Bayesian threshold selection for extremal models using measures of surprise

Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold. However, in practice a suitable threshold is unknown and must be determined for each analysis. While there are many threshold selection methods for univariate extremes, there are relatively few that can be applied in the multivariate setting. In addition, there are only a few Bayesian-based methods, which are naturally attractive in the modelling of extremes due to data scarcity. The use of Bayesian measures of surprise to determine suitable thresholds for extreme value models is proposed. Such measures quantify the level of support for the proposed extremal model and threshold, without the need to specify any model alternatives. This approach is easily implemented for both univariate and multivariate extremes.Comment: To appear in Computational Statistics and Data Analysi

The Radio and Gamma-Ray Luminosities of Blazars

Based on the $\gamma$-ray data of blazars in the third EGRET catalog and radio data at 5 GHz, we studied the correlation between the radio and $\gamma$-ray luminosities using two statistical methods. The first method was the partial correlation analysis method, which indicates that there exist correlations between the radio and $\gamma$-ray luminosities in both high and low states as well as in the average case. The second method involved a comparison of expected $\gamma$-ray luminosity distribution with the observed data using the Kolmogorov-- Smirnov (KS) test. In the second method, we assumed that there is a correlation between the radio and $\gamma$-ray luminosities and that the $\gamma$-ray luminosity function is proportional to the radio luminosity function. The KS test indicates that the expected gamma-ray luminosity distributions are consistent with the observed data in a reasonable parameter range. Finally, we used different $\gamma$-ray luminosity functions to estimate the possible 'observed' $\gamma$-ray luminosity distributions by GLAST.Comment: 8 pages, 4 figures, one table, PASJ, 53 (2001

Polarization and Variations of BL Lacertae Objects

BL Lacertae objects are an extreme subclass of AGNs showing rapid and large-amplitude variability, high and variable polarization, and core-dominated radio emissions. If a strong beaming effect is the cause of the extreme observation properties, one would expect that these properties would be correlated with each other. Based on the relativistic beaming model, relationships between the polarization and the magnitude variation in brightness, as well as the core- dominance parameter are derived and used statistically to compare with the observational data of a BL Lacertae object sample. The statistical results are consistent with these correlations, which suggests that the polarization, the variation, and the core-dominance parameter are possible indications of the beaming effect.Comment: 6 pages, two figures, one table, some revisions. PASJ, 53 (2001

Basic properties of Gamma-ray loud blazars

In this paper, a method is proposed to determine the basic properties of $\gamma$-ray loud blazars, among them the central black hole mass, M, the Doppler factor, $\delta$, the propagation angle of the $\gamma$-rays with respect to the symmetric axis of a two-temperature accretion disk, $\Phi$, and the distance (i.e. the height above the accretion disk), d at which the $\gamma$-rays are created, for seven $\gamma$-ray loud blazars with available GeV variability timescales and in which the absorption effect of a $\gamma$-ray and the beaming effect have been taken into account. Our results indicate that, if we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, $L_{\gamma}^{in} = \lambda L_{Edd.}$, the masses of the blazars are in the range of $(4 \sim 131)\times 10^{7}M_{\odot}$, the Doppler factors ($\delta$) lie in the range of 0.57 to 5.33 the angle ($\Phi$) is in the range of $13^{\circ}$ to 43$^{\circ}$ and the distance (d) is in the range of 26R_{g} to 411R_{g}. Our model results are independent of $\gamma$-ray emission mechanisms but they do depend on the X-ray emission mechanism of the accretion disk.Comment: 14 pages, 3 tables, A&A accepte

Topologically Robust Transport of Photons in a Synthetic Gauge Field

Electronic transport in low dimensions through a disordered medium leads to localization. The addition of gauge fields to disordered media leads to fundamental changes in the transport properties. For example, chiral edge states can emerge in two-dimensional systems with a perpendicular magnetic field. Here, we implement a "synthetic'' gauge field for photons using silicon-on-insulator technology. By determining the distribution of transport properties, we confirm the localized transport in the bulk and the suppression of localization in edge states, using the "gold standard'' for localization studies. Our system provides a new platform to investigate transport properties in the presence of synthetic gauge fields, which is important both from the fundamental perspective of studying photonic transport and for applications in classical and quantum information processing.Comment: 4.5 pages, 3 figures and supplementary materia

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure