Keywords of written reflection - a comparison between reflective and descriptive datasets

This study investigates reflection keywords by contrasting two datasets, one of reflective sentences and another of descriptive sentences. The log-likelihood statistic reveals several reflection keywords that are discussed in the context of a model for reflective writing. These keywords are seen as a useful building block for tools that can automatically analyse reflection in texts

An architecture for the automated detection of textual indicators of reflection

Manual annotation of evidence of reflection expressed in texts is time consuming, especially as fine-grained models of reflection require extensive training of coders, otherwise resulting in low inter-coder reliability. Automated reflection detection provides a solution to this problem. Within this paper, a new basic architecture for detecting evidence of reflection is proposed that allows for automated marking up of written accounts of certain, observable elements of reflection. Furthermore, three promising example annotators of elements of reflection are identified, implemented, and demonstrated: detecting reflective keywords, premise and conclusions of arguments, and questions. It appears that automated detection of reflections bears the potential to support learning with technology at least on three levels: it can foster creating awareness of the reflectivity of own writings, it can help in becoming aware of reflective writings of others, and it can make visible reflective writings of learning networks as a whole

A Counterexample to a Conjecture about Positive Scalar Curvature

Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg conjecture given in Schick: "A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture".Comment: v1: 4 pages, AMS-LaTeX; v2: small changes in presentation, typos corrected, v3: comment added, to appear in Proc AM

Completeness of compact Lorentzian manifolds with Abelian holonomy

We address the problem of finding conditions under which a compact Lorentzian manifold is geodesically complete, a property, which always holds for compact Riemannian manifolds. It is known that a compact Lorentzian manifold is geodesically complete if it is homogeneous, or has constant curvature, or admits a time-like conformal vector field. We consider certain Lorentzian manifolds with Abelian holonomy, which are locally modelled by the so called pp-waves, and which, in general, do not satisfy any of the above conditions. %the condition that their curvature sends vectors that are orthogonal to the vector field to a multiple of the vector field. We show that compact pp-waves are universally covered by a vector space, determine the metric on the universal cover, and prove that they are geodesically complete. Using this, we show that every Ricci-flat compact pp-wave is a plane wave.Comment: 30 pages, comments welcome; version 2 revised, references and a new result about compact, Ricci-flat pp-waves added. Version 3 is substantially revised with new title. We added Corollary 2 about completeness of indecomposable, compact locally symmetric Lorentzian manifold