Kepler RR Lyrae stars: beyond period doubling

We examined the complete short cadence sample of Kepler RR Lyrae stars to further investigate the recently discovered dynamical effects such as period doubling and additional modes. Here we present the findings on four stars. V450 Lyr may be a non-classical double-mode RR Lyrae star pulsating in the fundamental mode and the second overtone. In three cases we observe the interaction of three different modes. Since the period ratios are close to resonant values, we observe quasi-repetiting patterns in the pulsation cycles in the stars. These findings support the mode-resonance explanations of the Blazhko effect.Comment: 2 pages, 1 figure. Proceedings of the 301st IAU Symposium, Precision Asteroseismology, August 2013, Wroc{\l}aw. V2: small corrections to the wordin

Nonlinear dynamical analysis of the Blazhko effect with the Kepler space telescope: the case of V783 Cyg

We present a detailed nonlinear dynamical investigation of the Blazhko modulation of the Kepler RR Lyrae star V783 Cyg (KIC 5559631). We used different techniques to produce modulation curves, including the determination of amplitude maxima, the O-C diagram and the analytical function method. We were able to fit the modulation curves with chaotic signals with the global flow reconstruction method. However, when we investigated the effects of instrumental and data processing artefacts, we found that the chaotic nature of the modulation can not be proved because of the technical problems of data stitching, detrending and sparse sampling. Moreover, we found that a considerable part of the detected cycle-to-cycle variation of the modulation may originate from these effects. According to our results, even the four-year-long, unprecedented Kepler space photometry of V783 Cyg is too short for a reliable nonlinear dynamical analysis aiming at the detection of chaos from the Blazhko modulation. We estimate that two other stars could be suitable for similar analysis in the Kepler sample and in the future TESS and PLATO may provide additional candidates.Comment: 9 pages, 12 figures, accepted for publication in MNRA

Optimal Rates for the Random Fourier Feature Method

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives. While these methods show good versatility, they are computationally intensive and have poor scalability to large data as they require operations on Gram matrices. In order to mitigate this serious computational limitation, recently randomized methods have been proposed in the literature, which allow the application of fast linear algorithms. Random Fourier features (RFF) are among the most popular and widely applied constructions: they provide an easily computable, low-dimensional feature representation for shift-invariant kernels. Despite the popularity of RFFs, very little is understood theoretically about their approximation quality. In this talk, I am going to present the main ideas and results of a detailed finite-sample theoretical analysis about the approximation quality of RFFs by (i) establishing optimal (in terms of the RFF dimension, and growing set size) performance guarantees in uniform norm, and (ii) providing guarantees in Lr (1 <= r < \infty) norms. I will also propose an RFF approximation to derivatives of kernel with a theoretical study on its approximation quality

Long time-scale behavior of the Blazhko effect from rectified Kepler data

In order to benefit from the 4-year unprecedented precision of the Kepler data, we extracted light curves from the pixel photometric data of the Kepler space telescope for 15 Blazhko RR Lyrae stars. For collecting all the flux from a given target as accurately as possible, we defined tailor-made apertures for each star and quarter. In some cases the aperture finding process yielded sub-optimal result, because some flux have been lost even if the aperture contains all available pixels around the star. This fact stresses the importance of those methods that rely on the whole light curve instead of focusing on the extrema (O-C diagrams and other amplitude independent methods). We carried out detailed Fourier analysis of the light curves and the amplitude independent O-C diagram. We found 12 (80%) multiperiodically modulated stars in our sample. This ratio is much higher than previously found. Resonant coupling between radial modes, a recent theory to explain of the Blazhko effect, allows single, multiperiodic or even chaotic modulations. Among the stars with two modulations we found three stars (V355 Lyr, V366 Lyr and V450 Lyr) where one of the periods dominate in amplitude modulation, but the other period has larger frequency modulation amplitude. The ratio between the primary and secondary modulation periods is almost always very close to ratios of small integer numbers. It may indicate the effect of undiscovered resonances. Furthermore, we detected the excitation of the second radial overtone mode $f_2$ for three stars where this feature was formerly unknown. Our data set comprises the longest continuous, most precise observations of Blazhko RR Lyrae stars ever published. These data which is made publicly available will be unprecedented for years to come.Comment: 19 pages, 17 figures, accepted for publication in Astrophys. J. Suppl. Rectified data are here: http://www.konkoly.hu/KIK/data.htm

The curvature of the QCD phase transition line

We determine the curvature of the phase transition line in the mu-T plane through an analysis of various observables, including the Polyakov loop, the quark number susceptibilities and the susceptibility of the chiral condensate. The second derivative of these quantities with respect to mu was calculated. The measurements were carried out on N_T = 4,6,8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+1 flavour staggered fermion action using physical quark masses.Comment: Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, Virginia, USA. 7 pages, 6 figure

Comparison of soil erosion dynamics under extensive and intensive cultivation based on basic soil parameters

The conservation of soil and its elemental feature, t he soil fertility has not just national and agricultural business interest, since the fertile soil is an elemental part of the material turnover in the environment. The soil erosion can reach huge spatial e xtensions and starts with the most valuable part: the upper, fertile layer. So, its research is crucial for our future survival. Our studied area can be found in Gerézdpuszta at the Koppány -valley of Hungary, which is a sensitive erosion area. We sampled the upper 30 cm of soil layer in every 10 meters that resulted 32-32 point samples on the arable and on the grassland, respectively. One sample was taken under the forest as r eference. We analyzed the basic soil parameters: CaCO 3 , pH, AL-P 2 O 5 , AL-K 2 O, Kuron’s higroscopicity, SOM and the particle size di stribution was determined. Besides, we examined the connection between the given results from laboratory soil analyses and the Munsell-type and Google Earth satellite image colors. O ur results show the erosion dynamic on our sample slope, and the main differences in basic soil paramet ers between different intensities. The main indicator of soil erosion dynamic were the CaCO 3 , the SOM, AL-P 2 O 5 and the particle size distribution, where the SOM and CaCO 3 were correlate with the Munsell and Google Earth col or also

Point-contact spectroscopy of Al- and C-doped MgB2. Superconducting energy gaps and scattering studies

The two-band/two-gap superconductivity in aluminium and carbon doped MgB$_2$ has been addressed by the point-contact spectroscopy. Two gaps are preserved in all samples with $T_c's$ down to 22 K. The evolution of two gaps as a function of the critical temperature in the doped systems suggest the dominance of the band-filling effects but for the increased Al-doping the enhanced interband scattering approaching two gaps must be considered. The magnetic field dependences of the Andreev reflection excess currents as well as zero-energy density of states determined from the experimental data are used to analyze the intraband scattering. It is shown, that while the C-doping increases the intraband scattering in the $\pi$-band more rapidly then in the $\sigma$ band, the Al-doping does not change their relative weight.Comment: 8 pages, incl. 6 figure