2,888 research outputs found

    Partial Covering Arrays: Algorithms and Asymptotics

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    A covering array CA(N;t,k,v)\mathsf{CA}(N;t,k,v) is an N×kN\times k array with entries in {1,2,,v}\{1, 2, \ldots , v\}, for which every N×tN\times t subarray contains each tt-tuple of {1,2,,v}t\{1, 2, \ldots , v\}^t among its rows. Covering arrays find application in interaction testing, including software and hardware testing, advanced materials development, and biological systems. A central question is to determine or bound CAN(t,k,v)\mathsf{CAN}(t,k,v), the minimum number NN of rows of a CA(N;t,k,v)\mathsf{CA}(N;t,k,v). The well known bound CAN(t,k,v)=O((t1)vtlogk)\mathsf{CAN}(t,k,v)=O((t-1)v^t\log k) is not too far from being asymptotically optimal. Sensible relaxations of the covering requirement arise when (1) the set {1,2,,v}t\{1, 2, \ldots , v\}^t need only be contained among the rows of at least (1ϵ)(kt)(1-\epsilon)\binom{k}{t} of the N×tN\times t subarrays and (2) the rows of every N×tN\times t subarray need only contain a (large) subset of {1,2,,v}t\{1, 2, \ldots , v\}^t. In this paper, using probabilistic methods, significant improvements on the covering array upper bound are established for both relaxations, and for the conjunction of the two. In each case, a randomized algorithm constructs such arrays in expected polynomial time

    Identification of the Early Fermi LAT Gamma-Ray Bright Objects with Extragalactic VLBI sources

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    A list of 205 gamma-ray strong objects was reported recently as a result of a 3-month integration with the Large Area Telescope on board the Fermi Gamma-Ray Space Telescope. We attempted identification of these objects, cross-correlating the gamma-ray positions with VLBI positions of a large all-sky sample of extragalactic radio sources selected on the basis of their parsec-scale flux density. The original associations reported by the Fermi team are confirmed and six new identifications are suggested. A Monte-Carlo analysis shows that the fraction of chance associations in our analysis is less than 5 per cent, and confirms that the vast majority of gamma-ray bright extragalactic sources are radio loud blazars with strong parsec-scale jets. A correlation between the parsec-scale radio and gamma-ray flux is supported by our analysis of a complete VLBI flux-density-limited sample of extragalactic jets. The effectiveness of using a VLBI catalog to find associations between gamma-ray detections and compact extragalactic radio sources, especially near the Galactic plane, is demonstrated. It is suggested that VLBI catalogs should be used for future identification of Fermi LAT objects.Comment: 5 pages, 4 figures, 1 table, accepted by the Astrophysical Journal Letters; minor corrections to the text are made, one panel is added to Figure 1; full table 1 in electronic form can be extracted from the preprint sourc

    High Energy Gamma-Ray Emission From Blazars: EGRET Observations

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    We will present a summary of the observations of blazars by the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory (CGRO). EGRET has detected high energy gamma-ray emission at energies greater than 100 MeV from more that 50 blazars. These sources show inferred isotropic luminosities as large as 3×10493\times 10^{49} ergs s1^{-1}. One of the most remarkable characteristics of the EGRET observations is that the gamma-ray luminosity often dominates the bolometric power of the blazar. A few of the blazars are seen to exhibit variability on very short time-scales of one day or less. The combination of high luminosities and time variations seen in the gamma-ray data indicate that gamma-rays are an important component of the relativistic jet thought to characterize blazars. Currently most models for blazars involve a beaming scenario. In leptonic models, where electrons are the primary accelerated particles, gamma-ray emission is believed to be due to inverse Compton scattering of low energy photons, although opinions differ as to the source of the soft photons. Hardronic models involve secondary production or photomeson production followed by pair cascades, and predict associated neutrino production.Comment: 16 pages, 7 figures, style files included. Invited review paper in "Observational Evidence for Black Holes in the Universe," 1999, ed. S. K. Chakrabarti (Dordrecht: Kluwer), 215-23

    Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual

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    We study Vasiliev's system of higher spin gauge fields coupled to massive scalars in AdS_3, and compute the tree level two and three point functions. These are compared to the large N limit of the W_N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.Comment: 58 pages; typos corrected, references adde

    Eta Carinae -- Physics of the Inner Ejecta

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    Eta Carinae's inner ejecta are dominated observationally by the bright Weigelt blobs and their famously rich spectra of nebular emission and absorption lines. They are dense (n_e ~ 10^7 to 10^8 cm^-3), warm (T_e ~ 6000 to 7000 K) and slow moving (~40 km/s) condensations of mostly neutral (H^0) gas. Located within 1000 AU of the central star, they contain heavily CNO-processed material that was ejected from the star about a century ago. Outside the blobs, the inner ejecta include absorption-line clouds with similar conditions, plus emission-line gas that has generally lower densities and a wider range of speeds (reaching a few hundred km/s) compared to the blobs. The blobs appear to contain a negligible amount of dust and have a nearly dust-free view of the central source, but our view across the inner ejecta is severely affected by uncertain amounts of dust having a patchy distribution in the foreground. Emission lines from the inner ejecta are powered by photoionization and fluorescent processes. The variable nature of this emission, occurring in a 5.54 yr event cycle, requires specific changes to the incident flux that hold important clues to the nature of the central object.Comment: This is Chapter 5 in a book entitled: Eta Carinae and the Supernova Impostors, Kris Davidson and Roberta M. Humphreys, editors Springe

    Higher Spin Black Holes from CFT

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    Higher spin gravity in three dimensions has explicit black holes solutions, carrying higher spin charge. We compute the free energy of a charged black hole from the holographic dual, a 2d CFT with extended conformal symmetry, and find exact agreement with the bulk thermodynamics. In the CFT, higher spin corrections to the free energy can be calculated at high temperature from correlation functions of W-algebra currents.Comment: 24 pages; v2 reference adde

    Intra-tumor heterogeneity in breast cancer has limited impact on transcriptomic-based molecular profiling

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    Background: Transcriptomic profiling of breast tumors provides opportunity for subtyping and molecular-based patient stratification. In diagnostic applications the specimen profiled should be representative of the expression profile of the whole tumor and ideally capture properties of the most aggressive part of the tumor. However, breast cancers commonly exhibit intra-tumor heterogeneity at molecular, genomic and in phenotypic level, which can arise during tumor evolution. Currently it is not established to what extent a random sampling approach may influence molecular breast cancer diagnostics. Methods: In this study we applied RNA-sequencing to quantify gene expression in 43 pieces (2-5 pieces per tumor) from 12 breast tumors (Cohort 1). We determined molecular subtype and transcriptomic grade for all tumor pieces and analysed to what extent pieces originating from the same tumors are concordant or discordant with each other. Additionally, we validated our finding in an independent cohort consisting of 19 pieces (2-6 pieces per tumor) from 6 breast tumors (Cohort 2) profiled using microarray technique. Exome sequencing was also performed on this cohort, to investigate the extent of intra-tumor genomic heterogeneity versus the intra-tumor molecular subtype classifications. Results: Molecular subtyping was consistent in 11 out of 12 tumors and transcriptomic grade assignments were consistent in 11 out of 12 tumors as well. Molecular subtype predictions revealed consistent subtypes in four out of six patients in this cohort 2. Interestingly, we observed extensive intra-tumor genomic heterogeneity in these tumor pieces but not in their molecular subtype classifications. Conclusions: Our results suggest that macroscopic intra-tumoral transcriptomic heterogeneity is limited and unlikely to have an impact on molecular diagnostics for most patients.Peer reviewe
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