Explaining Pharmaceutical R&D Growth Rates at the Industry Level: New Perspectives and Insights

This paper uses aggregate data for the major pharmaceutical companies in the U.S. to study the rate of growth in pharmaceutical R&D intensity over the period from 1952 to 2001. The theoretical model argues and the empirical findings suggest that pharmaceutical R&D spending increases with real drug prices, after holding constant other determinants of R&D. Simulations based on our multiple regression model indicate that the capitalized value of pharmaceutical R&D spending would have been about 30 percent lower if the federal government had limited the rate of growth in drug price increases to the rate of growth in the general consumer price index during the period 1980 to 2001. Moreover, a drug price control regime would have resulted in 330 to 365 fewer new drugs brought to the global market during that same time period.Health and Safety

Critical decay index at the onset of solar eruptions

Magnetic flux ropes are topological structures consisting of twisted magnetic field lines that globally wrap around an axis. The torus instability model predicts that a magnetic flux rope of major radius $R$ undergoes an eruption when its axis reaches a location where the decay index $-d(\ln B_{ex})/d(\ln R)$ of the ambient magnetic field $B_{ex}$ is larger than a critical value. In the current-wire model, the critical value depends on the thickness and time-evolution of the current channel. We use magneto-hydrodynamic (MHD) simulations to investigate if the critical value of the decay index at the onset of the eruption is affected by the magnetic flux rope's internal current profile and/or by the particular pre-eruptive photospheric dynamics. The evolution of an asymmetric, bipolar active region is driven by applying different classes of photospheric motions. We find that the critical value of the decay index at the onset of the eruption is not significantly affected by either the pre-eruptive photospheric evolution of the active region or by the resulting different magnetic flux ropes. As in the case of the current-wire model, we find that there is a `critical range' $[1.3-1.5]$, rather than a `critical value' for the onset of the torus instability. This range is in good agreement with the predictions of the current-wire model, despite the inclusion of line-tying effects and the occurrence of tether-cutting magnetic reconnection.Comment: 15 pages, 9 figures. To appear in The Astrophysical Journa

Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear Polarization

The minor axes of, and the normals to, the polarization ellipses that surround singular lines of linear polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips and into structures we call rippled rings (r-rings). The Mobius strips have two full twists, and can be either right- or left-handed. The major axes of the surrounding ellipses generate cone-like structures. Three orthogonal projections that give rise to 15 indices are used to characterize the different structures. These indices, if independent, could generate 839,808 geometrically and topologically distinct lines; selection rules are presented that reduce the number of lines to 8,248, some 5,562 of which have been observed in a computer simulation. Statistical probabilities are presented for the most important index combinations in random fields. It is argued that it is presently feasible to perform experimental measurements of the Mobius strips, r-rings, and cones described here theoretically