A Fast and Accurate Algorithm for Spherical Harmonic Analysis on HEALPix Grids with Applications to the Cosmic Microwave Background Radiation

The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, which is a central component to computing and analyzing the angular power spectrum of the massive CMB data sets. The method uses a novel combination of a non-uniform fast Fourier transform, the double Fourier sphere method, and Slevinsky's fast spherical harmonic transform (Slevinsky, 2019). For a HEALPix grid with $N$ pixels (points), the computational complexity of the method is $\mathcal{O}(N\log^2 N)$, with an initial set-up cost of $\mathcal{O}(N^{3/2}\log N)$. This compares favorably with $\mathcal{O}(N^{3/2})$ runtime complexity of the current methods available in the HEALPix software when multiple maps need to be analyzed at the same time. Using numerical experiments, we demonstrate that the new method also appears to provide better accuracy over the entire angular power spectrum of synthetic data when compared to the current methods, with a convergence rate at least two times higher

Observational Signatures of Quantum Gravity in Interferometers

We consider the uncertainty in the arm length of an interferometer due to metric fluctuations from the quantum nature of gravity, proposing a concrete microscopic model of energy fluctuations in holographic degrees of freedom on the surface bounding a causally connected region of spacetime. In our model, fluctuations longitudinal to the beam direction accumulate in the infrared and feature strong long distance correlation in the transverse direction. This leads to a signal that could be observed in a gravitational wave interferometer. We connect the positional uncertainty principle arising from our calculations to the 't Hooft gravitational S-matrix.Comment: 6 pages, 1 figur

Tenure and Output

A key tenet of the theory of human capital is that investment in skills results in higher productivity. The previous literature has estimated the degree of investment in human capital for individuals by looking at individual wage growth as a proxy for productivity growth. In this paper, we have both wage and personal productivity data, and thus are able to measure of the increase in workers' output with tenure. The data is from an autoglass company. Most of production occurs at the individual level so measures of output are clear. We find a very steep learning curve in the year on the job: output is 53 percent higher after one year than it is initially when hired. These output gains with tenure are not reflected in equal percentage pay gains: pay profiles are much flatter than output profiles in the first year and a half on the job. For these data, using wage profiles significantly underestimates the amount of investment compared to the gains evident in output-tenure profiles. The pattern of productivity rising more rapidly than pay reverses after two years of tenure. Worker selection is also important. Workers who stay longer have higher output levels and faster early learning.

hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form.

In this paper we consider the a posteriori and a priori analysis of hp-discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments

Measuring the Impacts of Improving Research Capacity: The Case of Training in Wheat Disease Resistance

It is notoriously difficult to assess the economic value of research aimed at improving research capacity, particularly in enhancing human capital. In this paper, a framework is developed and an analysis is undertaken of the value of training for scientists in wheat rust resistance in India. The value of the training is assessed through marginal analysis of the improvement in the level of disease resistence flowing from the increased capacity. On that basis, the value of programs to build human capacity through training or further education can be estimated. While such estimates need to be highly qualified, they provide a basis for quantifying the value of R&D capacity building.capacity building, training, economic, rust, wheat, Research Methods/ Statistical Methods,

Genetics of, and Breeding for, Rust Resistance in Wheat in India and Pakistan

Crop Production/Industries,

Wage Structure, Raises and Mobility: International Comparisons of the Structure of Wages Within and Across Firms

The returns to talent or performance have grown over time in developed countries. Is talent concentrated in a few firms or are firms virtual microcosms of the economy, each having close to identical distributions of talent? The data show that talent is not concentrated in a few companies, but is widely dispersed across companies. Wage dispersion within firms is nearly as high as the wage dispersion overall. The standard deviation of wages within the firm is about 80% of the standard deviation across all workers in the economy. Firms are more similar than they are dissimilar, but they are not identical: the firm mean wage displays considerable dispersion across the population of firms. There is evidence that talent is becoming more concentrated over time within some firms relative to others. In four countries that estimated wage regressions with firm fixed effects, the firm fixed effects are contributing more to the R-squared of the wage regression over time. Law firms have more lawyers than janitors. Janitorial firms have more janitors than lawyers and the differences between firms have become more pronounced. Still, the variance of wages within the average firms remains high.

Towards the measurement of the impacts of improving research capacity: an economic evaluation of training in wheat disease resistance

It is notoriously difficult to assess the economic value of research aimed at improving research capacity, particularly for the human capital component of research capacity. In this paper, a framework is developed and an analysis is undertaken of the value of training for scientists in wheat rust resistance. The value of improving human capital is assessed through a framework based on marginal analysis of the improvement in productivity outcomes flowing from the increased capacity. On that basis, the value of programs to build human capacity through training or further education can be estimated. Although such estimates are necessarily qualified, they provide a basis for quantifying the value of building research and development capacity.capacity building, economic, rust, training, wheat, Crop Production/Industries, Research and Development/Tech Change/Emerging Technologies,