Surface spectral function in the superconducting state of a topological insulator

We discuss the surface spectral function of superconductors realized from a topological insulator, such as the copper-intercalated Bi$_{2}$Se$_{3}$. These functions are calculated by projecting bulk states to the surface for two different models proposed previously for the topological insulator. Dependence of the surface spectra on the symmetry of the bulk pairing order parameter is discussed with particular emphasis on the odd-parity pairing. Exotic spectra like an Andreev bound state connected to the topological surface states are presented.Comment: 12 pages, 9 figures, 1 tabl

Fast k-means based on KNN Graph

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well known that the processing bottleneck of k-means lies in the operation of seeking closest centroid in each iteration. In this paper, a novel solution towards the scalability issue of k-means is presented. In the proposal, k-means is supported by an approximate k-nearest neighbors graph. In the k-means iteration, each data sample is only compared to clusters that its nearest neighbors reside. Since the number of nearest neighbors we consider is much less than k, the processing cost in this step becomes minor and irrelevant to k. The processing bottleneck is therefore overcome. The most interesting thing is that k-nearest neighbor graph is constructed by iteratively calling the fast $k$-means itself. Comparing with existing fast k-means variants, the proposed algorithm achieves hundreds to thousands times speed-up while maintaining high clustering quality. As it is tested on 10 million 512-dimensional data, it takes only 5.2 hours to produce 1 million clusters. In contrast, to fulfill the same scale of clustering, it would take 3 years for traditional k-means

Dust in Active Galactic Nuclei: Anomalous Silicate to Optical Extinction Ratios?

Dust plays a central role in the unification theory of active galactic nuclei (AGNs). However, little is known about the nature (e.g., size, composition) of the dust which forms a torus around the AGN. In this Letter we report a systematic exploration of the optical extinction (A_V) and the silicate absorption optical depth (\Delta\tau9.7) of 110 type 2 AGNs. We derive A_V from the Balmer decrement based on the Sloan Digital Sky Survey data, and \Delta\tau9.7 from the Spitzer/Infrared Spectrograph data. We find that with a mean ratio of A_V/\Delta\tau9.7 ~ 5.5, the optical-to-silicate extinction ratios of these AGNs are substantially lower than that of the Galactic diffuse interstellar medium (ISM) for which A_V/\Delta\tau9.7 ~ 18.5. We argue that the anomalously low A_V/\Delta\tau9.7 ratio could be due to the predominance of larger grains in the AGN torus compared to that in the Galactic diffuse ISM.Comment: ApJL, 792, L9, in prin