Cooperative Games on Antimatroids

AMS classification: 90D12;game theory;cooperative games;antimatroids

The automatic calibration of Korean VLBI Network data

The calibration of Very Long Baseline Interferometry (VLBI) data has long been a time consuming process. The Korean VLBI Network (KVN) is a simple array consisting of three identical antennas. Because four frequencies are observed simultaneously, phase solutions can be transferred from lower frequencies to higher frequencies in order to improve phase coherence and hence sensitivity at higher frequencies. Due to the homogeneous nature of the array, the KVN is also well suited for automatic calibration. In this paper we describe the automatic calibration of single-polarisation KVN data using the KVN Pipeline and comparing the results against VLBI data that has been manually reduced. We find that the pipelined data using phase transfer produces better results than a manually reduced dataset not using the phase transfer. Additionally we compared the pipeline results with a manually reduced phase-transferred dataset and found the results to be identical

Ejection of Double knots from the radio core of PKS 1510--089 during the strong gamma-ray flares in 2015

PKS 1510--089 is a bright and active $\gamma$-ray source that showed strong and complex $\gamma$-ray flares in mid-2015 during which the Major Atmospheric Gamma Imaging Cherenkov telescopes detected variable very high energy (VHE; photon energies $>$100 GeV) emission. We present long-term multi-frequency radio, optical, and $\gamma$-ray light curves of PKS 1510--089 from 2013 to 2018, and results of an analysis of the jet kinematics and linear polarization using 43 GHz Very Long Baseline Array data observed between late 2015 and mid-2017. We find that a strong radio flare trails the $\gamma$-ray flares in 2015, showing an optically thick spectrum at the beginning and becoming optically thin over time. Two laterally separated knots of emission are observed to emerge from the radio core nearly simultaneously during the $\gamma$-ray flares. We detect an edge-brightened linear polarization near the core in the active jet state in 2016, similar to the quiescent jet state in 2008--2013. These observations indicate that the $\gamma$-ray flares may originate from compression of the knots by a standing shock in the core and the jet might consist of multiple complex layers showing time-dependent behavior, rather than of a simple structure of a fast jet spine and a slow jet sheath.Comment: 11 pages, 7 figures, To appear in Ap

Axiomatizations of the Shapley Value for Cooperative Games on Antimatroids

AMS classification: 91A12;cooperative games;antimatroid;permission structure;Shapley value

The 15-43 GHz parsec-scale circular polarization of 41 active galactic nuclei

We present the results of parsec-scale circular-polarization measurements based on Very Long Baseline Array data for a number of radio-bright, core-dominated active galactic nuclei obtained simultaneously at 15, 22 and 43 GHz. The degrees of circular polarization m(c) for the Very Long Baseline Interferometry (VLBI) core region at 15 GHz are similar to the values reported earlier at this wavelength, with typical values of a few tenths of a per cent. We find that mc as often rises as falls with increasing frequency between 15 and 22 GHz, while the degree of circular polarization at 43 GHz is in all cases higher than at 22 and 15 GHz. This behaviour seems contrary to expectations, since the degree of circular polarization from both synchrotron radiation and the Faraday conversion of linear to circular polarization - the two main mechanisms considered thus far in the literature - should decrease towards higher frequencies if the source is homogeneous. The increase in mc at 43 GHz may be due to the presence of regions of both positive and negative circular polarization with different frequency dependences ( but decreasing with increasing frequency) on small scales within the core region; alternatively, it may be associated with the intrinsic inhomogeneity of a Blandford-Konigl like jet. In several objects, the detected circular polarization appears to be near, but not coincident with, the core, although further observations are needed to confirm this. We find several cases of changes in sign with frequency, most often between 22 and 43 GHz. We find tentative evidence for transverse structure in the circular polarization of 1055+018 and 1334-127, that is consistent with their being generated by either the synchrotron mechanism or the Faraday conversion in a helical magnetic field. Our results confirm the earlier finding that the sign of the circular polarization at a given observing frequency is generally consistent across epochs separated by several years or more, suggesting stability of the magnetic-field orientation in the innermost jets

An Axiomatization of the Banzhaf Value for Cooperative Games on Antimatroids

Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the restricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Banzhaf value on antimatroids by conditions on the cooperative game and the structure determined by the antimatroid. The set of given axioms generalize the axiomatizations given for the Banzhaf permission values. We also give an axomatization of the restricted Banzhaf value for the smaller class of poset antimatroids. Finally, we apply the above results to auction situations