Nighttime satellite imagery from the Defense Meteorological Satellite Programs’ Operational Linescan System (DMSP OLS) is being used for myriad applications including population mapping, characterizing economic activity, disaggregate estimation of CO2 emissions, wildfire monitoring, and more. Here we present a method for in situ radiance calibration of the DMSP OLS using a ground based light so...

In this short note, we observe that the techniques of [WWE15] can be used to provide a new proof of some of the residually reducible modularity lifting results of Skinner and Wiles [SW99]. In these cases, we have found that a deformation ring of ordinary pseudorepresentations is equal to the Eisenstein local component of a Hida Hecke algebra. We also show that Vandiver’s conjecture implies Shar...

The parallel solution of Initial Value Problems for Ordinary Diierential Equations has become an active area of research during the past few years. We brieey survey the recent developments in this area, with particular emphasis on traditional forward-step methods that ooer the potential for eeective small-scale parallelism on currently existing machines.

This research was supported in part by grant DMS from the National Science Foundation A normalized modular eigenform f is said to be ordinary at a prime p if p does not divide the p-th Fourier coefficient of f. We take f to be a modular form of level 1 and weight k f12, 16, 18, 20, 22, 26g and search for primes where f is not ordinary. To do this, we need an efficient way to compute the reducti...

This article is expanded from a talk given by the author in (the preliminary version of) the Student Algebraic Topology seminar in University of Michigan, Ann Arbor. The rst part will be a review of ordinary sheaf cohomology which is done in such a way that generalization to generalized sheaf cohomology theory becomes automatic. The second part is a quick introduction of the approach to general...

Theorem 15.1. Let E/Fq be an elliptic curve over a finite field, and let πE be the Frobenius endomorphism of E. Then E is supersingular if and only if trπE ≡ 0 mod p. Proof. Let q = pn and let π be the p-power Frobenius map π(x, y) = (xp, yp) (note that π is an isogeny, but not necessarily an endomorphism, since E need not be defined over Fp). We have π̂π = [p], where [p] denotes the multiplicat...

Sensitivity analysis stands in contrast to diagnostic testing in that sensitivity analysis aims to answer the question of whether it matters that a nuisance parameter is non-zero, whereas a diagnostic test ascertains explicitly if the nuisance parameter is different from zero. In this paper, we introduce and derive the finite sample properties of a sensitivity statistic measuring the sensitivit...

The authenticity and reliability of urbanization levels measured by different indicators in China have not reached a consensus, which may impede our understanding of the process of urbanization and its impacts on the environment. The objective of this study was to describe a reliable method of estimating urbanization level based on the Operational Line-scan System (OLS) on the Defense Meteorolo...