Homotopy theory of Hopf Galois extensions

We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.Comment: 28 page

Light Propagation in Arbitrary Spacetimes and the Gravitational Lens Approximation

We reformulate the transport equation which determines the size, shape and orientation of infinitesimal light beams in arbitrary spacetimes. The behaviour of such light beams near vertices and conjugate points is investigated, with special attention to the singular behaviour of the optical scalars. We then specialize the general transport equation to the case of an approximate metric of an inhomogeneous universe, which is a Friedmann metric `on average' with superposed isolated weak matter inhomogeneities. In a series of well-defined approximations, the equations of gravitational lens theory are derived. Finally, we derive a relative optical focusing equation which describes the focusing of light beams relative to the case that the beam is unaffected by matter inhomogeneities in the universe, from which it follows immediately that no beam can be focused less than one which is unaffected by matter clumps, before it propagates through its first conjugate point.Comment: 31 pages, uuencoded compressed postscript; preprint MPA 78

3DMOTFormer: Graph Transformer for Online 3D Multi-Object Tracking

Tracking 3D objects accurately and consistently is crucial for autonomous vehicles, enabling more reliable downstream tasks such as trajectory prediction and motion planning. Based on the substantial progress in object detection in recent years, the tracking-by-detection paradigm has become a popular choice due to its simplicity and efficiency. State-of-the-art 3D multi-object tracking (MOT) approaches typically rely on non-learned model-based algorithms such as Kalman Filter but require many manually tuned parameters. On the other hand, learning-based approaches face the problem of adapting the training to the online setting, leading to inevitable distribution mismatch between training and inference as well as suboptimal performance. In this work, we propose 3DMOTFormer, a learned geometry-based 3D MOT framework building upon the transformer architecture. We use an Edge-Augmented Graph Transformer to reason on the track-detection bipartite graph frame-by-frame and conduct data association via edge classification. To reduce the distribution mismatch between training and inference, we propose a novel online training strategy with an autoregressive and recurrent forward pass as well as sequential batch optimization. Using CenterPoint detections, our approach achieves 71.2% and 68.2% AMOTA on the nuScenes validation and test split, respectively. In addition, a trained 3DMOTFormer model generalizes well across different object detectors. Code is available at: https://github.com/dsx0511/3DMOTFormer.Comment: 17 pages, 8 figures, accepted by ICCV202

Education and mental health: Do psychosocial resources matter?

Prevalence rates for mental health problems are higher when an individual's socioeconomic status (SES) is low, but the underlying mechanisms are not clearly understood. We investigated associations between education as indicator for SES and depressive symptoms as well as positive mental health (PMH). Moreover, we hypothesized that low education is associated with a lack of psychosocial resources and more daily hassles, which in turn mediate the relationships between education and mental health. In a German representative sample (N = 7937), we cross-sectionally first examined whether a person's educational level was associated with depressive symptoms and PMH. Educational level was defined as the highest academic qualification achieved. Second, we investigated whether also sense of control, resilience, delay of gratification, cultural activity and daily hassles followed gradients along the educational level. Third, we investigated whether they mediated the relationship between education and mental health. Results showed that depressive symptoms measured by items from the DASS-42 depression subscale were more prevalent for persons with a low educational level, PMH operationalized by the Positive Mental Health Scale was equally distributed, and all psychosocial characteristics followed the gradient of educational level. In addition, the group with a high school diploma was particularly burdened. Structural equation modeling indicated that the associations between education and mental health were mediated by all psychosocial characteristics and daily hassles, apart from the delay of gratification. In the group with the lowest educational level the model fit indices for depressive symptoms and PMH were acceptable (χ2 = 10007.243 (627), CFI = 0.869, RMSEA = 0.04 (90% CI [0.04, 0.04], SRMR = 0.05; and χ2 = 12779.968 (741), CFI = 0.86, RMSEA = 0.05 (90% CI [0.05, 0.05], SRMR = 0.05), respectively). The effect size Pm refers to the proportion of the total effect that is mediated by one or more variables (“M”), and the effect size of all indirect effects in the model for depressive symptoms was Pm = .80 and for PMH it was Pm = .68. The results support our hypotheses that low education is associated with less psychosocial resources, which in turn serve together with daily hassles as pathways between education and depressive symptoms as well as PMH. Building on these findings, longitudinal studies are necessary to investigate causality

