Consumption and Real Exchange Rates in Dynamic Economies with Non-Traded Goods

We examine the possibility that nontraded goods may account for several striking features of international macroeconomic data: large, persistent deviations from purchasing power parity, small correlations of aggregate consumption fluctuations across countries, and substantial international real interest rate differentials. A dynamic, exchange economy is used to show that nontraded goods in principle can account for each of these phenomena. In the theory there is a close relation between fluctuations in consumption ratios and those in bilateral real exchange rates, but we find little evidence for this relation in time series data for eight OECD countries.consumption correlations, purchasing power parity, real exchange rates

Consumption and real exchange rates in dynamic economies with non-traded goods

We examine the possibility that nontraded goods may account for several striking features of international macroeconomic data: large, persistent deviations from purchasing power parity, small correlations of aggregate consumption fluctuations across countries, and substantial international real interest rate differentials. A dynamic, exchange economy is used to show that nontraded goods in principle can account for each of these phenomena. In the theory there is a close relation between fluctuations in consumption ratios and those in bilateral real exchange rates, but we find little evidence for this relation in time series data for eight OECD countries

Developing a Shared Understanding: Paraeducator Supports for Students with Disabilities in General Education

In order for groups of people to become effective teams it is vital that they develop a shared understanding of the underlying beliefs, values, and principles that will guide their work together. This shared understanding evolves over time as members learn about each other, spend time together, and engage in the work of their group. Having a shared understanding provides a basic structure within which teams: • develop common goals; determine actions that will lead toward the attainment of their goals; ensure that their actions are consistent with their beliefs; and judge whether their efforts have been successful

Geotomography with solar and supernova neutrinos

We show how by studying the Earth matter effect on oscillations of solar and supernova neutrinos inside the Earth one can in principle reconstruct the electron number density profile of the Earth. A direct inversion of the oscillation problem is possible due to the existence of a very simple analytic formula for the Earth matter effect on oscillations of solar and supernova neutrinos. From the point of view of the Earth tomography, these oscillations have a number of advantages over the oscillations of the accelerator or atmospheric neutrinos, which stem from the fact that solar and supernova neutrinos are coming to the Earth as mass eigenstates rather than flavour eigenstates. In particular, this allows reconstruction of density profiles even over relatively short neutrino path lengths in the Earth, and also of asymmetric profiles. We study the requirements that future experiments must meet to achieve a given accuracy of the tomography of the Earth.Comment: 35 pages, 7 figures; minor textual changes in section

Building Skills and Building Community Through Ongoing Virtual Professional Development: The Columbia University School of Social Work’s Award-Winning Annual Online Faculty Development Series

This article shares a case study of an award-winning faculty and staff training series. During AY2018–19, the Columbia University School of Social Work (CSSW) Online Campus launched a five-session virtual Annual Online Faculty Development Series, which recently completed its fifth year. Each year, the series includes five highly interactive 2-hour synchronous sessions. The sessions serve as a forum to share CSSW and Online Campus news and updates, build community, get to know CSSW deans and directors via guest visits, demonstrate and discuss best practices for online teaching, update the community on recent technology developments, and learn from guest presentations about innovations in online education and the field of social work

Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries