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Thousands of RR Lyrae stars have been observed by the \textit{Kepler} space telescope so far. We developed a photometric pipeline tailored to the light variations of these stars, called the Extended Aperture Photometry (EAP). We present the comparison of our photometric solutions for Campaigns 0 through 6 with the other pipelines available, e.g., SAP/PDCSAP, K2P2, EVEREST, and others. We focus on the problems caused by instrumental effects and the detectability of the low-amplitude additional modes., Comment: 5 pages, 3 figures, to be published in the proceedings of "The RR Lyrae 2017 Conference", Niepolomice, Poland, 17-21 September 2017

The second data release of the Gaia mission includes an advance catalog of variable stars. The classification of these stars are based on sparse photometry from the first 22 months of the mission. We set out to investigate the purity and completeness of the all-sky Gaia classification results with the help of the continuous light curves of the observed targets from the Kepler and K2 missions, focusing specifically on RR Lyrae and Cepheid pulsators, outside the Galactic Bulge region. We crossmatched the Gaia identifications with the observations collected by the Kepler space telescope. We inspected the light curves visually, then calculated the relative Fourier coefficients and period ratios for the single- and double-mode K2 RR Lyrae stars to further classify them. We identified 1443 and 41 stars classified as RR Lyrae or Cepheid variables in Gaia DR2 in the targeted observations of the two missions and 263 more RR Lyre targets in the Full-Frame Images (FFI) of the original mission. We provide the crossmatch of these sources. We conclude that the RR Lyrae catalog has a completeness between 70-78%, and provide a purity estimate between 92-98% (targeted observations) with lower limits of 75% (FFI stars) and 51% (K2 worst-case scenario). The low number of Cepheids prevents us from drawing detailed conclusions but the purity of the DR2 sample is estimated to be around 66%., Comment: 15 pages, 12 figures, 10 tables, accepted into the Gaia DR2 Special Issue in A&A. V1: submitted version, v2: accepted version. Lists available at http://konkoly.hu/~lmolnar/gaiakepler_datafiles_R1.zip

We highlight the power of the Gaia DR2 in studying many fine structures of the Hertzsprung-Russell diagram (HRD). Gaia allows us to present many different HRDs, depending in particular on stellar population selections. We do not aim here for completeness in terms of types of stars or stellar evolutionary aspects. Instead, we have chosen several illustrative examples. We describe some of the selections that can be made in Gaia DR2 to highlight the main structures of the Gaia HRDs. We select both field and cluster (open and globular) stars, compare the observations with previous classifications and with stellar evolutionary tracks, and we present variations of the Gaia HRD with age, metallicity, and kinematics. Late stages of stellar evolution such as hot subdwarfs, post-AGB stars, planetary nebulae, and white dwarfs are also analysed, as well as low-mass brown dwarf objects. The Gaia HRDs are unprecedented in both precision and coverage of the various Milky Way stellar populations and stellar evolutionary phases. Many fine structures of the HRDs are presented. The clear split of the white dwarf sequence into hydrogen and helium white dwarfs is presented for the first time in an HRD. The relation between kinematics and the HRD is nicely illustrated. Two different populations in a classical kinematic selection of the halo are unambiguously identified in the HRD. Membership and mean parameters for a selected list of open clusters are provided. They allow drawing very detailed cluster sequences, highlighting fine structures, and providing extremely precise empirical isochrones that will lead to more insight in stellar physics. Gaia DR2 demonstrates the potential of combining precise astrometry and photometry for large samples for studies in stellar evolution and stellar population and opens an entire new area for HRD-based studies., Comment: Published in the A&A Gaia Data Release 2 special issue. Tables 2 and A.4 corrected. Tables available at http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/616/A10

