The Rockefeller Brothers Fund's Democratic Practice Global Governance Portfolio: Impact Assessment, 20102015

This report evaluates the progress of the Rockefeller Brothers Fund (RBF) Democratic Practice–Global Governance (DP-GG) portfolio in the context of the program-specific goal, strategies, and the RBF mission. The overarching goal of the DP-GG program is to "strengthen the vitality of democracy in global governance." It is pursued through support for three strategies (transparency and accountability, access and participation, and innovation), and focused on three substantive areas (trade, climate, and development finance). Over the six-year period 2010 through 2015, the RBF invested $17.3 million in grants and appropriations in the Global Governance portfolio. This includes182 grants to 79 organizations, as well as support for 18 meetings at The Pocantico Center and 13 nongrant appropriations for consultancies and outside meetings. The average annual budget of the DP-GG portfolio is$2.95 million, a modest figure given the complexity and scale of issues these grants endeavor to tackle

Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models

In the study of $\mathcal{P}\mathcal{T}$-symmetric quantum systems with non-Hermitian perturbations, one of the most important questions is whether eigenvalues stay real or whether $\mathcal{P}\mathcal{T}$-symmetry is spontaneously broken when eigenvalues meet. A particularly interesting set of eigenstates is provided by the degenerate ground-state subspace of systems with topological order. In this paper, we present simple criteria that guarantee the protection of $\mathcal{P}\mathcal{T}$-symmetry and, thus, the reality of the eigenvalues in topological many-body systems. We formulate these criteria in both geometric and algebraic form, and demonstrate them using the toric code and several different fracton models as examples. Our analysis reveals that $\mathcal{P}\mathcal{T}$-symmetry is robust against a remarkably large class of non-Hermitian perturbations in these models; this is particularly striking in the case of fracton models due to the exponentially large number of degenerate states.Comment: 20 pages, 6 figure

A snakes and ladders representation of stock prices and returns

Snakes and ladders is an ancient Indian game of chance that offers amusement as well as a metaphor for life’s many ups and downs. Games offer useful and fun ways of conveying ideas as well as solution techniques and this game has considerable mathematical tractability. This note shows how snakes and ladders can be used to represent the ups and downs of share ownership and solve for fair values of a multistage project that pays fixed dividends at uncertain completion times and has random returns

Cenozoic paleoceanography 1986: An introduction

New developments in Cenozoic paleoceanography include the application of climate models and atmospheric general circulation models to questions of climate reconstruction, the refinement of conceptual models for interpretation of the carbon isotope record in terms of carbon mass balance, paleocirculation, paleoproductivity, and the regional mapping of paleoceanographic events by acoustic stratigraphy. Sea level change emerges as a master variable to which changes in the ocean environment must be traced in many cases, and tests of the onlap-offlap paradigm therefore are of crucial importance