The Inertial Theorem

We present a new theorem describing stable solutions for a driven quantum system. The theorem, coined `inertial theorem', is applicable for fast driving, provided the acceleration rate is small. The theorem states that in the inertial limit eigenoperators of the propagator remain invariant throughout the dynamics, accumulating dynamical and geometric phases. The proof of the theorem utilizes the structure of Liouville space and a closed Lie algebra of operators. We demonstrate the theorem by studying three explicit solutions of a harmonic oscillator, a two-level and three-level system models. These examples demonstrate that the inertial solution is superior to that obtained with the adiabatic approximation. The inertial theorem is then employed to extend the validity of the Markovian Master equation to strongly driven open quantum systems. In addition, we explore the consequence of new geometric phases associated with the driving parameters

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

Active regulation of the epidermal calcium profile

A distinct calcium profile is strongly implicated in regulating the multi-layered structure of the epidermis. However, the mechanisms that govern the regulation of this calcium profile are currently unclear. It clearly depends on the relatively impermeable barrier of the stratum corneum (passive regulation) but may also depend on calcium exchanges between keratinocytes and extracellular fluid (active regulation). Using a mathematical model that treats the viable sublayers of unwounded human and murine epidermis as porous media and assumes that their calcium profiles are passively regulated, we demonstrate that these profiles are also actively regulated. To obtain this result, we found that diffusion governs extracellular calcium motion in the viable epidermis and hence intracellular calcium is the main source of the epidermal calcium profile. Then, by comparison with experimental calcium profiles and combination with a hypothesised cell velocity distribution in the viable epidermis, we found that the net influx of calcium ions into keratinocytes from extracellular fluid may be constant and positive throughout the stratum basale and stratum spinosum, and that there is a net outflux of these ions in the stratum granulosum. Hence the calcium exchange between keratinocytes and extracellular fluid differs distinctly between the stratum granulosum and the underlying sublayers, and these differences actively regulate the epidermal calcium profile. Our results also indicate that plasma membrane dysfunction may be an early event during keratinocyte disintegration in the stratum granulosum