Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure

Evidence for Strong-coupling S-wave Superconductivity in MgB2 :11B NMR Study

We have investigated a gap structure in a newly-discovered superconductor, MgB2 through the measurement of 11B nuclear spin-lattice relaxation rate, ^{11}(1/T_1). ^{11}(1/T_1) is proportional to the temperature (T) in the normal state, and decreases exponentially in the superconducting (SC) state, revealing a tiny coherence peak just below T_c. The T dependence of 1/T_1 in the SC state can be accounted for by an s-wave SC model with a large gap size of 2\Delta /k_BT_c \sim 5 which suggests to be in a strong-coupling regime.Comment: 2 pages with 1 figur

Bayesian Approach to Find a Long-Term Trend in Erratic Polarization Variations Observed in Blazars

We developed a method to separate a long-term trend from observed temporal variations of polarization in blazars using a Bayesian approach. The temporal variation of the polarization vector is apparently erratic in most blazars, while several objects occasionally exhibited systematic variations, for example, an increase of the polarization degree associated with a flare of the total flux. We assume that the observed polarization vector is a superposition of distinct two components, a long-term trend and a short-term variation component responsible for short flares. Our Bayesian model estimates the long-term trend which satisfies the condition that the total flux correlates with the polarized flux of the short-term component. We demonstrate that assumed long-term polarization components are successfully separated by the Bayesian model for artificial data. We applied this method to photopolarimetric data of OJ 287, S5 0716+714, and S2 0109+224. Simple and systematic long-term trends were obtained in OJ 287 and S2 0109+224, while no such a trend was identified in S5 0716+714. We propose that the apparently erratic variations of polarization in OJ 287 and S2 0109+224 are due to the presence of the long-term polarization component. The behavior of polarization in S5 0716+714 during our observation period implies the presence of a number of polarization components having a quite short time-scale of variations.Comment: 12 pages, 7 figures, accepted for publication in PAS

Multigap Superconductivity in Y2_2C3_3: A 13^{13}C-NMR Study

We report on the superconducting (SC) properties of Y$_2$C$_3$ with a relatively high transition temperature $T_{\rm c}=15.7$ K investigated by $^{13}$C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The $^{13}$C Knight shift has revealed a significant decrease below $T_{\rm c}$, suggesting a spin-singlet superconductivity. From an analysis of the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ in the SC state, Y$_2$C$_3$ is demonstrated to be a multigap superconductor that exhibits a large gap $2\Delta/k_{\rm B}T_{\rm c}=5$ at the main band and a small gap $2\Delta/k_{\rm B}T_{\rm c}=2$ at other bands. These results have revealed that Y$_2$C$_3$ is a unique multigap s-wave superconductor similar to MgB$_2$.Comment: 4 pages, 5 figure

Spectropolarimetric Study on Circumstellar Structure of Microquasar LS I +61deg 303

We present optical linear spectropolarimetry of the microquasar LS I +61$^{\circ}$ 303. The continuum emission is mildly polarized (up to 1.3 %) and shows almost no temporal change. We find a distinct change of polarization across the H$\alpha$ emission line, indicating the existence of polarization component intrinsic to the microquasar. We estimate the interstellar polarization (ISP) component from polarization of the H$\alpha$ line and derive the intrinsic polarization component. The wavelength dependence of the intrinsic component is well explained by Thomson scattering in equatorial disk of the Be-type mass donor. The position angle (PA) of the intrinsic polarization $\sim 25^{\circ}$ represents the rotational axis of the Be disk. This PA is nearly perpendicular to the PA of the radio jet found during quiescent phases. Assuming an orthogonal disk-jet geometry around the compact star, the rotational axis of the accretion disk is almost perpendicular to that of the Be disk. Moreover, according to the orbital parameters of the microquasar, the compact star is likely to get across the Be disk around their periastron passage. We discuss the peculiar circumstellar structure of this microquasar inferred from our observation and possible connection with its high-energy activities.Comment: 17pages, 7figures; accepted for Publications of the Astronomical Society of Japa

Antiferromagnetic phase transition in four-layered high-T_c superconductors Ba_2Ca_3Cu_4O_8(F_yO_{1-y})_2 with T_c=55-102 K: Cu- and F-NMR studies

We report on magnetic characteristics in four-layered high-T_c superconductors Ba_2Ca_3Cu_4O_8(F_yO_{1-y})_2 with apical fluorine through Cu- and F-NMR measurements. The substitution of oxygen for fluorine at the apical site increases the carrier density (N_h) and T_c from 55 K up to 102 K. The NMR measurements reveal that antiferromagnetic order, which can uniformly coexist with superconductivity, exists up to N_h = 0.15, which is somewhat smaller than N_h = 0.17 being the quantum critical point (QCP) for five-layered compounds. The fact that the QCP for the four-layered compounds moves to a region of lower carrier density than for five-layered ones ensures that the decrease in the number of CuO_2 layers makes an interlayer magnetic coupling weaker.Comment: 7 pages, 6 gigures, Submitted to J. Phys. Soc. Jp

Photopolarimetric Monitoring of Blazars in the Optical and Near-Infrared Bands with the Kanata Telescope. I. Correlations between Flux, Color, and Polarization

We report on the correlation between the flux, color and polarization variations on time scales of days--months in blazars, and discuss their universal aspects. We performed monitoring of 42 blazars in the optical and near-infrared bands from 2008 to 2010 using TRISPEC attached to the "Kanata" 1.5-m telescope. We found that 28 blazars exhibited "bluer-when-brighter" trends in their whole or a part of time-series data sets. This corresponds to 88% of objects that were observed for >10 days. Thus, our observation unambiguously confirmed that the "bluer-when-brighter" trend is common in the emission from blazar jets. This trend was apparently generated by a variation component with a constant and relatively blue color and an underlying red component. Prominent short-term flares on time scales of days--weeks tended to exhibit a spectral hysteresis; their rising phases were bluer than their decay phases around the flare maxima. In contrast to the strong flux--color correlation, the correlation of the flux and polarization degree was relatively weak; only 10 objects showed significant positive correlations. Rotations of polarization were detected only in three objects: PKS 1510-089, 3C 454.3, and PKS 1749+096, and possibly in S5 0716+714. We also investigated the dependence of the degree of variability on the luminosity and the synchrotron peak frequency, \nu_peak. As a result, we found that lower luminosity and higher \nu_peak objects had smaller variations in their amplitudes both in the flux, color, and polarization degree. Our observation suggests the presence of several distinct emitting sources, which have different variation time-scales, colors, and polarizations. We propose that the energy injection by, for example, internal shocks in relativistic shells is a major factor for blazar variations on time scales of both days and months.Comment: 39 pages, accepted for publication in PAS

Infrared/optical - X-ray simultaneous observations of X-ray flares in GRB 071112C and GRB 080506

We investigate the origin of short X-ray flares which are occasionally observed in early stages of afterglows of gamma-ray bursts (GRBs). We observed two events, GRB 071112C and GRB 080506, before the start of X-ray flares in the optical and near-infrared (NIR) bands with the 1.5-m Kanata telescope. In conjunction with published X-ray and optical data, we analyzed densely sampled light curves of the early afterglows and spectral energy distributions (SEDs) in the NIR-X-ray ranges. We found that the SEDs had a break between the optical and X-ray bands in the normal decay phases of both GRBs regardless of the model for the correction of the interstellar extinction in host galaxies of GRBs. In the X-ray flares, X-ray flux increased by 3 and 15 times in the case of GRB 071112C and 080506, respectively, and the X-ray spectra became harder than those in the normal decay phases. No significant variation in the optical-NIR range was detected together with the X-ray flares. These results suggest that the X-ray flares were associated with either late internal shocks or external shocks from two-component jets.Comment: 10 pages, 5 figures, accepted to Astronomy and Astrophysic