Minimum Principles for Ill-Posed Problems

Ill-posed problems Ax = h are discussed in which A is Hermitian,and postive definite; a bound ║Bx║ ≤ β is prescribed. A minimum principle is given for an approximate solution x^. Comparisons are made with the least-squares solutions of K. Miller, A. Tikhonov, et al. Applications are made to deconvolution, the backward heat equation, and the inversion of ill-conditioned matrices. If A and B are positive-definite, commuting matrices, the approximation x^ is shown to be about as accurate as the least-squares solution and to be more quickly and accurately computable

Numerical Simulation of Stationary and Non-Stationary Gaussian Random Processes

The purpose of this paper is to present numerical methods for the computation of samples of a Gaussian random process x(t) with prescribed autocorrelation or power spectral density

Confidence Intervals for Stereological Estimators with Infinite Variance

A statistical estimator is discussed for using two-dimensional electron-microscope data to estimate NV, the number of organelles per unit volume. Under general assumptions, the estimator is shown to be the unique unbiased estimator of NV. Though the estimator has infinite variance, large samples are shown to yield an approximately normally distributed statistic from which confidence intervals for NV can be obtained

Environmental, economic, and social changes in rural America visible in survey data and satellite images

This brief focuses on the changing landscapes of different types of rural America where social, economic, and ecological changes are occurring over large areas: the Northern Forest, Central Appalachia, and the Pacific Northwest. These three study sites embody varying historical reliance on land and natural resources and represent very different socioeconomic dynamics. Their common and unique challenges are explored, along with the far-reaching implications of land-cover change in their areas. Data used includes both telephone surveys and satellite imagery to illustrate the unique changes seen in rural America in recent years. (Please note that it is best to print this brief in color.