Representation Theory of Finite Semigroups over Semirings

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the results for a field. Special attention is paid to the boolean semiring, where we also characterize the simple representations and introduce the beginnings of a character theory

Testing the Baobab’s Mettle: An Evaluation of the Sustainability and Economic Potential of Harvesting Adansonia digitata

In light of southern Africa’s growing population and economy, as well as the increasing international market for Adansonia digitata products, it seems important to ascertain whether or not rural baobab harvesting is having an impact on the health of the trees and whether it could be improved or expanded to increase benefits to communities. This study focused on 72 trees in and around the village of Gweta, Botswana, examining local usage and harvesting practices and exploring their correlations with the health of the trees. Results suggest that baobab harvesting in its current form is detrimental to the trees’ health and may not be sustainable in the long term, given Botswana’s rapid population growth. Human usage was linked to increased branch loss and to the severity of infection by rot fungi. However, recovery from these effects seems possible with time, meaning that altering harvesting practices and techniques could result in a marked improvement in both the trees’ health and their yield. This would protect the baobabs—and their important ecological niche along with them—while increasing long-term benefits to the community. Further research is necessary, but this study’s preliminary recommendation is to refine methods of fruit, bark, and root removal and to promote the protection of a set percentage of the area’s trees in order to facilitate recovery. If these goals can be met, it may be possible to sustainably expand Gweta’s local baobab usage or perhaps even to delve into larger economic ventures

EVALUATING RESTORATION OUTCOMES: RED SPRUCE REFORESTATION IN THE WEST VIRGINIA HIGHLANDS

Red spruce (Picea rubens) is the keystone species of the red spruce-northern hardwood forest, a unique high-elevation plant community that supports hundreds of animal species in the Central Appalachians. These forests were devastated by the Industrial Logging Era of the late 1800s and early 1900s, and they remain in a degraded and fragmented state. Current restoration efforts include red spruce plantings on old field sites and reclaimed coal mines. This project seeks to aid those efforts by evaluating restoration outcomes for vegetation and soils along a ten-year chronosequence. Specifically, the study aims to determine whether restoration site soils and vegetation are trending towards reference conditions, and how those trends vary between old field and reclaimed mine planting sites. Analysis revealed several promising trends in vegetation and soils. Additionally, red spruce planted on mined lands perform as well or better than those planted on old fields, owing in part to greater availability of soil nutrients on reclaimed surface mines

The genetics of human C-reactive protein and complement C3 expression in health and disease

C-reactive protein (CRP) and complement component C3 are both plasma proteins involved in antigen recognition by the innate immune system. They may play a role in the pathogenesis of immune-mediated diseases including systemic lupus erythematosus (SLE) and coronary heart disease. CRP is heritable, but there is uncertainty over the key genetic variants influencing expression. C3 heritability has not been demonstrated, although a single report suggests C3 variation influences serum C3 level and susceptibility to SLE. This thesis presents an association analysis of CRP genotype and serum CRP from four ethnically diverse cohorts. Two cohorts were diseased based (UK European and Filipino SLE family cohorts) allowing the additional analysis of CRP genotype/disease association, and one (UK rheumatoid arthritis cases) consisted of individuals with active inflammatory disease. CRP genotype was associated with serum CRP in all cohorts. Analysis of an African- American cohort (which had an informative pattern of linkage disequilibrium at CRP) highlighted a single CRP SNP, rs3091244, likely to be a key regulator of expression at this locus. No association was observed between CRP genotype and SLE. The UK European SLE cohort was also used to demonstrate C3 heritability and explore associations between C3 genotype, serum C3 and SLE. Cis-acting associations were identified with both serum C3 and SLE. The recognition that serum CRP and C3 levels are, in part, genetically determined traits has implications for their use in the monitoring and diagnosis of disease. For neither protein does a single cis-acting variant explain most of the variation in serum level: this may be determined by multiple interacting variants, many of which have yet to be identified