Geometry of Complexity in Conformal Field Theory

We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories with a view that they provide the simplest setting to find a gravity dual to complexity. Our work pursues a geometric understanding of complexity of conformal transformations and embeds Fubini-Study state complexity and direct counting of stress tensor insertion in the relevant circuits in a unified mathematical language. In the former case, we iteratively solve the emerging integro-differential equation for sample optimal circuits and discuss the sectional curvature of the underlying geometry. In the latter case, we recognize that optimal circuits are governed by Euler-Arnold type equations and discuss relevant results for three well-known equations of this type in the context of complexity.Comment: 5+2 pages, an extended version is available as arXiv:2007.11555 v3: title change, added appendix, 1 figur

Conformal field theory complexity from Euler-Arnold equations

Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and operator complexity in the universal sector of their energy-momentum tensor. The unifying conceptual ideas are Euler-Arnold equations and their integro-differential generalization, which guarantee well-posedness of the optimization problem between two generic states or transformations of interest. The present work provides an in-depth discussion of the results reported in arXiv:2005.02415 and techniques used in their derivation. Among the most important topics we cover are usage of differential regularization, solution of the integro-differential equation describing Fubini-Study state complexity and probing the underlying geometry.Comment: 31 pages + appendicies, 2 figures, extended version of arXiv:2005.02415 v2: added references and minor improvement

COMPARISON OF FOOT-STRETCHER FORCE PROFILES BETWEEN ON-WATER AND ERGOMETER ROWING

The purpose of this study was to compare the reaction forces at the foot stretcher of a Concept2 ergometer with and without slides to those of the boat in single scull rowing. Four male elite rowers were tested at rates of 20 and 30 strokes per minute on the ergometer with and without slides as well as in a single scull. The coefficient of multiple determination showed a high consistency about five time-normalised successive strokes in all conditions (about 0.99). Cross-correlation calculations between on-water force curves and force curves obtained under both ergometer conditions showed higher similarities for the ergometer on slides

Recognising human activity in free-living using multiple body-worn accelerometers

Objectives: Recognising human activity is very useful for an investigator about a patient's behaviour and can aid in prescribing activity in future recommendations. The use of body worn accelerometers has been demonstrated to be an accurate measure of human activity, however research looking at the use of multiple body worn accelerometers in a free living environment to recognise a wide range of activities is not evident. This study aimed to successfully recognise activity and sub-category activity types through the use of multiple body worn accelerometers in a free living environment. Method: Ten participants (Age = 23.1 ± 1.7 years, height =171.0 ± 4.7 cm, mass = 78.2 ± 12.5 Kg) wore nine body-worn accelerometers for a day of free living. Activity type was identified through the use of a wearable camera, and sub category activities were quantified through a combination of free-living and controlled testing. A variety of machine learning techniques consisting of pre-processing algorithms, feature and classifier selections were tested, accuracy and computing time were reported. Results: A fine k-nearest neighbour classifier with mean and standard deviation features of unfiltered data reported a recognition accuracy of 97.6%. Controlled and free-living testing provided highly accurate recognition for sub-category activities (>95.0%). Decision tree classifiers and maximum features demonstrated to have the lowest computing time. Conclusions: Results show recognition of activity and sub-category activity types is possible in a free living environment through the use of multiple body worn accelerometers. This method can aid in prescribing recommendations for activity and sedentary periods for healthy living

Professionalisierung als Programm. Vom Versuch, durch die rekursive Anwendung von Gestaltungsprinzipien eine Leerstelle der Hochschuldidaktik zu füllen

Der Bericht beschreibt als Zwischenergebnis die Planung eines didaktischen Designs zur Förderung der individuellen Kompetenzentwicklung Lehrender in der wissenschaftlichen Weiterbildung. Am Beispiel der Entwicklung von Kompetenzen zur transferförderlichen Lehre soll mittels eines Designexperiments modellhaft gezeigt werden, wie dies unter den gegebenen Rahmenbedingen der Weiterbildung an Hochschulen gelingen und als akzeptierte Unterstützungsleistung etabliert werden könnte

ANALYSIS OF METHODS FOR ASSESSING THE AIMING PROCESS IN BIATHLON SHOOTING

In rifle shooting disciplines coaches and athletes are interested in the motion of the rifle just before and immediately after shooting. Normally, commercial laser systems (e.g. Noptel, Finland) are used to measure and store the hit point of the shot and the on-target trajectory of the alignment of the weapon. A major drawback of this method lies in the necessity of attaching the laser device to the rifle. The purpose of this study was to analyse the usefulness of a video-based system developed by Baca & Kornfeind (2006), which is able to track the 2D-movement of the muzzle of the weapon automatically. The results show considerable correspondence of the on-target-trajectory and the 2D-movement of the muzzle, in particular in vertical direction. However, translation movements of the shoulder during aiming, which are rather difficult to diagnose, may cause differences in the horizontal plane