Generalized balanced power diagrams for 3D representations of polycrystals

Characterizing the grain structure of polycrystalline material is an important task in material science. The present paper introduces the concept of generalized balanced power diagrams as a concise alternative to voxelated mappings. Here, each grain is represented by (measured approximations of) its center-of-mass position, its volume and, if available, by its second-order moments (in the non-equiaxed case). Such parameters may be obtained from 3D x-ray diffraction. As the exact global optimum of our model results from the solution of a suitable linear program it can be computed quite efficiently. Based on verified real-world measurements we show that from the few parameters per grain (3, respectively 6 in 2D and 4, respectively 10 in 3D) we obtain excellent representations of both equiaxed and non-equiaxed structures. Hence our approach seems to capture the physical principles governing the forming of such polycrystals in the underlying process quite well

Additive scales in degenerative disease - calculation of effect sizes and clinical judgment

<p>Abstract</p> <p>Background</p> <p>The therapeutic efficacy of an intervention is often assessed in clinical trials by scales measuring multiple diverse activities that are added to produce a cumulative global score. Medical communities and health care systems subsequently use these data to calculate pooled effect sizes to compare treatments. This is done because major doubt has been cast over the clinical relevance of statistically significant findings relying on <it>p </it>values with the potential to report chance findings. Hence in an aim to overcome this pooling the results of clinical studies into a meta-analyses with a statistical calculus has been assumed to be a more definitive way of deciding of efficacy.</p> <p>Methods</p> <p>We simulate the therapeutic effects as measured with additive scales in patient cohorts with different disease severity and assess the limitations of an effect size calculation of additive scales which are proven mathematically.</p> <p>Results</p> <p>We demonstrate that the major problem, which cannot be overcome by current numerical methods, is the complex nature and neurobiological foundation of clinical psychiatric endpoints in particular and additive scales in general. This is particularly relevant for endpoints used in dementia research. 'Cognition' is composed of functions such as memory, attention, orientation and many more. These individual functions decline in varied and non-linear ways. Here we demonstrate that with progressive diseases cumulative values from multidimensional scales are subject to distortion by the limitations of the additive scale. The non-linearity of the decline of function impedes the calculation of effect sizes based on cumulative values from these multidimensional scales.</p> <p>Conclusions</p> <p>Statistical analysis needs to be guided by boundaries of the biological condition. Alternatively, we suggest a different approach avoiding the error imposed by over-analysis of cumulative global scores from additive scales.</p

Cliques in high-dimensional random geometric graphs

International audienceRandom geometric graphs have become now a popular object of research. Defined rather simply, these graphs describe real networks much better than classical Erdős–Rényi graphs due to their ability to produce tightly connected communities. The $n$ vertices of a random geometric graph are points in $d$-dimensional Euclidean space, and two vertices are adjacent if they are close to each other. Many properties of these graphs have been revealed in the case when $d$ is fixed. However, the case of growing dimension $d$ is practically unexplored. This regime corresponds to a real-life situation when one has a data set of n observations with a significant number of features, a quite common case in data science today. In this paper, we study the clique structure of random geometric graphs when $n \to \infty$, and $d \to \infty$, and average vertex degree grows significantly slower than $n$. We show that under these conditions, random geometric graphs do not contain cliques of size 4 a.s. if only $d >> \log^{1+\epsilon}(n)$. As for the cliques of size 3, we present new bounds on the expected number of triangles in the case $\log^2(n) << d << \log^3(n)$ that improve previously known results. In addition, we provide new numerical results showing that the underlying geometry can be detected using the number of triangles even for small $n$

Praxissemester (Religion) in NRW: Bilanz und Perspektiven

Das Praxissemester ist seit dem Wintersemester 2014 / 2015 integraler Bestandteil des zweiten Mastersemesters an Hochschulen Nordrhein-Westfalens. Dieser Band bietet eine Zusammenführung von Perspektiven auf das Praxissemester in Nordrhein-Westfalen. Ein besonderer Blick fällt dabei auf das Praxissemester Religionslehre. In diesem Band stellen Bardo Herzig und Christoph Wiethoff einleitend vor, wie das Praxissemester an der Universität Paderborn konzeptionell, strukturell und inhaltlich gestaltet ist. Petra Herzmann und Anke B. Liegmann geben einen umfassenden Überblick zu qualitativen Forschungsbefunden zum Praxissemester und stellen Überlegungen zu einem qualitativen Forschungsprogramm dar. Carina Caruso und Andreas Seifert fokussieren die Entwicklung pädagogischen Wissens bei angehenden Religionslehrkräften. Malte Kling fasst Befunde zusammen, die sich auf den Rollenwechsel angehender evangelischer Religionslehrkräfte beziehen. In besonderem Maße richtet sich der Band auf das Praxissemester Religionslehre, indem Guido Hunze und Gudrun Lohkemper das Theorie-Praxis-Verständnis als Gelingensbedingung von Professionalisierung thematisieren, Norbert Brieden und Monika Tautz die Praxissemesterbegleitung an den Studienorten Köln und Wuppertal vergleichen und hochschuldidaktische Impulse formulieren, Mirjam Zimmermann Spiritualität als Gegenstand religiöser Bildung betrachtet und Guido Meyer und Carsten Misera Heterogenität im Religionsunterricht als einen Ausgangspunkt für die Entwicklung eines Lehrerhabitus im Praxissemester definieren. Weitere Perspektiven bieten Christoph Vogelsang (Didaktik der Physik) und Ulrich Feeser-Lichterfeld (Pastoralpsychologie). Carina Caruso und Jan Woppowa ziehen ein abschließendes Resümee unter besonderer Beachtung zukünftiger Aufgaben zur Gestaltung des Praxissemesters Religionslehre.Since the winter semester 2014 / 2015 long-term internships have become an integral part of the second master semester at universities in North Rhine-Westphalia. One aim is to improve the development of competencies of prospective teachers. This anthology provides an insight into perspectives of long-term internships in North Rhine-Westphalia referring especially to internships of those prospective teachers, who are going to be teachers for religious education. First Bardo Herzig and Christoph Wiethoff present the plan, the structure and the content of long-term internship at Paderborn University. They take pedagogy as their example. Petra Herzmann and Anke B. Liegmann provide a comprehensive survey of qualitative research on long-term internships and present ideas of a qualitative research programme. Carina Caruso and Andreas Seifert focus on the development of pedagogical knowledge of prospective teachers of religious education during the practice phase. Malte Kling gives a summary of his thesis referring to the change of roles of prospective teachers of religious education. Guido Hunze und Gudrun Lohkemper have a look at the relation between theory and practice for a successful professionalization. Norbert Brieden and Monika Tautz compare the accompaniment of students at Cologne and Wuppertal University and put forward an impetus for teaching at university. Mirjam Zimmermann looks at spirituality in internships. Guido Meyer and Carsten Misera give a definition of heterogeneity as a starting point of the development of the teacher habitus. Christoph Vogelsang and Ulrich Feeser-Lichterfeld contribute to a further combination of perspectives on internships. Carina Caruso and Jan Woppowa give a final summary looking especially at future tasks of the design of long-term internships in theology.Carina Caruso, Jan Woppowa (Hg.