Potential one-forms for hyperk\"ahler structures with torsion

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure

Supersymmetric heterotic string backgrounds

We present the main features of the solution of the gravitino and dilatino Killing spinor equations derived in hep-th/0510176 and hep-th/0703143 which have led to the classification of geometric types of all type I backgrounds. We then apply these results to the supersymmetric backgrounds of the heterotic string. In particular, we solve the gaugino Killing spinor equation together with the other two Killing spinor equations of the theory. We also use our results to classify all supersymmetry conditions of ten-dimensional gauge theory.Comment: 12 pages, v2: gauge theory applications are stressed and references adde

Highest weight modules over quantum queer Lie superalgebra U_q(q(n))

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for $U_q(q(n))$-modules in the category $O_q^{\geq 0}$.Comment: Definition 1.5 and Definition 6.1 are changed, and a remark is added in the new versio

Potentials for hyper-Kahler metrics with torsion

We prove that locally any hyper-K\"ahler metric with torsion admits an HKT potential.Comment: 9 page

The odd side of torsion geometry

We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of K\"ahler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is shown to admit such a structure; in this case the structure is left-invariant and has closed torsion form. We illustrate the relation between ST structures and other generalizations of Sasaki geometry, and explain how some standard constructions in Sasaki geometry can be adapted to this setting. In particular, we relate the ST structure to a KT structure on the space of leaves, and show that both the cylinder and the cone over an ST manifold are KT, although only the cylinder behaves well with respect to closedness of the torsion form. Finally, we introduce a notion of `G-moment map'. We provide criteria based on equivariant cohomology ensuring the existence of these maps, and then apply them as a tool for reducing ST structures.Comment: 34 pages; v2: added a small generalization (Proposition 3.6) of the cone construction; two references added. To appear on Ann. Mat. Pura App

Instructor feedback versus no instructor feedback on performance in a laparoscopic virtual reality simulator: a randomized educational trial

<p>Abstract</p> <p>Background</p> <p>Several studies have found a positive effect on the learning curve as well as the improvement of basic psychomotor skills in the operating room after virtual reality training. Despite this, the majority of surgical and gynecological departments encounter hurdles when implementing this form of training. This is mainly due to lack of knowledge concerning the time and human resources needed to train novice surgeons to an adequate level. The purpose of this trial is to investigate the impact of instructor feedback regarding time, repetitions and self-perception when training complex operational tasks on a virtual reality simulator.</p> <p>Methods/Design</p> <p>The study population consists of medical students on their 4^thto 6^thyear without prior laparoscopic experience. The study is conducted in a skills laboratory at a centralized university hospital. Based on a sample size estimation 98 participants will be randomized to an intervention group or a control group. Both groups have to achieve a predefined proficiency level when conducting a laparoscopic salpingectomy using a surgical virtual reality simulator. The intervention group receives standardized instructor feedback of 10 to 12 min a maximum of three times. The control group receives no instructor feedback. Both groups receive the automated feedback generated by the virtual reality simulator. The study follows the CONSORT Statement for randomized trials. Main outcome measures are time and repetitions to reach the predefined proficiency level on the simulator. We include focus on potential sex differences, computer gaming experience and self-perception.</p> <p>Discussion</p> <p>The findings will contribute to a better understanding of optimal training methods in surgical education.</p> <p>Trial Registration</p> <p><a href="http://www.clinicaltrials.gov/ct2/show/NCT01497782">NCT01497782</a></p