26,906 research outputs found

    Metrics for Graph Comparison: A Practitioner's Guide

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    Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as λ\lambda distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work

    The close circumstellar environment of Betelgeuse - Adaptive optics spectro-imaging in the near-IR with VLT/NACO

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    Context: Betelgeuse is one the largest stars in the sky in terms of angular diameter. Structures on the stellar photosphere have been detected in the visible and near-infrared as well as a compact molecular environment called the MOLsphere. Mid-infrared observations have revealed the nature of some of the molecules in the MOLsphere, some being the precursor of dust. Aims: Betelgeuse is an excellent candidate to understand the process of mass loss in red supergiants. Using diffraction-limited adaptive optics (AO) in the near-infrared, we probe the photosphere and close environment of Betelgeuse to study the wavelength dependence of its extension, and to search for asymmetries. Methods: We obtained AO images with the VLT/NACO instrument, taking advantage of the "cube" mode of the CONICA camera to record separately a large number of short-exposure frames. This allowed us to adopt a "lucky imaging" approach for the data reduction, and obtain diffraction-limited images over the spectral range 1.04-2.17 ÎĽ\mum in 10 narrow-band filters. Results: In all filters, the photosphere of Betelgeuse appears partly resolved. We identify an asymmetric envelope around the star, with in particular a relatively bright "plume" extending in the southwestern quadrant up to a radius of approximately six times the photosphere. The CN molecule provides an excellent match to the 1.09 mic bandhead in absorption in front of the stellar photosphere, but the emission spectrum of the plume is more difficult to interpret. Conclusions: Our AO images show that the envelope surrounding Betelgeuse has a complex and irregular structure. We propose that the southwestern plume is linked either to the presence of a convective hot spot on the photosphere, or to the rotation of the star.Comment: 12 pages. Astronomy and Astrophysics (2009) in pres

    The preferentially magnified active nucleus in IRAS F10214+4724 - II. Spatially resolved cold molecular gas

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    We present JVLA observations of the cold (CO (1-0)) molecular gas in IRAS F10214+4724, a lensed ULIRG at z=2.3 with an obscured active nucleus. The galaxy is spatially and spectrally well-resolved in the CO (1-0) emission line. A CO (1-0) counter-image is detected at the 3-sigma level. Five of the 42 km/s channels (with >5-sigma detections) are mapped back into the source plane and their total magnification posterior PDFs sampled. This reveals a roughly linear arrangement, tentatively a rotating disk. We derive a molecular gas mass of M_gas = 1.2 +- 0.2 x 10^10 M_sun, assuming a ULIRG L_{CO}-to-M_{gas} conversion ratio of \alpha = 0.8 M_sun / (K km/s pc^2) that agrees well with the derived range of \alpha = 0.3 - 1.3 for separate dynamical mass estimates at assumed inclinations of i = 90 - 30 degrees. Based on the AGN and CO (1-0) peak emission positions and the lens model, we predict a distortion of the CO Spectral Line Energy Distribution (SLED) where higher order J lines that may be partially excited by AGN heating will be preferentially lensed owing to their smaller solid angles and closer proximity to the AGN and therefore the cusp of the caustic. Comparison with other lensing inversion results shows that the narrow line region and AGN radio core in IRAS F10214+4724 are preferentially lensed by a factor >~ 3 and 11 respectively, relative to the molecular gas emission. This distorts the global continuum emission Spectral Energy Distribution (SED) and suggests caution in unsophisticated uses of IRAS F10214+4724 as an archetype high-redshift ULIRG. We explore two Large Velocity Gradient (LVG) models, incorporating spatial CO (1-0) and (3-2) information and present tentative evidence for an extended, low excitation cold gas component that implies that the total molecular gas mass in IRAS F10214+4724 is a factor >~2 greater than that calculated using spatially unresolved CO observations.Comment: Dedicated to Steve Rawlings. Accepted for publication in MNRAS. 16 pages, 11 figure

    Multi-Frequency Synthesis of VLBI Images Using a Generalized Maximum Entropy Method

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    A new multi-frequency synthesis algorithm for reconstructing images from multi-frequency VLBI data is proposed. The algorithm is based on a generalized maximum-entropy method, and makes it possible to derive an effective spectral correction for images over a broad frequency bandwidth, while simultaneously reconstructing the spectral-index distribution over the source. The results of numerical simulations demonstrating the capabilities of the algorithm are presented.Comment: 17 pages, 8 figure

    Self-imaging silicon Raman amplifier

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    We propose a new type of waveguide optical amplifier. The device consists of collinearly propagating pump and amplified Stokes beams with periodic imaging of the Stokes beam due to the Talbot effect. The application of this device as an Image preamplifier for Mid Wave Infrared (MWIR) remote sensing is discussed and its performance is described. Silicon is the preferred material for this application in MWIR due to its excellent transmission properties, high thermal conductivity, high damage threshold and the mature fabrication technology. In these devices, the Raman amplification process also includes four-wave-mixing between various spatial modes of pump and Stokes signals. This phenomenon is unique to nonlinear interactions in multimode waveguides and places a limit on the maximum achievable gain, beyond which the image begins to distort. Another source of image distortion is the preferential amplification of Stokes modes that have the highest overlap with the pump. These effects introduce a tradeoff between the gain and image quality. We show that a possible solution to this trade-off is to restrict the pump into a single higher order waveguide mode.Comment: 11 pages, 5 figures and 5 sections. Submitted to Optics Expres

    Purcell factor enhanced scattering efficiency in optical microcavities

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    Scattering processes in an optical microcavity are investigated for the case of silicon nanocrystals embedded in an ultra-high Q toroid microcavity. Using a novel measurement technique based on the observable mode-splitting, we demonstrate that light scattering is highly preferential: more than 99.8% of the scattered photon flux is scattered into the original doubly-degenerate cavity modes. The large capture efficiency is attributed to an increased scattering rate into the cavity mode, due to the enhancement of the optical density of states over the free space value and has the same origin as the Purcell effect in spontaneous emission. The experimentally determined Purcell factor amounts to 883

    Preparation and characterization of α-Fe nanowires located inside double wall carbon nanotubes

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    Capillary effect was used to fill double wall carbon nanotubes (DWCNT) with iron. The samples are characterized by Mössbauer and Raman spectroscopies, TEM, SAED, and magnetization. The experimental results indicate the presence of a-Fe nanowires inside the DWCNTs. The samples are ferromagnetic at room temperature. There are three striking results due to the confinement effects on the physical behavior of a-Fe: the hyperfine fields increase, the Debye temperature decreases and Raman modes are observed
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