On the exponential convergence of the Kaczmarz algorithm

The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds

A Bark Thickness Model for White Spruce in Alaska Northern Forests

Here we developed a simple linear model to estimate white spruce bark thickness in the northern forests of Alaska. Data were collected from six areas throughout interior and southcentral Alaska. Geographic variation of bark thickness was tested between the Alaska statewide model and for each geographic area. The results show that the Alaska statewide model is accurate, simple, and robust, and has no practical geographic variation over the six areas. The model provides accurate estimates of the bark thickness for white spruce trees in Alaska for a wide array of future studies, and it is in demand by landowners and forest managers to support their management decisions.We are obligated to Carol E. Lewis and Edmond C. Packee for supporting this bark thickness research. This research was also supported in part by the United States Department of Agriculture, McIntire-Stennis Act Fund ALK-03-12, and by the School of Natural Resources and Agricultural Sciences, University of Alaska Fairbanks.We thank the associate editor, Han Chen, and an anonymous reviewer for their helpful comments

Post-Baccalaureate Wage Growth within Four Years of Graduation: The Effects of College Quality and College Major

This paper examines the impact of college quality and academic major on the earnings of a nationally representative sample of baccalaureate recipients. We extend previous work in this area by analyzing the magnitude of change in the influence of these factors at two points in the early career of these graduates. Our results demonstrate that, despite significant variation, graduates from higher quality colleges enjoy a greater rate of growth in earnings during their early career. We also show that growth in earnings varies significantly by the graduates’ major field of study. Wage growth for women and racial minorities is also examined

Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles

A ring-kinetic theory for Vicsek-style models of self-propelled agents is derived from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle pre-collisional correlations and cluster formation which both seem important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small density expansion of the collision operator and derive the first two equations of the BBGKY-hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not too small noises and mean free paths. This shows that there is parameter ranges in Vicsek-like models where the correlated closure of the BBGKY-hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed

MP 2012-01

In 1994 the University of Alaska Fairbanks, School of Natural Resources and Agricultural Sciences, Agricultural and Forestry Experiment Station began a project to establish permanent sample plots (PSP) throughout the forests of northern and southcentral Alaska. Objectives of the project are to establish and maintain a system of PSPs to monitor forest growth, yield, forest health, and ecological conditions/change (Malone et al., 2009). To date, 603 PSPs have been established on 201 sites throughout interior and southcentral Alaska. The PSPs are square and 0.1 acre in size and in clusters of three. PSPs are remeasured at a five-year interval. The number of plot remeasurements after establishment ranges from one to three times. A large amount of data is collected at each site at time of establishment and at subsequent remeasurements. Four databases contain all the data: tree measurement and characteristics, site description, regeneration, and vegetation data. Vegetation data collected on the 0.1 acre PSPs includes species (trees shrub, herb, grass, and non-vascular plants) and cover, an estimate of the amount of the plot covered by the crown of each species (cover class) (Daubenmire, 1959). The vegetation database can be used by land managers and researchers to study species diversity and forest succession in addition to long-term monitoring of forest health. The species listed in Appendix 1 and in the vegetation database are presented by categories: tree, shrub, herb, grass, rush, sedge, fern, club moss, lichen, moss, and liverwort

Total and Merchantable Volume of White Spruce in Alaska

White spruce (Picea glauca [Moench] Voss) is a valuable commercial species found in interior and southcentral Alaska. Numerous regional and local volume tables or equations exist; however, no statewide model exists or has been tested for accuracy. There is a demand for an accurate model to determine the cubic-foot volume of white spruce trees in Alaska. Multiple models were developed for white spruce to estimate total and merchantable cubic-foot volume to a 2-, 4-, and 6-in. top. These multiple-entry (diameter and height) models were developed for both inside and outside bark volume from a 6-in. stump. The models were tested on a regional basis at various geographic locations and were shown to be highly accurate. The Alaska models chosen have R2 at or near 0.99 and mean square error from 0 to 0.16 for all models. These models are shown to be superior to other white spruce models in Alaska.This research was supported in part by the US Department of Agriculture, McIntire-Stennis Act Fund ALK-03-12, and by the School of Natural Resources and Agricultural Sciences, University of Alaska Fairbanks