Replication, Communication, and the Population Dynamics of Scientific Discovery

Many published research results are false, and controversy continues over the roles of replication and publication policy in improving the reliability of research. Addressing these problems is frustrated by the lack of a formal framework that jointly represents hypothesis formation, replication, publication bias, and variation in research quality. We develop a mathematical model of scientific discovery that combines all of these elements. This model provides both a dynamic model of research as well as a formal framework for reasoning about the normative structure of science. We show that replication may serve as a ratchet that gradually separates true hypotheses from false, but the same factors that make initial findings unreliable also make replications unreliable. The most important factors in improving the reliability of research are the rate of false positives and the base rate of true hypotheses, and we offer suggestions for addressing each. Our results also bring clarity to verbal debates about the communication of research. Surprisingly, publication bias is not always an obstacle, but instead may have positive impacts---suppression of negative novel findings is often beneficial. We also find that communication of negative replications may aid true discovery even when attempts to replicate have diminished power. The model speaks constructively to ongoing debates about the design and conduct of science, focusing analysis and discussion on precise, internally consistent models, as well as highlighting the importance of population dynamics

Agglomeration, Integration and Tax Harmonization

We show that agglomeration forces can reverse standard international-tax-competition results. Closer integration may result first in a race to the top' and then a race to the bottom, a result that is consistent with recent empirical work showing that the tax gap between rich and poor nations follows a bell-shaped path (Devereux, Griffith and Klemm 2002). Moreover, split-the-difference tax harmonization can make both nations worse off. This may help explain why tax harmonisation which is Pareto improving in the standard model is so difficult in the real world. The key theoretical insight is that agglomeration forces create quasi-rents that can be taxed without inducing delocation. This suggests that the tax game is something subtler than a race to the bottom. Advanced 'core' nations may act like limit-pricing monopolists toward less advanced 'periphery' countries. Since agglomeration rents are a bell-shaped function of the level of integration, the equilibrium tax gap in our tax game is also bell shaped.

The Persistence of the U.S. Trade Deficit

macroeconomics, trade deficit, dollar

LES of an Inclined Jet into a Supersonic Turbulent Crossflow

This short article describes flow parameters, numerical method, and animations of the fluid dynamics video "LES of an Inclined Jet into a Supersonic Turbulent Crossflow" (http://ecommons.library.cornell.edu/bitstream/1813/14073/3/GFM-2009.mpg [high-resolution] and http://ecommons.library.cornell.edu/bitstream/1813/14073/2/GFM-2009-web.m1v [low-resolution] video). We performed large-eddy simulation with the sub-grid scale (LES-SGS) stretched-vortex model of momentum and scalar transport to study the gas-dynamics interactions of a helium inclined round jet into a supersonic ($M=3.6$) turbulent (\Reth$=13\times10^3$) air flow over a flat surface. The video shows the temporal development of Mach-number and magnitude of density-gradient in the mid-span plane, and isosurface of helium mass-fraction and \lam_2 (vortical structures). The identified vortical structures are sheets, tilted tubes, and discontinuous rings. The vortical structures are shown to be well correlated in space and time with helium mass-fraction isosurface ($Y_{\rm He}=0.25$).Comment: 7 pages, 1 figure, 1 table, article describing fluid dynamics video submitted to Gallery of Fluid Motion, APS-DFD 200

Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium discrete Langevin dynamics simulations

Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite time step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that even with a time-independent Hamiltonian, finite time step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate work-like quantity is defined -- here called the shadow work -- recently developed nonequilibrium fluctuation theorems can be used to measure or correct for the errors introduced by the use of finite time steps. In particular, we demonstrate that amending estimators based on nonequilibrium work theorems to include this shadow work removes the time step dependent error from estimates of free energies. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. While these deviations can be large, they can be eliminated altogether by Metropolization or greatly diminished by small reductions in the time step. Through this connection with driven processes, further developments in nonequilibrium fluctuation theorems can provide additional analytical tools for dealing with errors in finite time step integrators.Comment: 11 pages, 4 figure