Some Surprising Properties of Power Indices

A troubling aspect about power indices is how the values assigned to players can depend upon the index. As shown, the problem is more severe; different indices can generate radically different rankings; e.g., a 15-player game exists with over a trillion different strict power index rankings of the players. It is shown that certain indices always share the same ranking, but this assertion depends on the number of players; e.g., the Shapley and Banzhaf rankings agree with three players, but with more players they can even have opposite rankings. It is also shown how changes in certain assumptions affect the outcomes. This includes demonstrating how the rankings change when players drop out of a game.

Effects of the network structural properties on its controllability

In a recent paper, it has been suggested that the controllability of a diffusively coupled complex network, subject to localized feedback loops at some of its vertices, can be assessed by means of a Master Stability Function approach, where the network controllability is defined in terms of the spectral properties of an appropriate Laplacian matrix. Following that approach, a comparison study is reported here among different network topologies in terms of their controllability. The effects of heterogeneity in the degree distribution, as well as of degree correlation and community structure, are discussed.Comment: Also available online at: http://link.aip.org/link/?CHA/17/03310

A CRITICAL REAPPRAISAL OF SOME VOTING POWER PARADOXES

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are called "voting power paradoxes". In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.Voting power, decisiveness, success, voting rules, voting behavior, postulates, paradoxes.

Confinement and Condensates Without Fine Tuning in Supergravity Duals of Gauge Theories

We discuss a solution of the equations of motion of five-dimensional gauged type IIB supergravity that describes confining SU(N) gauge theories at large N and large 't Hooft parameter. We prove confinement by computing the Wilson loop, and we show that our solution is generic, independent of most of the details of the theory. In particular, the Einstein-frame metric near its singularity, and the condensates of scalar, composite operators are universal. Also universal is the discreteness of the glueball mass spectrum and the existence of a mass gap. The metric is also identical to a generically confining solution recently found in type 0B theory.Comment: 19 pages, Late

Chandra Observations of X-ray Weak Narrow-Line Seyfert 1 Galaxies

We present Chandra observations of 17 optically-selected, X-ray weak narrow-line Seyfert 1 (NLS1) galaxies. These objects were optically identified by Williams et al. (2002) in the Sloan Digital Sky Survey Early Data Release, but were not found in the ROSAT All-Sky Survey (RASS) despite having optical properties similar to RASS-detected NLS1s. All objects in this sample were detected by Chandra and exhibit a range of 0.5-2 keV photon indices Gamma=1.1-3.4. One object was not detected in the soft band, but has a best-fit Gamma=0.25 over the full 0.5-8 keV range. These photon indices extend to values far below what are normally observed in NLS1s. A composite X-ray spectrum of the hardest objects in this sample does not show any signs of absorption, although the data do not prohibit one or two of the objects from being highly absorbed. We also find a strong correlation between Gamma and L_1keV; this may be due to differences in L_bol/L_Edd among the NLS1s in this sample. Such variations are seemingly in conflict with the current paradigm that NLS1s accrete near the Eddington limit. Most importantly, this sample shows that strong, ultrasoft X-ray emission is not a universal characteristic of NLS1s; in fact, a substantial number may exhibit weak and/or low-Gamma X-ray emission.Comment: Minor changes, added section on X-ray weakness. 25 pages incl. 6 figures, 3 tables, accepted to Ap

Radio continuum observations of local star-forming galaxies using the Caltech Continuum Backend on the Green Bank Telescope

We observed radio continuum emission in 27 local (D < 70 Mpc) star-forming galaxies with the Robert C. Byrd Green Bank Telescope between 26 GHz and 40 GHz using the Caltech Continuum Backend. We obtained detections for 22 of these galaxies at all four sub-bands and four more marginal detections by taking the average flux across the entire bandwidth. This is the first detection (full or marginal) at these frequencies for 22 of these galaxies. We fit spectral energy distributions (SEDs) for all of the four-sub-band detections. For 14 of the galaxies, SEDs were best fit by a combination of thermal free-free and nonthermal synchrotron components. Eight galaxies with four-sub-band detections had steep spectra that were only fit by a single nonthermal component. Using these fits, we calculated supernova rates, total number of equivalent O stars, and star formation rates within each ~23 arcsecond beam. For unresolved galaxies, these physical properties characterize the galaxies' recent star formation on a global scale. We confirm that the radio-far-infrared correlation holds for the unresolved galaxies' total 33 GHz flux regardless of their thermal fractions, though the scatter on this correlation is larger than that at 1.4 GHz. In addition, we found that for the unresolved galaxies, there is an inverse relationship between the ratio of 33 GHz flux to total far-infrared flux and the steepness of the galaxy's spectral index between 1.4 GHz and 33 GHz. This relationship could be an indicator of the timescale of the observed episode of star formation.Comment: 36 pages, 9 figures; accepted for publication in ApJ. First and second author affiliation updated to reflect departmental name chang