Digital Transitions: Nonprofit Investigative Journalism: Evaluation Report on the Center for Public Integrity

Summarizes outcomes of a one-year grant to CPI to transform itself into a leader in digital nonprofit journalism. Examines CPI's track record, use of new tools and methods, capacity as an effective and credible online presence, and areas for improvement

Coordinate sum and difference sets of dd-dimensional modular hyperbolas

Many problems in additive number theory, such as Fermat's last theorem and the twin prime conjecture, can be understood by examining sums or differences of a set with itself. A finite set $A \subset \mathbb{Z}$ is considered sum-dominant if $|A+A|>|A-A|$. If we consider all subsets of ${0, 1, ..., n-1}$, as $n\to\infty$ it is natural to expect that almost all subsets should be difference-dominant, as addition is commutative but subtraction is not; however, Martin and O'Bryant in 2007 proved that a positive percentage are sum-dominant as $n\to\infty$. This motivates the study of "coordinate sum dominance". Given $V \subset (\Z/n\Z)^2$, we call $S:={x+y: (x,y) \in V}$ a coordinate sumset and $D:=\{x-y: (x,y) \in V\}$ a coordinate difference set, and we say $V$ is coordinate sum dominant if $|S|>|D|$. An arithmetically interesting choice of $V$ is $\bar{H}_2(a;n)$, which is the reduction modulo $n$ of the modular hyperbola $H_2(a;n) := {(x,y): xy \equiv a \bmod n, 1 \le x,y < n}$. In 2009, Eichhorn, Khan, Stein, and Yankov determined the sizes of $S$ and $D$ for $V=\bar{H}_2(1;n)$ and investigated conditions for coordinate sum dominance. We extend their results to reduced $d$-dimensional modular hyperbolas $\bar{H}_d(a;n)$ with $a$ coprime to $n$.Comment: Version 1.0, 14 pages, 2 figure

The Effects of Different Footprint Sizes and Cloud Algorithms on the Top-Of-Atmosphere Radiative Flux Calculation from the Clouds and Earths Radiant Energy System (CERES) Instrument on Suomi National Polar-Orbiting Partnership (NPP)

Only one Clouds and Earths Radiant Energy System (CERES) instrument is onboard the Suomi National Polar-orbiting Partnership (NPP) and it has been placed in cross-track mode since launch; it is thus not possible to construct a set of angular distribution models (ADMs) specific for CERES on NPP. Edition 4 Aqua ADMs are used for flux inversions for NPP CERES measurements. However, the footprint size of NPP CERES is greater than that of Aqua CERES, as the altitude of the NPP orbit is higher than that of the Aqua orbit. Furthermore, cloud retrievals from the Visible Infrared Imaging Radiometer Suite (VIIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS), which are the imagers sharing the spacecraft with NPP CERES and Aqua CERES, are also different. To quantify the flux uncertainties due to the footprint size difference between Aqua CERES and NPP CERES, and due to both the footprint size difference and cloud property difference, a simulation is designed using the MODIS pixel-level data, which are convolved with the Aqua CERES and NPP CERES point spread functions (PSFs) into their respective footprints. The simulation is designed to isolate the effects of footprint size and cloud property differences on flux uncertainty from calibration and orbital differences between NPP CERES and Aqua CERES. The footprint size difference between Aqua CERES and NPP CERES introduces instantaneous flux uncertainties in monthly gridded NPP CERES measurements of less than 4.0 W/sq. m for SW (shortwave) and less than 1.0 W/sq. m for both daytime and nighttime LW (longwave). The global monthly mean instantaneous SW flux from simulated NPP CERES has a low bias of 0.4 W/sq. m when compared to simulated Aqua CERES, and the root-mean-square (RMS) error is 2.2 W/sq. m between them; the biases of daytime and night- time LW flux are close to zero with RMS errors of 0.8 and 0.2 W/sq. m. These uncertainties are within the uncertainties of CERES ADMs. When both footprint size and cloud property (cloud fraction and optical depth) differences are considered, the uncertainties of monthly gridded NPP CERES SW flux can be up to 20 W/sq. m in the Arctic regions where cloud optical depth retrievals from VIIRS differ significantly from MODIS. The global monthly mean instantaneous SW flux from simulated NPP CERES has a high bias of 1.1 W/sq. m and the RMS error increases to 5.2 W/sq. m. LW flux shows less sensitivity to cloud property differences than SW flux, with uncertainties of about 2 W/sq. m in the monthly gridded LW flux, and the RMS errors of global monthly mean daytime and nighttime fluxes increase only slightly. These results highlight the importance of consistent cloud retrieval algorithms to maintain the accuracy and stability of the CERES climate data record