Mapping Submerged Aquatic Vegetation Using RapidEye Satellite Data: The Example of Lake Kummerow (Germany)

Submersed aquatic vegetation (SAV) is sensitive to changes in environmental conditions and plays an important role as a long-term indictor for the trophic state of freshwater lakes. Variations in water level height, nutrient condition, light availability and water temperature affect the growth and species composition of SAV. Detailed information about seasonal variations in littoral bottom coverage are still unknown, although these effects are expected to mask climate change-related long-term changes, as derived by snapshots of standard monitoring methods included in the European Water Framework Directive. Remote sensing offers concepts to map SAV quickly, within large areas, and at short intervals. This study analyses the potential of a semi-empirical method to map littoral bottom coverage by a multi-seasonal approach. Depth-invariant indices were calculated for four Atmospheric & Topographic Correction (ATCOR2) atmospheric corrected RapidEye data sets acquired at Lake Kummerow, Germany, between June and August 2015. RapidEye data evaluation was supported by in situ measurements of the diffuse attenuation coefficient of the water column and bottom reflectance. The processing chain was able to differentiate between SAV and sandy sediment. The successive increase of SAV coverage from June to August was correctly monitored. Comparisons with in situ and Google Earth imagery revealed medium accuracies (kappa coefficient = 0.61, overall accuracy = 72.2%). The analysed time series further revealed how water constituents and temporary surface phenomena such as sun glint or algal blooms influence the identification success of lake bottom substrates. An abundant algal bloom biased the interpretability of shallow water substrate such that a differentiation of sediments and SAV patches failed completely. Despite the documented limitations, mapping of SAV using RapidEye seems possible, even in eutrophic lakes

Stress Resistance and Longevity Are Not Directly Linked to Levels of Enzymatic Antioxidants in the Ponerine Ant Harpegnathos saltator

BACKGROUND: The molecular mechanisms of variations in individual longevity are not well understood, even though longevity can be increased substantially by means of diverse experimental manipulations. One of the factors supposed to be involved in the increase of longevity is a higher stress resistance. To test this hypothesis in a natural system, eusocial insects such as bees or ants are ideally suited. In contrast to most other eusocial insects, ponerine ants show a peculiar life history that comprises the possibility to switch during adult life from a normal worker to a reproductive gamergate, therewith increasing their life expectancy significantly. RESULTS: We show that increased resistance against major stressors, such as reactive oxygen species and infection accompanies the switch from a life-history trait with normal lifespan to one with a longer life expectancy. A short period of social isolation was sufficient to enhance stress resistance of workers from the ponerine ant species Harpegnathos saltator significantly. All ant groups with increased stress resistances (reproducing gamergates and socially isolated workers) have lower catalase activities and glutathione levels than normal workers. Therewith, these ants resemble the characteristics of the youngest ants in the colony. CONCLUSIONS: Social insects with their specific life history including a switch from normal workers to reproducing gamergates during adult life are well suited for ageing research. The regulation of stress resistance in gamergates seemed to be modified compared to foraging workers in an economic way. Interestingly, a switch towards more stress resistant animals can also be induced by a brief period of social isolation, which may already be associated with a shift to a reproductive trajectory. In Harpegnathos saltator, stress resistances are differently and potentially more economically regulated in reproductive individuals, highlighting the significance of reproduction for an increase in longevity in social insects. As already shown for other organisms with a long lifespan, this trait is not directly coupled to higher levels of enzymatic and non-enzymatic antioxidants