Is There an Environmental Kuznets Curve for Sulfur?

The environmental Kuznets curve (EKC) hypothesis proposes that there is an inverted U-shape relation between environmental degradation and income per capita. Various explanations for this phenomenon have been put forward and some authors argue that important explanatory variables are omitted from conventional EKC estimates. Inclusion of these omitted variables is argued to increase the estimated "turning point" - the level of GDP per capita above which environmental degradation is declining. In this paper we use a new cross-section/time-series data base of sulfur emissions for a wide range of developed and developing countries. The methodology involves estimating EKCs for subsets of this database as well as for the sample as a whole. The results show that estimating an EKC using data for only the OECD countries, as has often been the case, leads to estimates where the turning point is at a much lower level than when the EKC is estimated using data for the World as a whole. The paper explores possible explanations of these results using Monte Carlo analysis, and other statistical tests.We conclude that the simple EKC model is fundamentally misspecified and that there are omitted variables which are correlated with GDP

Data-Driven Reduced-Order Modeling of Unsteady Nonlinear Shock Wave using Physics-Informed Neural Network (PINN) Based Solution

This article presents a preliminary study on data-driven reduced-order modeling (ROM) of unsteady nonlinear shock wave. A basic form of such problem can be modeled using the Burgers’ equation. The physics-informed neural networks (PINN) approach is used to obtain numerical solutions to the problem at certain time steps. PINN is a cutting-edge computational framework that seamlessly integrates deep neural networks with the governing physics of the problem and is turning out to be promising for enhancing the accuracy and efficiency of numerical solutions in a wide array of scientific and engineering applications. Next, extraction of the Proper Orthogonal Decomposition (POD) modes from the solution field is carried out, providing a compact representation of the system’s dominant spatial patterns. Subsequently, temporal coefficients are computed at specific time intervals, allowing for a reduced-order representation of the temporal evolution of the system. These temporal coefficients are then employed as input data to train a deep neural network (DNN) model designed to predict the temporal coefficient at various time steps. The predicted coefficient can be used to form the solution. The synergy between the POD-based spatial decomposition and the data-driven capabilities of DNN results in an efficient and accurate model for approximating the solution. The trained ANN subsequently takes the value of the Reynolds number and historical POD coefficients as inputs, generating predictions for future temporal coefficients. The study demonstrates the potential of combining model reduction techniques with machine learning approaches for solving complex partial differential equations. It showcases the use of physics-informed deep learning for obtaining numerical solutions. The idea presented can be extended to solve more complicated problems involving Navier-Stokes equations

CMB mapping experiments: a designer's guide

We apply state-of-the art data analysis methods to a number of fictitious CMB mapping experiments, including 1/f noise, distilling the cosmological information from time-ordered data to maps to power spectrum estimates, and find that in all cases, the resulting error bars can we well approximated by simple and intuitive analytic expressions. Using these approximations, we discuss how to maximize the scientific return of CMB mapping experiments given the practical constraints at hand, and our main conclusions are as follows. (1) For a given resolution and sensitivity, it is best to cover a sky area such that the signal-to-noise ratio per resolution element (pixel) is of order unity. (2) It is best to avoid excessively skinny observing regions, narrower than a few degrees. (3) The minimum-variance mapmaking method can reduce the effects of 1/f noise by a substantial factor, but only if the scan pattern is thoroughly interconnected. (4) 1/f noise produces a 1/l contribution to the angular power spectrum for well connected single-beam scanning, as compared to virtually white noise for a two-beam scan pattern such as that of the MAP satellite.Comment: 28 pages, with 13 figures included. Minor revisions to match accepted version. Color figures and links at http://www.sns.ias.edu/~max/strategy.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/strategy.html (faster from Europe) or from [email protected]