and organization theory, in addition to theorizing leadership and teaching as cultural-historical and critical-hermeneutic activity. Globalisation and contemporary challenges to deliberative democracy also call for rethinking modern nation-state based theorizing of education in a cosmopolitan light. Non-affirmative education theory allows us to understand and promote recognition based democratic citizenship (political, economical and cultural) that respects cultural, ethical and epistemological variations in a globopolitan era. We hope an American-European-Asian comparative dialogue is enhanced by theorizing education with a non-affirmative approach