Arithmetic of singular Enriques Surfaces

We study the arithmetic of Enriques surfaces whose universal covers are singular K3 surfaces. If a singular K3 surface X has discriminant d, then it has a model over the ring class field d. Our main theorem is that the same holds true for any Enriques quotient of X. It is based on a study on Neron-Severi groups of singular K3 surfaces. We also comment on Galois actions on divisors of Enriques surfaces.Comment: 32 pages; v2: Section 2 expanded, minor additions and edit

QSO-galaxy correlations due to weak lensing in arbitrary Friedmann-Lemaitre cosmologies

We calculate the angular cross-correlation function between background QSOs and foreground galaxies induced by the weak lensing effect of large-scale structures. Results are given for arbitrary Friedmann-Lemaitre cosmologies. The non-linear growth of density perturbations is included. Compared to the linear growth, the non-linear growth increases the correlation amplitude by about an order of magnitude in an Einstein-de Sitter universe, and by even more for lower Omega_0. The dependence of the correlation amplitude on the cosmological parameters strongly depends on the normalization of the power spectrum. The QSO-galaxy cross-correlation function is most sensitive to density structures on scales in the range (1-10) Mpc/h, where the normalization of the power spectrum to the observed cluster abundance appears most appropriate. In that case, the correlation strength changes by less than a factor of <~ 2 when Omega_0 varies between 0.3 and 1, quite independent of the value of Omega_Lambda. For Omega_0 <~ 0.3, the correlation strength increases with decreasing Omega_0, and it scales approximately linearly with the Hubble constant h.Comment: revised version, accepted by MNRA

Charge correlations in the weakly doped t-J model calculated by projection technique

We study frequency- and wave-vector dependent charge correlations in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t-J model. The ground state is expressed within a cumulant formalism which has been successfully applied to study magnetic properties of the weakly doped system. Within this approach the ground state contains independent spin-bag quasiparticles (magnetic polarons). We present results for the charge-density response function and for the optical conductivity at zero temperature for different values of t/J. They agree well with numerical results calculated by exact diagonalization techniques. The density response function for intermediate and large momenta shows a broad continuum on energy scales of order of several t whereas the optical conductivity for \omega > 0 is dominated by low energy excitations (at 1.5 - 2 J). We show that these weak-doping properties can be well understood by transitions between excited states of spin-bag quasiparticles.Comment: 10 pages, 5 figs., to appear in Europ. Phys. J.

Modularity of Calabi-Yau varieties

In this paper we discuss recent progress on the modularity of Calabi-Yau varieties. We focus mostly on the case of surfaces and threefolds. We will also discuss some progress on the structure of the L-function in connection with mirror symmetry. Finally, we address some questions and open problems.Comment: Further references adde

Sodium chloride transport of normal and dietary enlarged rat cecum in vitro

Sodium chloride transport across isolated cecum mucosa was investigated in normal rats and rats with adaptive cecum growth induced by dietary polyethylene glycol (PEG). The normal cecum absorbed CI in excess of Na with a small short-circuit current (Isc). Dietary adaptation led to large equivalent increments of Na and Cl net absorption without adequate Ise change. Inhibitor studies (mucosal amiloride 10(-3) and 10(-4) M; mucosal 4,4-diisolhiocyanatostilbene-2,2-disulfonic acid 5 x 10(-5) M;serosal furosemide 10(-3) M;serosal ouabain 10(-3) M) suggested that normal cecal NaCl absorption involves electroneutral Na/N and Cl/HCO3 exchange at the apical and Na-K-ATPase-mediated exit across the basolateral cell membrane. Dietary adaptation stimulates the loosely coupled antiports and possibly activates a small serosally located NaCl cotransport. Comparative histology showed flattening of all tissue layers and widening of crypts in PEG animals. Crypt widening may facilitate ion access to underutilized transport sites and, at least in part, explain the increased absorption of the enlarged cecum

The temperature-mass relation in magnetized galaxy clusters

We use cosmological, magneto-hydrodynamic simulations of galaxy clusters to quantify the dynamical importance of magnetic fields in these clusters. The set-up of initial magnetic field strengths at high redshifts is chosen such that observed Faraday-rotation measurements in low-redshift clusters are well reproduced in the simulations. We compute the radial profiles of the intracluster gas temperature and of the thermal and magnetic pressure in a set of clusters simulated in the framework of an Einstein-de Sitter and a low-density, spatially-flat CDM cosmological model. We find that, for a realistic range of initial magnetic field strengths, the temperature of the intracluster gas changes by less than $\approx5$.Comment: Accepted for publication in A&

This Far, No Further: Introducing Virtual Borders to Mobile Robots Using a Laser Pointer

We address the problem of controlling the workspace of a 3-DoF mobile robot. In a human-robot shared space, robots should navigate in a human-acceptable way according to the users' demands. For this purpose, we employ virtual borders, that are non-physical borders, to allow a user the restriction of the robot's workspace. To this end, we propose an interaction method based on a laser pointer to intuitively define virtual borders. This interaction method uses a previously developed framework based on robot guidance to change the robot's navigational behavior. Furthermore, we extend this framework to increase the flexibility by considering different types of virtual borders, i.e. polygons and curves separating an area. We evaluated our method with 15 non-expert users concerning correctness, accuracy and teaching time. The experimental results revealed a high accuracy and linear teaching time with respect to the border length while correctly incorporating the borders into the robot's navigational map. Finally, our user study showed that non-expert users can employ our interaction method.Comment: Accepted at 2019 Third IEEE International Conference on Robotic Computing (IRC), supplementary video: https://youtu.be/lKsGp8xtyI

Virtual Borders: Accurate Definition of a Mobile Robot's Workspace Using Augmented Reality

We address the problem of interactively controlling the workspace of a mobile robot to ensure a human-aware navigation. This is especially of relevance for non-expert users living in human-robot shared spaces, e.g. home environments, since they want to keep the control of their mobile robots, such as vacuum cleaning or companion robots. Therefore, we introduce virtual borders that are respected by a robot while performing its tasks. For this purpose, we employ a RGB-D Google Tango tablet as human-robot interface in combination with an augmented reality application to flexibly define virtual borders. We evaluated our system with 15 non-expert users concerning accuracy, teaching time and correctness and compared the results with other baseline methods based on visual markers and a laser pointer. The experimental results show that our method features an equally high accuracy while reducing the teaching time significantly compared to the baseline methods. This holds for different border lengths, shapes and variations in the teaching process. Finally, we demonstrated the correctness of the approach, i.e. the mobile robot changes its navigational behavior according to the user-defined virtual borders.Comment: Accepted on 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), supplementary video: https://youtu.be/oQO8sQ0JBR