Bloch Theory and Quantization of Magnetic Systems

Quantizing the motion of particles on a Riemannian manifold in the presence of a magnetic field poses the problems of existence and uniqueness of quantizations. Both of them are settled since the early days of geometric quantization but there is still some structural insight to gain from spectral theory. Following the work of Asch, Over & Seiler (1994) for the 2-torus we describe the relation between quantization on the manifold and Bloch theory on its covering space for more general compact manifolds.Comment: 20 page

Direct Detection of Electroweak-Interacting Dark Matter

Assuming that the lightest neutral component in an SU(2)L gauge multiplet is the main ingredient of dark matter in the universe, we calculate the elastic scattering cross section of the dark matter with nucleon, which is an important quantity for the direct detection experiments. When the dark matter is a real scalar or a Majorana fermion which has only electroweak gauge interactions, the scattering with quarks and gluon are induced through one- and two-loop quantum processes, respectively, and both of them give rise to comparable contributions to the elastic scattering cross section. We evaluate all of the contributions at the leading order and find that there is an accidental cancellation among them. As a result, the spin-independent cross section is found to be O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio

Weyl-Underhill-Emmrich quantization and the Stratonovich-Weyl quantizer

Weyl-Underhill-Emmrich (WUE) quantization and its generalization are considered. It is shown that an axiomatic definition of the Stratonovich-Weyl (SW) quantizer leads to severe difficulties. Quantization on the cylinder within the WUE formalism is discussed.Comment: 15+1 pages, no figure

Effects of fish predation on density and size spectra of prey fish communities in lakes

Planktivorous and benthivorous fish have been documented to influence the density and size structure of their prey communities in lakes. We hypothesized that piscivorous fish modify their prey fish communities in the same way and sought to find evidence for such predation effects from a comparison across 356 lakes located in nine European ecoregions. We categorized individual fish as being either piscivore, non-piscivore or prey of piscivores, depending on species and individual size. We calculated piscivore, non-piscivore and piscivore prey densities, respectively, and fit linear abundance size spectra (SS) on lake-specific piscivore, non-piscivore and piscivore prey size distributions. Multiple linear regressions were calculated to quantify the effect of piscivore density and SS slopes on non-piscivore and piscivore prey densities and SS slopes, by accounting for potentially confounding factors arising from lake morphometry, productivity and local air temperature. Piscivore density correlated positively with piscivore prey density, but was uncorrelated to density of non-piscivores. Across a subset of 76 lakes for which SS slopes of piscivores were statistically significant, SS slopes of piscivores were uncorrelated with SS slopes of either non-piscivores or piscivore prey. However, densities of piscivores, non-piscivores or piscivore prey were a significant negative predictor of SS slopes of the respective groups. Our analyses suggest that direct predation effects by piscivorous fish on density and size structure of prey fish communities are weak in European lakes, likely caused by low predator-prey size ratios and the resulting size refuges for prey fish. In contrast, competition may substantially contribute to between-lake variability in fish density and size

Refining Humane Endpoints in Mouse Models of Disease by Systematic Review and Machine Learning-Based Endpoint Definition

Ideally, humane endpoints allow for early termination of experiments by minimizing an animal’s discomfort, distress and pain, while ensuring that scientific objectives are reached. Yet, lack of commonly agreed methodology and heterogeneity of cut-off values published in the literature remain a challenge to the accurate determination and application of humane endpoints. With the aim to synthesize and appraise existing humane endpoint definitions for commonly used physiological parameters, we conducted a systematic review of mouse studies of acute and chronic disease models, which used body weight, temperature and/or sickness scores for endpoint definition. In the second part of the study, we used previously published and unpublished data on weight, temperature and sickness scores from mouse models of sepsis and stroke and applied machine learning algorithms to assess the usefulness of this method for parameter selection and endpoint definition across models. Studies were searched for in two electronic databases (MEDLINE/Pubmed and Embase). Out of 110 retrieved full-text manuscripts, 34 studies were included. We found large intra- and inter-model variance in humane endpoint determination and application due to varying animal models, lack of standardized experimental protocols and heterogeneity of performance metrics (part 1). Machine learning models trained with physiological data and sickness severity score or modified DeSimoni neuroscore identified animals with a high risk of death at an early time point in both mouse models of stroke (male: 93.2% at 72h post-treatment; female: 93.0% at 48h post-treatment) and sepsis (96.2% at 24h post-treatment), thus demonstrating generalizability in endpoint determination across models (part 2)

Nonlinear stochastic evolution equations of second order with damping

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.Comment: This is the version of the article accepted for publication. The final publication is available at http://link.springer.co