Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel

The mixed membership stochastic blockmodel is a statistical model for a graph, which extends the stochastic blockmodel by allowing every node to randomly choose a different community each time a decision of whether to form an edge is made. Whereas spectral analysis for the stochastic blockmodel is increasingly well established, theory for the mixed membership case is considerably less developed. Here we show that adjacency spectral embedding into $\mathbb{R}^k$, followed by fitting the minimum volume enclosing convex $k$-polytope to the $k-1$ principal components, leads to a consistent estimate of a $k$-community mixed membership stochastic blockmodel. The key is to identify a direct correspondence between the mixed membership stochastic blockmodel and the random dot product graph, which greatly facilitates theoretical analysis. Specifically, a $2 \rightarrow \infty$ norm and central limit theorem for the random dot product graph are exploited to respectively show consistency and partially correct the bias of the procedure.Comment: 12 pages, 6 figure

Low-energy behavior of spin-liquid electron spectral functions

We calculate the electron spectral function for a spin-liquid with a spinon Fermi surface and a Dirac spin-liquid. Calculations are based upon the slave-rotor mean-field theory. We consider the effect of gauge fluctuations using a simple model and find the behavior is not strongly modified. The results, distinct from conventional Mott insulator or band theory predictions, suggest that measuring the spectral function e.g. via ARPES could help in the experimental verification and characterization of spin liquids.Comment: 7 pages, 7 figure

The Perceptions of Macao Undergraduates Regarding Help Websites for Problem Gambling

This study conducted a web-surfing exercise and a questionnaire survey among a group of Macao undergraduate students regarding the websites that offered help with problem gambling. The results of this study found that most help websites in Macao and Hong Kong provided basic information-sharing service. The students indicated that they would choose their preferred help organization based on factors such as trust, familiarity, and the characteristics of the websites. They also gave comments/suggestions related to the publicity, design, contents, and focus of the websites. This study discussed the results and their implications for future research and practice

Observations and Analysis of High-Resolution Magnetic Field Structures in Molecular Clouds

Recent high-angular-resolution (up to 0.7") dust polarization observations toward star forming regions are summarized. With the Sub-Millimeter Array, the emission from the dense structures is traced and resolved. The detected magnetic field morphologies vary from hourglass-like structures to isolated patches depending on the evolutionary stage of the source. These observed features have also served as a testbed to develop new analysis methods, with a particular focus on quantifying the role of the magnetic field in the star formation process.Comment: 4 pages, 2 figures; To appear in Proceedings of Magnetic Fields in the Universe: From Laboratory and Stars to Primordial Structures Aug. 21st - 27th 2011, Zakopane, Poland Eds. M. Soida, K. Otmianowska-Mazur, E.M. de Gouveia Dal Pino & A. Lazaria

Dust continuum and Polarization from Envelope to Cores in Star Formation: A Case Study in the W51 North region

We present the first high-angular resolution (up to 0.7", ~5000 AU) polarization and thermal dust continuum images toward the massive star-forming region W51 North. The observations were carried out with the Submillimeter Array (SMA) in both the subcompact (SMA-SubC) and extended (SMA-Ext) configurations at a wavelength of 870 micron. W51 North is resolved into four cores (SMA1 to SMA4) in the 870 micron continuum image. The associated dust polarization exhibits more complex structures than seen at lower angular resolution. We analyze the inferred morphologies of the plane-of-sky magnetic field (B_bot) in the SMA1 to SMA4 cores and in the envelope using the SMA-Ext and SMA-SubC data. These results are compared with the B_bot archive images obtained from the CSO and JCMT. A correlation between dust intensity gradient position angles (phi_{nabla I}) and magnetic field position angles (phi_B) is found in the CSO, JCMT and both SMA data sets. This correlation is further analyzed quantitatively. A systematically tighter correlation between phi_{nabla I} and phi_B is found in the cores, whereas the correlation decreases in outside-core regions. Magnetic field-to-gravity force ratio (Sigma_B) maps are derived using the newly developed polarization - intensity gradient method by Koch, Tang & Ho 2012. We find that the force ratios tend to be small (Sigma_B <= 0.5) in the cores in all 4 data sets. In regions outside of the cores, the ratios increase or the field is even dominating gravity (Sigma_B > 1). This possibly provides a physical explanation of the tightening correlation between phi_{nabla I} and phi_B in the cores: the more the B field lines are dragged and aligned by gravity, the tighter the correlation is. Finally, we propose a schematic scenario for the magnetic field in W51 North to interpret the four polarization observations at different physical scales.Comment: Accepted for publication in ApJ. 10 pages. 7 figure

Herpes simplex keratitis: Challenges in diagnosis and clinical management

Herpes simplex virus is responsible for numerous ocular diseases, the most common of which is herpetic stromal keratitis. This is a recurrent infection of the cornea that typically begins with a subclinical infection of the cornea that establishes a latent infection of sensory ganglia, most often the trigeminal ganglia. Recurring infections occur when the virus is reactivated from latency and travels back to the cornea, where it restimulates an inflammatory response. This inflammatory response can lead to decreased corneal sensation, scarring, and blindness. The diagnosis of these lesions as the result of a recurrent herpes simplex virus infection can at times be problematic. Currently, herpetic stromal keratitis is diagnosed by its clinical presentation on the slit-lamp examination, but the literature does not always support the accuracy of these clinical findings. Other diagnostic tests such as polymerase chain reaction assay, enzyme-linked immunosorbent assay, immunofluorescent antibody, and viral cultures have provided more definitive diagnosis, but also have some limitations. That said, accurate diagnosis is necessary for proper treatment, in order to prevent serious consequences. Current treatment reduces the severity of lesions and controls further viral spread, but does not provide a cure

Fano Resonances in Mid-Infrared Spectra of Single-Walled Carbon Nanotubes

This work revisits the physics giving rise to the carbon nanotubes phonon bands in the mid- infrared. Our measurements of doped and undoped samples of single-walled carbon nanotubes in Fourier transform infrared spectroscopy show that the phonon bands exhibit an asymmetric lineshape and that their effective cross-section is enhanced upon doping. We relate these observations to electron-phonon coupling or, more specifically, to a Fano resonance phenomenon. We note that only the dopant-induced intraband continuum couples to the phonon modes and that defects induced in the sidewall increase the resonance probabilities.Comment: 5 pages, 4 figures and 1 Supplementary Information File (in pdf