Locally Estimating Core Numbers

Graphs are a powerful way to model interactions and relationships in data from a wide variety of application domains. In this setting, entities represented by vertices at the "center" of the graph are often more important than those associated with vertices on the "fringes". For example, central nodes tend to be more critical in the spread of information or disease and play an important role in clustering/community formation. Identifying such "core" vertices has recently received additional attention in the context of {\em network experiments}, which analyze the response when a random subset of vertices are exposed to a treatment (e.g. inoculation, free product samples, etc). Specifically, the likelihood of having many central vertices in any exposure subset can have a significant impact on the experiment. We focus on using $k$-cores and core numbers to measure the extent to which a vertex is central in a graph. Existing algorithms for computing the core number of a vertex require the entire graph as input, an unrealistic scenario in many real world applications. Moreover, in the context of network experiments, the subgraph induced by the treated vertices is only known in a probabilistic sense. We introduce a new method for estimating the core number based only on the properties of the graph within a region of radius $\delta$ around the vertex, and prove an asymptotic error bound of our estimator on random graphs. Further, we empirically validate the accuracy of our estimator for small values of $\delta$ on a representative corpus of real data sets. Finally, we evaluate the impact of improved local estimation on an open problem in network experimentation posed by Ugander et al.Comment: Main paper body is identical to previous version (ICDM version). Appendix with additional data sets and enlarged figures has been added to the en

Superconducting re-entrant cavity transducer for a resonant bar gravitational radiation antenna

Copyright @ American Institute of PhysicsA 10‐GHz superconducting niobium re‐entrant cavity parametric transducer was developed for use in a cryogenic 1.5‐tonne Nb resonant bar gravitational radiation antenna. The transducer has a very high electrical Q (6×105 at 4.2 K), and was operated at high cavity fields without degrading the Q. A very high electromechanical coupling between the antenna and the transducer was therefore achieved. The highest coupling attained, constrained by the available pump power, was 0.11. If the transducer were to be operated in conjunction with a wideband impedance matching element, an antenna bandwidth comparable to the frequency of the antenna would be attained. The temperature dependence of the Q of the transducer was in good agreement with theory. At temperatures above about 6 K the Q was degraded by the increase in the BCS surface resistance, while at lower temperatures the Q was limited by radiative losses

The effects of inlet turbulence and rotor/stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. Volume 2: Heat transfer data tabulation. 15 percent axial spacing

A combined experimental and analytical program was conducted to examine the effects of inlet turbulence on airfoil heat transfer. The experimental portion of the study was conducted in a large-scale (approx 5X engine), ambient temperature, rotating turbine model configured in both single stage and stage-and-a-half arrangements. Heat transfer measurements were obtained using low-conductivity airfoils with miniature thermcouples welded to a thin, electrically heated surface skin. Heat transfer data were acquired for various combinations of low or high inlet turbulence intensity, flow coefficient, first-stator/rotor axial spacing, Reynolds number and relative circumferential position of the first and second stators. Aerodynamic measurements obtained as part of the program include distributions of the mean and fluctuating velocities at the turbine inlet and, for each airfoil row, midspan airfoil surface pressures and circumferential distributions of the downstream steady state pressures and fluctuating velocities. Analytical results include airfoil heat transfer predictions produced using existing 2-D boundary layer computation schemes and an examination of solutions of the unsteady boundary layer equations. The results are reported in four separate volumes, of which this is Volume 2: Heat Transfer Data Tabulation; 15 Percent Axial Spacing

The effects of inlet turbulence and rotor/stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. Volume 3: Heat transfer data tabulation 65 percent axial spacing

This is Volume 3 - Heat Transfer Data Tabulation (65 percent Axial Spacing) of a combined experimental and analytical program which was conducted to examine the effects of inlet turbulence on airfoil heat transfer. The experimental portion of the study was conducted in a large-scale (approximately 5X engine), ambient temperature, rotating turbine model configured in both single stage and stage-and-a-half arrangements. Heat transfer measurements were obtained using low-conductivity airfoils with miniature thermocouples welded to a thin, electrically heated surface skin. Heat transfer data were acquired for various combinations of low or high inlet turbulence intensity, flow coefficient, first-stator/rotor axial spacing, Reynolds number and relative circumferential position of the first and second stators

The effects of inlet turbulence and rotor/stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. Part 4: Aerodynamic data tabulation

A combined experimental and analytical program was conducted to examine the effects of inlet turbulence and airfoil heat transfer. The experimental portion of the study was conducted in a large-scale (approx. 5X engine), ambient temperature, rotating turbine model configured in both single-stage and stage-and-a-half arrangements. Heat transfer measurements were obtained using low-conductivity airfoils with miniature thermocouples welded to a thin, electrically heated surface skin. Heat transfer data were acquired for various combinations of low or high inlet turbulence intensity, flow coefficient, first stator-rotor axial spacing, Reynolds number and relative circumferential position of the first and second stators. Aerodynamic measurements obtained include distributions of the mean and fluctuating velocities at the turbine inlet and, for each airfoil row, midspan airfoil surface pressures and circumferential distributions of the downstream steady state pressures and fluctuating velocities. Results include airfoil heat transfer predictions produced using existing 2-D boundary layer computation schemes and an examination of solutions of the unsteady boundary layer equations