The Gaia Data Release 2 (DR2): we summarise the processing and results of the identification of variable source candidates of RR Lyrae stars, Cepheids, long period variables (LPVs), rotation modulation (BY Dra-type) stars, delta Scuti & SX Phoenicis stars, and short-timescale variables. In this release we aim to provide useful but not necessarily complete samples of candidates. The processed Gaia data consist of the G, BP, and RP photometry during the first 22 months of operations as well as positions and parallaxes. Various methods from classical statistics, data mining and time series analysis were applied and tailored to the specific properties of Gaia data, as well as various visualisation tools. The DR2 variability release contains: 228'904 RR Lyrae stars, 11'438 Cepheids, 151'761 LPVs, 147'535 stars with rotation modulation, 8'882 delta Scuti & SX Phoenicis stars, and 3'018 short-timescale variables. These results are distributed over a classification and various Specific Object Studies (SOS) tables in the Gaia archive, along with the three-band time series and associated statistics for the underlying 550'737 unique sources. We estimate that about half of them are newly identified variables. The variability type completeness varies strongly as function of sky position due to the non-uniform sky coverage and intermediate calibration level of this data. The probabilistic and automated nature of this work implies certain completeness and contamination rates which are quantified so that users can anticipate their effects. This means that even well-known variable sources can be missed or misidentified in the published data. The DR2 variability release only represents a small subset of the processed data. Future releases will include more variable sources and data products; however, DR2 shows the (already) very high quality of the data and great promise for variability studies., Comment: 21 pages, 10 figures, 5 tables, accepted by Astronomy & Astrophysics, added several language corrections, and expanded Gaia archive query examples

The second Gaia data release is expected to contain data products from about 22 months of observation. Based on these data, we aim to provide an advance publication of a full-sky Gaia map of RR Lyrae stars. Although comprehensive, these data still contain a significant fraction of sources which are insufficiently sampled for Fourier series decomposition of the periodic light variations. The challenges in the identification of RR Lyrae candidates with (much) fewer than 20 field-of-view transits are described. General considerations of the results, their limitations, and interpretation are presented together with prospects for improvement in subsequent Gaia data releases., Comment: 5 pages, 1 figure, Proceedings of the RR Lyrae 2017 Conference (Revival of the Classical Pulsators: from Galactic Structure to Stellar Interior Diagnostics), to be published in the Proceedings of the Polish Astronomical Society

In this paper we report the discovery of 35 new RR Lyrae variables. These stars were found by a special searching technique. We crossmatched the catalog of the PanSTARRS (PS) sky survey with K2 space photometry data to the validate candidates. It turns out that this technique can find eclipsing binaries as well., Comment: 2 pages, to be published in the proceedings of "The RR Lyrae 2017 Conference", Niepolomice, Poland, 17-21 September 2017

Space-based photometric missions revealed a surprising abundance of millimagnitude-level additional modes in RR Lyrae stars. The modes that appear in the modulated fundamental-mode (RRab) stars can be ordered into four major categories. Here we present the distribution of these groups in the Petersen diagram, and discuss their characteristics and connections to additional modes observed in other RR Lyrae stars., Comment: 4 pages, 4 figures, proceedings of the Joint TASC2-KASC9-SPACEINN-HELAS8 Conference "Seismology of the Sun and the Distant Stars 2016", to be published in EPJ WoC

Bitcoin is a digital currency and electronic payment system operating over a peer-to-peer network on the Internet. One of its most important properties is the high level of anonymity it provides for its users. The users are identified by their Bitcoin addresses, which are random strings in the public records of transactions, the blockchain. When a user initiates a Bitcoin-transaction, his Bitcoin client program relays messages to other clients through the Bitcoin network. Monitoring the propagation of these messages and analyzing them carefully reveal hidden relations. In this paper, we develop a mathematical model using a probabilistic approach to link Bitcoin addresses and transactions to the originator IP address. To utilize our model, we carried out experiments by installing more than a hundred modified Bitcoin clients distributed in the network to observe as many messages as possible. During a two month observation period we were able to identify several thousand Bitcoin clients and bind their transactions to geographical locations.

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces with virtual quadratic spaces, we can unify certain enumerative properties of finite fields, without distinguishing between even and odd characteristics, such as the number of non-isomorphic non-degenerate quadratic forms, and the order of groups of isometries.

We analysed the light curve of four, apparently extremely metal-rich fundamental-mode RR Lyrae stars. We identified two stars, MT Tel and ASAS J091803-3022.6 as RRc (first-overtone) pulsators that were misclassified as RRab ones in the ASAS survey. In the case of the other two stars, V397 Gem and ASAS J075127-4136.3, we could not decide conclusively, as they are outliers in the period-Fourier-coefficient space from the loci of both classes, but their photometric metallicities also favour the RRc classification., Comment: 5 pages, 2 figures, published in IBVS: http://ibvs.konkoly.hu/cgi-bin/IBVS?6175