Assessing Dynamic Efficiency: Theory and Evidence

The issue of dynamic efficiency is central to analyses of capital accumulation and economic growth. Yet the question of what operating characteristics of an economy subject to productivity shocks should be examined to determine whether or not it is efficient has not been resolved. This paper develops criterion based on observables for determining whether or not an economy is dynamically efficient. The criterion involves a comparison of the cash flows generated by capital with the volume of investment. Its application to the United States economy and the economies of other major OECD nations suggests that they are dynamically efficient.

Black hole evolution by spectral methods

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast to finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.Comment: 20 pages, 17 figures, submitted to PR

A data model of the Climate and Forecast metadata conventions (CF-1.6) with a software implementation (cf-python v2.1)

The CF (Climate and Forecast) metadata conventions are designed to promote the creation, processing, and sharing of climate and forecasting data using Network Common Data Form (netCDF) files and libraries. The CF conventions provide a description of the physical meaning of data and of their spatial and temporal properties, but they depend on the netCDF file encoding which can currently only be fully understood and interpreted by someone familiar with the rules and relationships specified in the conventions documentation. To aid in development of CF-compliant software and to capture with a minimal set of elements all of the information contained in the CF conventions, we propose a formal data model for CF which is independent of netCDF and describes all possible CF-compliant data. Because such data will often be analysed and visualised using software based on other data models, we compare our CF data model with the ISO 19123 coverage model, the Open Geospatial Consortium CF netCDF standard, and the Unidata Common Data Model. To demonstrate that this CF data model can in fact be implemented, we present cf-python, a Python software library that conforms to the model and can manipulate any CF-compliant dataset

Background Adaptive Faster R-CNN for Semi-Supervised Convolutional Object Detection of Threats in X-Ray Images

Recently, progress has been made in the supervised training of Convolutional Object Detectors (e.g. Faster R-CNN) for threat recognition in carry-on luggage using X-ray images. This is part of the Transportation Security Administration's (TSA's) mission to protect air travelers in the United States. While more training data with threats may reliably improve performance for this class of deep algorithm, it is expensive to stage in realistic contexts. By contrast, data from the real world can be collected quickly with minimal cost. In this paper, we present a semi-supervised approach for threat recognition which we call Background Adaptive Faster R-CNN. This approach is a training method for two-stage object detectors which uses Domain Adaptation methods from the field of deep learning. The data sources described earlier make two "domains": a hand-collected data domain of images with threats, and a real-world domain of images assumed without threats. Two domain discriminators, one for discriminating object proposals and one for image features, are adversarially trained to prevent encoding domain-specific information. Without this penalty a Convolutional Neural Network (CNN) can learn to identify domains based on superficial characteristics, and minimize a supervised loss function without improving its ability to recognize objects. For the hand-collected data, only object proposals and image features from backgrounds are used. The losses for these domain-adaptive discriminators are added to the Faster R-CNN losses of images from both domains. This can reduce threat detection false alarm rates by matching the statistics of extracted features from hand-collected backgrounds to real world data. Performance improvements are demonstrated on two independently-collected datasets of labeled threats

Assessing Dynamic Efficiency: Theory and Evidence

The issue of dynamic efficiency is central to analyses of capital accumulation and economic growth. Yet the question of what characteristics should be examined to determine whether actual economies are dynamically efficient is unresolved. This paper develops a criterion for determining whether an economy is dynamically efficient. The criterion, which holds for economies in which technological progress and population growth are stochastic, involves a comparison of the cash flows generated by capital with the level of investment. Its application to the United States economy and the economies of other major OECD nations suggests that they are dynamically efficient

High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Numerical simulations of 15 orbits of an equal-mass binary black hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasi-circular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $\sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, {\em generic} time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6--7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.Comment: Updated to agree with published version (various minor clarifications; added description of AH finder in Sec IIB; added discussion of tidal heating in Sec VC

Spatial patterns of soil nitrification and nitrate export from forested headwaters in the northeastern United States

Nitrogen export from small forested watersheds is known to be affected by N deposition but with high regional variability. We studied 10 headwater catchments in the northeastern United States across a gradient of N deposition (5.4 - 9.4 kg ha-1 yr-1) to determine if soil nitrification rates could explain differences in stream water NO 3- export. Average annual export of two years (October 2002 through September 2004) varied from 0.1 kg NO3--N ha-1 yr-1 at Cone Pond watershed in New Hampshire to 5.1 kg ha-1 yr-1 at Buck Creek South in the western Adirondack Mountains of New York. Potential net nitrification rates and relative nitrification (fraction of inorganic N as NO3-) were measured in Oa or A soil horizons at 21-130 sampling points throughout each watershed. Stream NO3- export was positively related to nitrification rates (r2 = 0.34, p = 0.04) and the relative nitrification (r2 = 0.37, p = 0.04). These relationships were much improved by restricting consideration to the 6 watersheds with a higher number of rate measurements (59-130) taken in transects parallel to the streams (r 2 of 0.84 and 0.70 for the nitrification rate and relative nitrification, respectively). Potential nitrification rates were also a better predictor of NO3- export when data were limited to either the 6 sampling points closest to the watershed outlet (r2 = 0.75) or sampling points \u3c250 m from the watershed outlet (r2 = 0.68). The basal area of conifer species at the sampling plots was negatively related to NO3- export. These spatial relationships found here suggest a strong influence of near-stream and near-watershed-outlet soils on measured stream NO3- export. Copyright 2012 by the American Geophysical Union