Foundation Board Diversity: No Change in Diversity Since 2009

This analysis of the gender, racial, and ethnic makeup of the boards of directors of the largest 481 foundations in the nation reveals that 25 percent of the positions were held by people of color, including approximately 13 percent by African Americans, 6 percent by Latinos, and 6 percent by Asians. We were able to identify only one Native American board member in the 564 total board seats that we examined. The list of foundations was obtained fromthe Foundation Center's website and selectedthe top 50 foundations by asset size. We searched each foundation's website forinformation on the board of directors and recorded the race/ethnicity of each board member along with theirgender. To determine if the assessment of the race/ethnicity of each board member was correct, we crossreferencedtheir name with the NNDB (Notable Names Database, http://www.nndb.com/). After recording therace/ethnicity of each board member we contacted their respective foundations to obtain a confirmation of the accuracy of the assessment. Data was collected in July of 2012.Only 18 of the 48 foundations sampled responded to the request for confirmation of the race/ethnicity of their board members. Thus, it is possible that some of our data is not accurate. In the interest of transparency, we encourage all foundations to disclose their board of directors diversity data on their websites. Additionally, we were not able to obtain information about the executive boards of the Walton Family Foundation or the Susan Thompson Buffet Foundation, as they do not disclose such information about their board

New Global Minima for Thomson's Problem of Charges on a Sphere

Using numerical arguments we find that for $N$ = 306 a tetrahedral configuration ($T_h$) and for N=542 a dihedral configuration ($D_5$) are likely the global energy minimum for Thomson's problem of minimizing the energy of $N$ unit charges on the surface of a unit conducting sphere. These would be the largest $N$ by far, outside of the icosadeltahedral series, for which a global minimum for Thomson's problem is known. We also note that the current theoretical understanding of Thomson's problem does not rule out a symmetric configuration as the global minima for N=306 and 542. We explicitly find that analogues of the tetrahedral and dihedral configurations for $N$ larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory of Dodgson and Moore (Phys. Rev. B 55, 3816 (1997)) that as $N$ grows dislocation defects can lower the lattice strain of symmetric configurations and concomitantly the energy. As well, making explicit previous work by ourselves and others, for $N<1000$ we give a full accounting of icosadeltahedral configuration which are not global minima and those which appear to be, and discuss how this listing and our results for the tetahedral and dihedral configurations may be used to refine theoretical understanding of Thomson's problem.Comment: 1- Manuscript revised. 2- A new global minimum found for a dihedral (D_5) configuration found for N=54

Volume dependence in 2+1 Yang-Mills theory

We present the results of an analysis of a 2+1 dimensional pure SU(N) Yang-Mills theory formulated on a 2-dimensional spatial torus with non-trivial magnetic flux. We focus on investigating the dependence of the electric-flux spectrum, extracted from Polyakov loop correlators, with the spatial size l, the number of colours N, and the magnetic flux m. The size of the torus acts a parameter that allows to control the onset of non-perturbative effects. In the small volume regime, where perturbation theory holds, we derive the one-loop self-energy correction to the single-gluon spectrum, for arbitrary N and m. We discuss the transition from small to large volumes that has been investigated by means of Monte-Carlo simulations. We argue that the energy of electric flux e, for the lowest gluon momentum, depends solely on e/N and on the dimensionless variable x=lambda N l, with lambda the 't Hooft coupling. The variable x can be interpreted as the dimensionless 't Hooft coupling for an effective box size given by Nl. This implies a version of reduction that allows to trade l by N without modifying the electric-flux energy.Comment: 7 pages, 3 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia. Minor change: Fig. 1 modified to correctly account for the sign convention in Eq. (2.5