Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ≤ L ≤ 8. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for the 7, 14, and 21 independent simulations. The approximate values for the critical temperature of the infinite lattice, Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without logarithmic factor), 6.6921(22) (without logarithmic factor), 6.6909(2) (without logarithmic factor), 6.6822(13) (with logarithmic factor), 6.6819(11) (with logarithmic factor), 6.6808(8) (with logarithmic factor) are obtained from the intersection points of specific heat curves, the Binder parameter curves and the straight line fit of specific heat maxima for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results, 6.6802(1) and 6.6808(8), are in very good agreement with the series expansion results of Tc(∞) = 6.6817(15), 6.6802(2), the dynamic Monte Carlo result of Tc(∞) = 6.6803(1), the cluster Monte Carlo result of Tc(∞) = 6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm of Tc(∞) = 6.6802632 ± 5⋅10⁻⁵. The average values obtained for the critical exponent of the specific heat are calculated as α = –0.0402(15), –0.0393(12), –0.0391(11) for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained result, α = –0.0391(11), is agreement with the series expansions results of α = –0.12 ± 0.03 and the Monte Carlo using Metropolis and Wolff-cluster algorithm of α ≥ 0±0.04. However, α = –0.0391(11) isn’t consistent with the renormalization group prediction of α = 0

Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ? L ? 8. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for the 7, 14, and 21 independent simulations. The approximate values for the critical temperature of the infinite lattice, Tc(?) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without logarithmic factor), 6.6921(22) (without logarithmic factor), 6.6909(2) (without logarithmic factor), 6.6822(13) (with logarithmic factor), 6.6819(11) (with logarithmic factor), 6.6808(8) (with logarithmic factor) are obtained from the intersection points of specific heat curves, the Binder parameter curves and the straight line fit of specific heat maxima for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results, 6.6802(1) and 6.6808(8), are in very good agreement with the series expansion results of Tc(?) = 6.6817(15), 6.6802(2), the dynamic Monte Carlo result of Tc(?) = 6.6803(1), the cluster Monte Carlo result of Tc(?) = 6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm of Tc(?) = 6.6802632 ± 5-10-5 The average values obtained for the critical exponent of the specific heat are calculated as ? =-0.0402(15),-0.0393(12),-0.0391(11) for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained result, ? =-0.0391(11), is agreement with the series expansions results of ? =-0.12 ± 0.03 and the Monte Carlo using Metropolis and Wolff-cluster algorithm of a > 0+0.04. However, ? =-0.0391(11) isn't consistent with the renormalization group prediction of ? = 0. © Z. Merdan and E. Güzelsoy, 2011

Kulturelle Kompetenz und Global Health: Perspektiven für die medizinische Ausbildung - Positionspapier des GMA-Ausschusses Kulturelle Kompetenz und Global Health

Introduction: Routine medical care in Germany, Austria and Switzerland is being increasingly impacted by the cultural and linguistic diversity of an ever more complex world. Both at home and as part of international student exchanges, medical students are confronted with different ways of thinking and acting in relation to health and disease. Despite an increasing number of courses on cultural competence and global health at German-speaking medical schools, systematic approaches are lacking on how to integrate this topic into medical curricula.Methodological approach: This paper is based on a structured consensus-building process by a multidisciplinary committee composed of faculty and students. In a first step, a qualitative online survey was carried out in order to establish an inventory of definitions and concepts. After the second step, in which a literature search was conducted and definitions of global health and transcultural and intercultural competence were clarified, recommendations were formulated regarding content, teaching and institutional infrastructure. Based on small-group work and large-group discussions, different perspectives and critical issues were compiled using multiple feedback loops that served to ensure quality.Results: An inventory on the national and international level showed that great heterogeneity exists in regard to definitions, teaching strategies, teaching formats and faculty qualification. Definitions and central aspects considered essential to medical education were thus established for the use of the terms "cultural competence" and "global health". Recommendations are given for implementation, ranging from practical realization to qualification of teaching staff and education research.Outlook: High-quality healthcare as a goal calls for the systematic internationalization of undergraduate medical education. In addition to offering specific courses on cultural competence and global health, synergies would be created through the integration of cultural competence and global health content into the curricula of already existing subject areas. The NKLM (the national competence-based catalogue of learning objectives for undergraduate medical education) would serve as a basis for this.Einführung: Der medizinische Arbeitsalltag in Deutschland, Österreich und der Schweiz ist zunehmend durch kulturelle und sprachliche Diversität in einer komplexer werdenden Welt geprägt. Sowohl im Rahmen von Auslandsaufenthalten als auch im Inland kommen Medizinstudierende mit unterschiedlichen und ihnen teilweise fremd erscheinenden Denk- und Handlungsgewohnheiten bezogen auf Krankheit und Gesundheit in Berührung. Trotz einer steigenden Anzahl an Lehrangeboten zu den Themen Kulturelle Kompetenz und Global Health an den Fakultäten mangelt es bisher an systematischen Ansätzen zur Integration dieser Themenbereiche in die medizinischen Curricula.Methodisches Vorgehen: Das Papier basiert auf einem strukturierten Konsensfindungsprozess durch ein multidisziplinäres Gremium aus Lehrenden und Studierenden. Mittels einer qualitativen Online-Umfrage wurde in einem ersten Schritt eine Bestandsaufnahme zu Definitionen und Konzepten durchgeführt. Nach einer im zweiten Schritt erfolgten Literaturrecherche und Begriffsklärung zu den Bereichen Global Health und Trans- und Interkulturelle Kompetenz wurden in einem kontinuierlichen Arbeitsprozess inhaltliche, didaktische und strukturelle Empfehlungen erarbeitet. Über Kleingruppenarbeit und Plenumsdiskussionen wurden mit mehreren, der Qualitätssicherung dienenden Feedback-Schleifen unterschiedliche Perspektiven und kritische Standpunkte erarbeitet. Ergebnisse: Eine Bestandsaufnahme im nationalen und internationalen Raum ergab, dass eine große Heterogenität z.B. im Hinblick auf Definitionen, Lehrkonzepte und -formate oder die Qualifikation der Lehrenden besteht. Für die Nutzung der Begriffe Kulturelle Kompetenz und Global Health wurden daher für die medizinische Ausbildung als essentiell erachtete Definitionen und zentrale Aspekte benannt. Als Hilfe für die konkrete Umsetzung in der Lehre wurden Empfehlungen von der praktischen Umsetzung über die Qualifikation der Lehrenden bis hin zur Lehrforschung formuliert.Ausblick: Bei dem Ziel einer qualitativ hochwertigen Patientenversorgung besteht Bedarf an einer systematischen Internationalisierung des humanmedizinischen Studiums. Neben der Bereitstellung von spezifischen Lehrangeboten geht es im Sinne der Synergiebildung um eine Integration der Förderung Kultureller Kompetenz und der Vermittlung von Global Health-Inhalten in Angebote bestehender Fachdisziplinen. Der Nationale Kompetenzbasierte Lernzielkatalog Medizin (NKLM) bietet dafür eine Grundlage

A unified framework for multistage mixed integer linear optimization

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.</p