Deterministic Versus Randomized Kaczmarz Iterative Projection

Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully applied in computerized tomography. Since tomography generates a matrix A with highly coherent rows, randomized Kaczmarz algorithm is expected to provide faster convergence as it picks a row for each iteration at random, based on a certain probability distribution. It was recently shown that picking a row at random, proportional with its norm, makes the iteration converge exponentially in expectation with a decay constant that depends on the scaled condition number of A and not the number of equations. Since Kaczmarz's method is a subspace projection method, the convergence rate for simple Kaczmarz algorithm was developed in terms of subspace angles. This paper provides analyses of simple and randomized Kaczmarz algorithms and explain the link between them. It also propose new versions of randomization that may speed up convergence

WATER DEVELOPMENT - A POLICY EXERCISE

Resource /Energy Economics and Policy,

PROBLEMS AND POTENTIALS OF AGRICULTURAL ECONOMICS EXTENSION

Teaching/Communication/Extension/Profession,

A Bridge Too Far: The United Kingdom and the Transatlantic Relationship

For the past fifty years, British foreign policy has attempted to act as a 'bridge' between the continental European governments and US administrators. The end of the Cold War did not change this stance. First by John Major and more significantly by Tony Blair, British Prime Ministers continued to declare Britain's intent to remain 'at the heart of Europe' while also maintaining its 'special relationship' with the US. The period from September 11th 2001 to the invasion of Iraq, however, has severely shaken this concept as the British government has given its strong support to American policy. The argument of this chapter is that Prime Minister Blair's firm support came more from his personal conviction that Saddam Hussein's regime was a threat to global security than from his commitment to transatlantic cooperation under all circumstances. His support also resulted from the British preference for seeking influence within Washington through offering public support while moderating the direction of American policy through private criticism. Blair's double commitment to Europe and America, however, has created a diplomatic dilemma by deepening the level of distrust among its European partners about Britain's real intentions in the EU while also leaving its foreign policy success dependent on Washington's willingness to work with its NATO partners.U.K.; international relations

Using Airborne Laser Altimetry to Characterize Surface Fuels in Western Montana

Quantifying surface fuels in forests is problematic for land managers due to the difficulty in measuring fuels of different sizes and spatial variability. Estimating fuel loads is important for identifying departures from historical fire regimes, predicting fire behavior and effects, and prioritizing parcels for fuels reduction. Current field methods of estimation are not always cost-effective nor can they be practical for full coverage at landscape scales. Several studies have examined remote sensing techniques for estimating fuel loads. One of the most promising is Light Detection and Ranging (LiDAR), which thus far has been applied primarily to forest canopies. Metrics derived from LiDAR include canopy base height, canopy bulk density, biomass, crown height, basal area, and tree stem location. This study focuses on the surface fuel bed, defined as the two meter stratum above ground. The relationships between LiDAR-derived surface roughness and fuels were explored in mixed-conifer forest using a relatively sparse LiDAR dataset (~1 point/m2). Surface roughness was imputed as the standard deviation of ground height distribution of laser pulse returns. Field data were derived from the nationally-scoped Fire-Fire Surrogate Study for 432 plots using two opposing azimuth Brown’s transects at each sample point. Fuel loading and surface roughness were both highly variable at plot level across the study area. Total biomass could be predicted at a nine ha resolution (R2 = 0.73). Relationships for total biomass in the fuelbed, analyzed at 2.25 ha and 0.07 ha resolutions, showed less correlation (R2 = 0.56 and 0.094, respectively). Individual surface fuel components were analyzed for correlation with surface roughness. A combination of forest floor mass and 1-hour fuels produced the highest correlation (R2 = 0.86). Additionally, LiDAR-derived data were used to derive fire behavior fuel models. Fuel models were classified by decision tree, CART analysis, and unsupervised classification using LiDAR-derived inputs. Results were validated using 101 gridded forest inventory plots. While LiDAR consistently characterized the plots at fine scale, the subjective nature of fuel model designation made statistical validation difficult

Fraternization in Accounting Firms: A Case Study

This case study sheds light on how to avoid risks caused by manager-subordinate dating relationships (fraternization) such as employee misunderstandings, retaliation charges, favoritism complaints, wrongful termination lawsuits, and sexual harassment lawsuits, as well as associated ethical risks.  Risk avoidance can be accomplished through a better understanding of the pervasive guidance offered by judicial outcomes and typical accounting firm directives. This case study can be used in the classroom to amplify the difficult issues that accompany fraternization in accounting firms.  The authors estimate that classroom presentation and discussion of this case would require a minimum of 30 minutes of classroom time.  Background information and inherent risks associated with fraternization are discussed.  We conclude with practical steps to mitigate those risks.&nbsp

Development of an analytical-numerical model to predict radiant emission or absorption

The development of an analytical-numerical model to predict radiant emission or absorption is discussed. A voigt profile is assumed to predict the spectral qualities of a singlet atomic transition line for atomic species of interest to the OPAD program. The present state of this model is described in each progress report required under contract. Model and code development is guided by experimental data where available. When completed, the model will be used to provide estimates of specie erosion rates from spectral data collected from rocket exhaust plumes or other sources