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We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.
We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry.
The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general.
We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n(beta+1)) where nis the size of the matrix and O(n(beta)) is the cost of multiplying n x n-matrices, beta is an element of [2, 2.37286). We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.
The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
The “HPI Future SOC Lab” is a cooperation of the Hasso Plattner Institute (HPI) and industry partners. Its mission is to enable and promote exchange and interaction between the research community and the industry partners.
The HPI Future SOC Lab provides researchers with free of charge access to a complete infrastructure of state of the art hard and software. This infrastructure includes components, which might be too expensive for an ordinary research environment, such as servers with up to 64 cores and 2 TB main memory. The offerings address researchers particularly from but not limited to the areas of computer science and business information systems. Main areas of research include cloud computing, parallelization, and In-Memory technologies.
This technical report presents results of research projects executed in 2017. Selected projects have presented their results on April 25th and November 15th 2017 at the Future SOC Lab Day events.
We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.
We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions, its eigenvalues are the electromagnetic oscillation frequencies in vacuum without external sources. In general, the spectrum consists of the eigenvalue 0 with infinite multiplicity and further real discrete eigenvalues of finite multiplicity. We compute the Weyl asymptotics and study the zeta-function. We give a sharp lower eigenvalue bound for positively curved manifolds and analyze the equality case. Finally, we compute the spectrum for flat tori, round spheres, and 3-dimensional spherical space forms. Published under license by AIP Publishing.
Ribulose Monophosphate Shunt Provides Nearly All Biomass and Energy Required for Growth of E. coli
(2018)
The ribulose monophosphate (RuMP) cycle is a highly efficient route for the assimilation of reduced one-carbon compounds. Despite considerable research, the RuMP cycle has not been fully implemented in model biotechnological organisms such as Escherichia coli, mainly since the heterologous establishment of the pathway requires addressing multiple challenges: sufficient formaldehyde production, efficient formaldehyde assimilation, and sufficient regeneration of the formaldehyde acceptor, ribulose 5-phosphate. Here, by efficiently producing formaldehyde from sarcosine oxidation and ribulose 5-phosphate from exogenous xylose, we set aside two of these concerns, allowing us to focus on the particular challenge of establishing efficient formaldehyde assimilation via the RuMP shunt, the linear variant of the RuMP cycle. We have generated deletion strains whose growth depends, to different extents, on the activity of the RuMP shunt, thus incrementally increasing the selection pressure for the activity of the synthetic pathway. Our final strain depends on the activity of the RuMP shunt for providing the cell with almost all biomass and energy needs, presenting an absolute coupling between growth and activity of key RuMP cycle components. This study shows the value of a stepwise problem solving approach when establishing a difficult but promising pathway, and is a strong basis for future engineering, selection, and evolution of model organisms for growth via the RuMP cycle.
Symptoms of anxiety and depression in young athletes using the hospital anxiety and depression scale
(2018)
Elite young athletes have to cope with multiple psychological demands such as training volume, mental and physical fatigue, spatial separation of family and friends or time management problems may lead to reduced mental and physical recovery. While normative data regarding symptoms of anxiety and depression for the general population is available (Hinz and Brahler, 2011), hardly any information exists for adolescents in general and young athletes in particular. Therefore, the aim of this study was to assess overall symptoms of anxiety and depression in young athletes as well as possible sex differences. The survey was carried out within the scope of the study "Resistance Training in Young Athletes" (KINGS-Study). Between August 2015 and September 2016, 326 young athletes aged (mean +/- SD) 14.3 +/- 1.6 years completed the Hospital Anxiety and Depression Scale (HAD Scale). Regarding the analysis of age on the anxiety and depression subscales, age groups were classified as follows: late childhood (12-14 years) and late adolescence (15-18 years). The participating young athletes were recruited from Olympic weight lifting, handball, judo, track and field athletics, boxing, soccer, gymnastics, ice speed skating, volleyball, and rowing. Anxiety and depression scores were (mean +/- SD) 4.3 +/- 3.0 and 2.8 +/- 2.9, respectively. In the subscale anxiety, 22 cases (6.7%) showed subclinical scores and 11 cases (3.4%) showed clinical relevant score values. When analyzing the depression subscale, 31 cases (9.5%) showed subclinical score values and 12 cases (3.7%) showed clinically important values. No significant differences were found between male and female athletes (p >= 0.05). No statistically significant differences in the HADS scores were found between male athletes of late childhood and late adolescents (p >= 0.05). To the best of our knowledge, this is the first report describing questionnaire based indicators of symptoms of anxiety and depression in young athletes. Our data implies the need for sports medical as well as sports psychiatric support for young athletes. In addition, our results demonstrated that the chronological classification concerning age did not influence HAD Scale outcomes. Future research should focus on sports medical and sports psychiatric interventional approaches with the goal to prevent anxiety and depression as well as teaching coping strategies to young athletes.
Symptoms of anxiety and depression in young athletes using the Hospital Anxiety and Depression Scale
(2018)
Elite young athletes have to cope with multiple psychological demands such as training volume, mental and physical fatigue, spatial separation of family and friends or time management problems may lead to reduced mental and physical recovery. While normative data regarding symptoms of anxiety and depression for the general population is available (Hinz and Brahler, 2011), hardly any information exists for adolescents in general and young athletes in particular. Therefore, the aim of this study was to assess overall symptoms of anxiety and depression in young athletes as well as possible sex differences. The survey was carried out within the scope of the study "Resistance Training in Young Athletes" (KINGS-Study). Between August 2015 and September 2016, 326 young athletes aged (mean +/- SD) 14.3 +/- 1.6 years completed the Hospital Anxiety and Depression Scale (HAD Scale). Regarding the analysis of age on the anxiety and depression subscales, age groups were classified as follows: late childhood (12-14 years) and late adolescence (15-18 years). The participating young athletes were recruited from Olympic weight lifting, handball, judo, track and field athletics, boxing, soccer, gymnastics, ice speed skating, volleyball, and rowing. Anxiety and depression scores were (mean +/- SD) 4.3 +/- 3.0 and 2.8 +/- 2.9, respectively. In the subscale anxiety, 22 cases (6.7%) showed subclinical scores and 11 cases (3.4%) showed clinical relevant score values. When analyzing the depression subscale, 31 cases (9.5%) showed subclinical score values and 12 cases (3.7%) showed clinically important values. No significant differences were found between male and female athletes (p >= 0.05). No statistically significant differences in the HADS scores were found between male athletes of late childhood and late adolescents (p >= 0.05). To the best of our knowledge, this is the first report describing questionnaire based indicators of symptoms of anxiety and depression in young athletes. Our data implies the need for sports medical as well as sports psychiatric support for young athletes. In addition, our results demonstrated that the chronological classification concerning age did not influence HAD Scale outcomes. Future research should focus on sports medical and sports psychiatric interventional approaches with the goal to prevent anxiety and depression as well as teaching coping strategies to young athletes.