Bayesian Analysis

After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue of Bayesian analysis: the assignment of prior probabilities. The other example illustrates the use of Bayesian ideas in the real world of experimental physics.Comment: 14 pages, 5 figures, Workshop on Confidence Limits, CERN, 17-18 January, 200

Schalmont Central School District and Schalmont Teachers Association

In the Matter of the Fact-Finding Between SCHALMONT CENTRAL SCHOOL DISTRICT AND SCHALMONT TEACHERS ASSOCIATION. PERB Case No. M2006-107. Before: Peter A. Prosper, Fact Finder

Bulk contribution to magnetotransport properties of low defect-density Bi2_2Te3_3 topological insulator thin films

An important challenge in the field of topological materials is to carefully disentangle the electronic transport contribution of the topological surface states from that of the bulk. For Bi$_2$Te$_3$ topological insulator samples, bulk single crystals and thin films exposed to air during fabrication processes are known to be bulk conducting, with the chemical potential in the bulk conduction band. For Bi$_2$Te$_3$ thin films grown by molecular beam epitaxy, we combine structural characterization (transmission electron microscopy), chemical surface analysis as function of time (x-ray photoelectron spectroscopy) and magnetotransport analysis to understand the low defect density and record high bulk electron mobility once charge is doped into the bulk by surface degradation. Carrier densities and electronic mobilities extracted from the Hall effect and the quantum oscillations are consistent and reveal a large bulk carrier mobility. Because of the cylindrical shape of the bulk Fermi surface, the angle dependence of the bulk magnetoresistance oscillations is two-dimensional in nature.Comment: 12 pages, 5 figure

On word-representability of polyomino triangulations

A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)$ is an edge in $E$. Some graphs are word-representable, others are not. It is known that a graph is word-representable if and only if it accepts a so-called semi-transitive orientation. The main result of this paper is showing that a triangulation of any convex polyomino is word-representable if and only if it is 3-colorable. We demonstrate that this statement is not true for an arbitrary polyomino. We also show that the graph obtained by replacing each $4$-cycle in a polyomino by the complete graph $K_4$ is word-representable. We employ semi-transitive orientations to obtain our results

Quantifying nutrient cycling and fate within an abandoned feedlot and adjacent wetlands

Feedlot operations over the years have increased revenue and boosted economies of states and countries, but these operations have resulted in elevated concentrations of nutrients in soils, surface water, and groundwater. Feedlot operations generate large quantities of manure and other waste, which when not managed properly can result in environmental problems. It is hypothesized that nitrogen can cause a short-term contamination of soils and groundwater beneath abandoned feedlots, but phosphorus can cause both short- and long term contamination, especially in well-drained carbonate and iron-rich soils associated with Concentrated Animal Feeding Operations. It is also hypothesized that a spectral vegetation index can be used as an effective indicator of plant-available soil nutrients and optimum soil conditions for precise decision-making in fertilizer application. To test these hypotheses, analysis of soils, graminoid tissues, aerial spectral images, surface water, and groundwater samples from a former feedlot in northwest Minnesota were used to quantify the phosphorus budget, characterize nutrients movement and plant vigor, and determine the fate of nutrients. Soil analysis revealed elevated concentrations of sequestered phosphorus at the confined animal holding areas, in contrast to varying concentrations of nitrate in the wetlands. Groundwater analysis indicated a steady decline in nitrate concentration due to denitrification, leaching, and plant uptake, with sequestered phosphorus released in soluble form due to reduction conditions. These nutrients are transported into the wetlands for consumption by plants and microbes. Although there was no relationship observed between spectral vegetation indices and plant tissue nutrients, the indices correlated with soil-available nutrient and soil properties. Modified soil-adjusted vegetation index (MSAVI) was the best index for characterizing plant vigor and soil relationships due to its reduced sensitivity to atmospheric conditions and the changes in vegetative cover as compared to the other indices. The lack of any relationship between plant tissue and the spectral indices suggests that acid digestion approach used in plant tissue nutrient analysis may be problematic due to the volatility of some of the nutrients. This research provides insight into the viability of feedlots abandoned more than a decade as a source of phosphorus to supplement the primary sources of phosphorus used in fertilizer. It is estimated that crops remove approximately 2 to 15 mg kg-1 of phosphorus for growth. Phosphorus concentrations in some areas exceed 50 mg kg-1, which implies no soil phosphorus fertilization is required for plant growth. Agronomists and stakeholders in agriculture and food security should take a holistic approach and conduct feasibility studies on using sequestered phosphorus in abandoned feedlot soils as alternative source of phosphorus fertilizer