Calabi-Yau cones from contact reduction

We consider a generalization of Einstein-Sasaki manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable examples in seven dimensions. Then, we consider circle actions that preserve the structure, and determine conditions for the contact reduction to carry an induced structure of the same type. We apply this construction to obtain a new hypo-contact structure on S^2\times T^3.Comment: 30 pages; v2: typos corrected, presentation improved, one reference added. To appear in Ann. Glob. Analysis and Geometr

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

Retracting and seeking movements during laparoscopic goal-oriented movements. Is the shortest path length optimal?

Aims- Minimally invasive surgery (MIS) requires a high degree of eye–hand coordination from the surgeon. To facilitate the learning process, objective assessment systems based on analysis of the instruments’ motion are being developed. To investigate the influence of performance on motion characteristics, we examined goaloriented movements in a box trainer. In general, goal-oriented movements consist of a retracting and a seeking phase, and are, however, not performed via the shortest path length. Therefore, we hypothesized that the shortest path is not an optimal concept in MIS. Methods-Participants were divided into three groups (experts, residents, and novices). Each participant performed a number of one-hand positioning tasks in a box trainer. Movements of the instrument were recorded with the TrEndo tracking system. The movement from point A to B was divided into two phases: A-M (retracting) and M-B (seeking). Normalized path lengths (given in %) of the two phases were compared. Results- Thirty eight participants contributed. For the retracting phase, we found no significant difference between experts [median (range) %: 152 (129–178)], residents [164 (126–250)], and novices [168 (136–268)]. In the seeking phase, we find a significant difference (<0.001) between experts [180 (172–247)], residents [201 (163–287)], and novices [290 (244–469)]. Moreover, within each group, a significant difference between retracting and seeking phases was observed. Conclusions- Goal-oriented movements in MIS can be split into two phases: retracting and seeking. Novices are less effective than experts and residents in the seeking phase. Therefore, the seeking phase is characteristic of performance differences. Furthermore, the retracting phase is essential, because it improves safety by avoiding intermediate tissue contact. Therefore, the shortest path length, as presently used during the assessment of basic MIS skills, may be not a proper concept for analyzing optimal movements and, therefore, needs to be revised.Biomechanical EngineeringMechanical, Maritime and Materials Engineerin

The spinorial geometry of supersymmetric heterotic string backgrounds

We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\hat\nabla$ with torsion $H$, the NS$\otimes$NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups K\ltimes\bR^8 in $Spin(9,1)$, for $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\times SU(2)$ and $\{1\}$, and the Killing spinors of the timelike backgrounds have stability subgroups $G_2$, SU(3), SU(2) and $\{1\}$. The former admit a single null $\hat\nabla$-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike $\hat\nabla$-parallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian two-parameter family of Riemannian manifolds $B$ with skew-symmetric torsion. If the rotation of the null vector field vanishes, the holonomy of the connection with torsion of $B$ is contained in $K$. The spacetime of time-like backgrounds is a principal bundle $P$ with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skew-symmetric torsion. The principal bundle is equipped with a connection $\lambda$ which determines the non-horizontal part of the spacetime metric and of $H$. The curvature of $\lambda$ takes values in an appropriate Lie algebra constructed from that of $K$. In addition $dH$ has only horizontal components and contains the Pontrjagin class of $P$. We have computed in all cases the Killing spinor bilinears, expressed the fluxes in terms of the geometry and determine the field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change

Superstrings with Intrinsic Torsion

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the geometries always admit NS or type I/heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. In particular we find d=6 examples with a fibred structure which preserve N=1,2,3 supersymmetry in type II and include compact type I/heterotic geometries.Comment: 58 pages, LaTeX; v2: New section on solutions including an example with N=3 supersymmetry and discussion of heterotic compactifications. Details on conventions and references added. v3: added an explicit example of non-integrable product structure in Appendix C; some typos fixe

Postsurgical pain outcome of vertical and transverse abdominal incision: Design of a randomized controlled equivalence trial [ISRCTN60734227]

BACKGROUND: There are two ways to open the abdominal cavity in elective general surgery: vertically or transversely. Various clinical studies and a meta-analysis have postulated that the transverse approach is superior to other approaches as regards complications. However, in a recent survey it was shown that 90 % of all abdominal incisions in visceral surgery are still vertical incisions. This discrepancy between existing recommendations of clinical trials and clinical practice could be explained by the lack of acceptance of these results due to a number of deficits in the study design and analysis, subsequent low internal validity, and therefore limited external generalisability. The objective of this study is to address the issue from the patient's perspective. METHODS: This is an intraoperatively randomized controlled observer and patient-blinded two-group parallel equivalence trial. The study setting is the Department of General-, Visceral-, Trauma Surgery and Outpatient Clinic of the University of Heidelberg, Medical School. A total of 172 patients of both genders, aged over 18 years who are scheduled for an elective abdominal operation and are eligible for either a transverse or vertical incision. To show equivalence of the two approaches or the superiority of one of them from the perspective of the patient, a primary endpoint is defined: the pain experienced by the patient (VAS 0–100) on day two after surgery and the amount of analgesic required (piritramide [mg/h]). A confidence interval approach will be used for analysis. A global α-Level of 0.05 and a power of 0.8 is guaranteed, resulting in a size of 86 patients for each group. Secondary endpoints are: time interval to open and close the abdomen, early-onset complications (frequency of burst abdomen, postoperative pulmonary complications, and wound infection) and late complications (frequency of incisional hernias). Different outcome variables will be ranked by patients and surgeons to assess the relevance of possible endpoints from the patients' and surgeons' perspective. CONCLUSION: This is a randomized controlled observer and patient-blinded two-group parallel trial to answer the question if the transverse abdominal incision is equivalent to the vertical one due to the described endpoints

Suturing training in Augmented Reality: gaining proficiency in suturing skills faster

Background: Providing informative feedback and setting goals tends to motivate trainees to practice more extensively. Augmented Reality simulators retain the benefit of realistic haptic feedback and additionally generate objective assessment and informative feedback during the training. This study researched the performance curve of the adapted suturing module on the ProMIS Augmented Reality simulator. Methods: Eighteen novice participants were pretrained on the MIST-VR to become acquainted with laparoscopy. Subsequently, they practiced 16 knots on the suturing module, of which the assessment scores were recorded to evaluate the gain in laparoscopic suturing skills. The scoring of the assessment method was calculated from the “time spent in the correct area” during the knot tying and the quality of the knot. Both the baseline knot and the knot at the top of the performance curve were assessed by two independent objective observers, by means of a standardized evaluation form, to objectify the gain in suturing skills. Results: There was a statistically significant difference between the scores of the second knot (mean 72.59, standard deviation (SD) 16.28) and the top of the performance curve (mean 95.82, SD 3.05; p < 0.001, paired t-test). The scoring of the objective observers also differed significantly (mean 11.83 and 22.11, respectively; SD 3.37 and 3.89, respectively; p < 0.001) (interobserver reliability Cronbach’s alpha = 0.96). The median amount of repetitions to reach the top of the performance curve was eight, which also showed significant differences between both the assessment score (mean 88.14, SD 13.53, p < 0.001) and scoring of the objective observers of the second knot (mean 20.51, SD 4.14; p < 0.001). Conclusions: This adapted suturing module on the ProMIS Augmented Reality laparoscopic simulator is a potent tool for gaining laparoscopic suturing skills.Industrial DesignIndustrial Design Engineerin