Hopf Categories

We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation Theor

Supersymmetric Corrections to the Threshold Production of Top Quark Pairs

In this paper we investigate supersymmetric effects to the threshold production cross section of top quark pairs in electron positron annihilation. In particular, we consider the complete one-loop corrections from the strong and weak sector of the Minimal Supersymmetric Standard Model.Comment: 18 pages, 7 figure

p3d: a general data-reduction tool for fiber-fed integral-field spectrographs

The reduction of integral-field spectrograph (IFS) data is demanding work. Many repetitive operations are required in order to convert raw data into, typically a large number of, spectra. This effort can be markedly simplified through the use of a tool or pipeline, which is designed to complete many of the repetitive operations without human interaction. Here we present our semi-automatic data-reduction tool p3d that is designed to be used with fiber-fed IFSs. Important components of p3d include a novel algorithm for automatic finding and tracing of spectra on the detector, and two methods of optimal spectrum extraction in addition to standard aperture extraction. p3d also provides tools to combine several images, perform wavelength calibration and flat field data. p3d is at the moment configured for four IFSs. In order to evaluate its performance we have tested the different components of the tool. For these tests we used both simulated and observational data. We demonstrate that for three of the IFSs a correction for so-called cross-talk due to overlapping spectra on the detector is required. Without such a correction spectra will be inaccurate, in particular if there is a significant intensity gradient across the object. Our tests showed that p3d is able to produce accurate results. p3d is a highly general and freely available tool. It is easily extended to include improved algorithms, new visualization tools and support for additional instruments. The program code can be downloaded from the p3d-project web site http://p3d.sourceforge.netComment: 18 pages, 15 figures, 3 tables, accepted for publication in A&

Complex collective states in a one-dimensional two-atom system

We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We restrict our attention to states where one atom is excited and the other is in the ground state, in symmetric or anti-symmetric combinations. We obtain exact collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, leading to long-range cooperative effects. The decay rates and the energy oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates will either decrease, vanish or increase as compared with the one-atom decay rate. We have sub- and super-radiance at periodic intervals. Our model may be used to study two-cavity electron wave-guides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.

On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Serotonin attenuates feedback excitation onto O-LM interneurons

The serotonergic system is a subcortical neuromodulatory center that controls cortical information processing in a state-dependent manner. In the hippocampus, serotonin (5-HT) is released by ascending serotonergic fibers from the midbrain raphe nuclei, thereby mediating numerous modulatory functions on various neuronal subtypes. Here, we focus on the neuromodulatory effects of 5-HT on GABAergic inhibitory oriens lacunosum-moleculare (O-LM) cells in the hippocampal area CA1 of the rat. These interneurons are thought to receive primarily local excitatory input and are, via their axonal projections to stratum lacunosum-moleculare, ideally suited to control entorhinal cortex input. We show that 5-HT reduces excitatory glutamatergic transmission onto O-LM interneurons. By means of paired recordings from synaptically connected CA1 pyramidal cells and O-LM interneurons we reveal that this synapse is modulated by 5-HT. Furthermore, we demonstrate that the reduction of glutamatergic transmission by serotonin is likely to be mediated via a decrease of calcium influx into presynaptic terminals of CA1 pyramidal cells. This modulation of excitatory synaptic transmission onto O-LM interneurons by 5-HT might be a mechanism to vary the activation of O-LM interneurons during ongoing network activity and serve as a brain state-dependent switch gating the efficiency of entorhinal cortex input to CA1 pyramidal neurons

MAPPING THE SURROUNDINGS AS A REQUIREMENT FOR AUTONOMOUS DRIVING

Motivated by the hype around driverless cars and the challenges of the sensor integration and data processing, this paper presents a model for using a XBox One Microsoft Kinect stereo camera as sensor for mapping the surroundings. Today, the recognition of the environment of the car is mostly done by a mix of sensors like LiDAR, RADAR and cameras. In the case of the outdoor delivery challenge Robotour 2016 with model cars in scale 1:5, it is our goal to solve the task with one camera only. To this end, a three-stage approach was developed. The test results show that our approach can detect and locate objects at a range of up to eight meters in order to incorporate them as barriers in the navigation process