Mechanism of very high energy radiation in BL Lacertae object 3C 66A

Our goal is to understand the nature of blazars and the mechanisms for the generation of high-energy $\gamma$-rays, through the investigation of the blazar 3C 66A. We model the high energy spectrum of 3C 66A, which has been observed recently with the Fermi-LAT and VERITAS telescope. The spectrum has a hard change from the energy range of 0.2-100 GeV to 200-500 GeV in recent almost contemporaneous observations of two telescopes. The de-absorbed VERITAS spectrum greatly depends on the redshift, which is highly uncertain. If z=0.444 is adopted, we are able to use the SSC model to produce the Fermi-LAT component and the EC model to the VERITAS component. However, if z=0.1, the intrinsic VERITAS spectrum will be softer, there will be a smooth link between the Fermi-LAT and VERITAS spectra which can be explained using a SSC model.Comment: 5 pages, 3 figures. accepted for publication in A&

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure