The Sigma Commutator from Lattice QCD

As a direct source of information on chiral symmetry breaking within QCD, the sigma commutator is of considerable importance. Since hadron structure is a non-perturbative problem, numerical calculations on a space-time lattice are currently the only rigorous approach. With recent advances in the calculation of hadron masses within full QCD, it is of interest to see whether the sigma commutator can be calculated directly from the dependence of the nucleon mass on the input quark mass. We show that, provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses, one can indeed obtain a fairly reliable determination of the sigma commutator using present lattice data. For two-flavour dynamical fermion QCD the sigma commutator lies between 45 and 55 MeV based on recent data from CP-PACS and UKQCD.Comment: 4 pages, 3 figures, uses espcrc1.sty and epsfig.sty. Contribution to the proceedings of the International Conference on Quark Nuclear Physics held in Adelaide Feb. 200

Synthetic studies towards anthraquinones

The oxidation of substituted phenols with phenyliodonium diacetate in methanol was found to afford 2,4-cyclohexadienones, 2,5-cyclohexadienones or mixtures of isomers depending on the substrate being oxidized. A reaction mechanism was proposed for this oxidation which involved an intermediate aryloxenium ion. A strong correlation was observed between the experimentally determined product ratios and the results predicted by calculation of the LUMO coefficients of the proposed intermediates, Annulation of these cyclohexadienones with the anion derived from cyanophthalide afforded substituted anthraquinones in high yields. The chemistry relating to the annulation of Michael acceptors with phthalide anions was comprehensively reviewed. A mild selective method for the oxidation of hydroquinones to quinones using dibenzoyl peroxide and base is presented. A general synthetic approach to C-glycosylanthraquinones was presented, based on the annulation of a C-glycosylcyclohexadienone with the anion derived from cyanophthalide, A suitable precursor to a C-glycosylcyclohexadienone, 2-(2’,3’,4’,6’-tetra-0-acetyl-|3-D-glucopyranosyl)benzyloxybenzene, was prepared via the reaction of benzoylbromoglucose with 2-benzyloxyphenylmagnesium bromide, A group of molecules were prepared by a Marschalk reaction between /ewcoquinizarin and aldehydo-sugsrs. These compounds are potential bioreductive alkylating agents in which molecular simplicity can be achieved without overly sacrificing DNA binding ability

LAND USE CHANGE IN THE NORTHEAST UNITED STATES: RETAINING FOREST STRUCTURE AND ITS SOIL HYDRAULIC PROPERTIES THROUGH SILVOPASTURE

Growing demand for locally produced agriculture in the Northeast US could result in significant land use change from forests to open pasture and other agricultural uses. This conversion may reduce the soil hydrologic flow due to tree removal and increased soil compaction, leading to increasing surface runoff and erosion. Silvopasture—an agroforestry system that integrates trees with livestock—offers a potentially more sustainable alternative to conversion to open pasture, and has recently gained interest with local land owners and farmers in the region. The retention of trees within pastures may help maintain critical hydrologic functions of forest soils by promoting higher infiltration rates and hydraulic conductivity, and thereby avoiding degradation of forest hydrologic functions. We assessed the impacts of forest-to-pasture vs. forest-to-silvopasture conversion on soil hydraulic properties at two study sites, an unreplicated treatment site at the UNH Organic Dairy Research Farm (ODRF) in Lee, NH and a replicated treatment site at the North Branch Farm (NBF) in Saranac, NY. Specifically, we measured unsaturated hydraulic conductivity (K(h)) at the soil surface and saturated hydraulic conductivity (K(sat)) at 15 cm and 30 cm depths under three land uses: intact forest, open pasture, and silvopasture. Differences between land uses were observed in K(sat) results at both sites. At the ODRF, the K(sat) at 15cm depth was highest in intact forest, intermediate in silvopasture, and lowest in open pasture. However, at the 30 cm depth there were no distinct differences. The NBF site exhibited a different pattern, where the 15 cm K(sat) in silvopasture and open pasture were similar and both lower than the intact forest, but at the 30 cm depth, silvopasture K(sat) was higher than open pasture and comparable to the slightly higher intact forest. The reduced soil hydraulic conductivity under open pasture may have consequences for increasing surface runoff and soil erosion in response to high intensity rainfall. Soil hydraulic properties in silvopasture, although variable, have some potential to function as an intermediate between higher levels in the intact forest and lower levels in the open pasture which would partially maintain ecosystem and hydrologic services

Graph Algorithms and Complexity Aspects on Special Graph Classes

Graphs are a very flexible tool within mathematics, as such, numerous problems can be solved by formulating them as an instance of a graph. As a result, however, some of the structures found in real world problems may be lost in a more general graph. An example of this is the 4-Colouring problem which, as a graph problem, is NP-complete. However, when a map is converted into a graph, we observe that this graph has structural properties, namely being (K_5, K_{3,3})-minor-free which can be exploited and as such there exist algorithms which can find 4-colourings of maps in polynomial time. This thesis looks at problems which are NP-complete in general and determines the complexity of the problem when various restrictions are placed on the input, both for the purpose of finding tractable solutions for inputs which have certain structures, and to increase our understanding of the point at which a problem becomes NP-complete. This thesis looks at four problems over four chapters, the first being Parallel Knock-Out. This chapter will show that Parallel Knock-Out can be solved in O(n+m) time on P_4-free graphs, also known as cographs, however, remains hard on split graphs, a subclass of P_5-free graphs. From this a dichotomy is shown on $P_k$-free graphs for any fixed integer $k$. The second chapter looks at Minimal Disconnected Cut. Along with some smaller results, the main result in this chapter is another dichotomy theorem which states that Minimal Disconnected Cut is polynomial time solvable for 3-connected planar graphs but NP-hard for 2-connected planar graphs. The third chapter looks at Square Root. Whilst a number of results were found, the work in this thesis focuses on the Square Root problem when restricted to some classes of graphs with low clique number. The final chapter looks at Surjective H-Colouring. This chapter shows that Surjective H-Colouring is NP-complete, for any fixed, non-loop connected graph H with two reflexive vertices and for any fixed graph H’ which can be obtained from H by replacing vertices with true twins. This result enabled us to determine the complexity of Surjective H-Colouring on all fixed graphs H of size at most 4

"What is a Black Man Without His Paranoia?" : Clinical Depression and the Politics of African American Anxieties Toward Emotional Vulnerability

In an interview after his departure from television and a rumored "breakdown," the comedian Dave Chappelle asked Oprah Winfrey, "What is a black man without his paranoia?" This question forms the crux of a dissertation which addresses African Americans' attitudes toward clinical depression, in general, and black men's anxieties toward emotional vulnerability, in specific. Using the concept of "paranoia" as an indicator of a healthy skepticism toward medical authority, this dissertation deconstructs the concept of depression as a discursive construct and moves it out of the bounds of science and into the precincts of cultural emotion theory. Opting for theory over science, this dissertation argues against the erasure of social and cultural narratives and explores how race and gender can inform our interpretation of depression. Using textual readings, historical comparison, and ethnography, this dissertation examines the politics involved in addressing the emotionality of black men. It is concerned with how definitions of blackness, manhood, crisis, worth, and belonging impact black men's understandings of emotional wellness and inform African Americans' attitudes toward the emotional performances of black men. Two popular books on African American's mental health (Black Rage by William H. Grier and Price M. Cobbs (1968) and Black Pain by Terri Williams (2008)) are examined within their respective historical and social contexts to track the changing cultural discourse on African Americans' mental health and the role of gender in understanding narratives of wellness. And concepts family, labor, and responsibility are explored as implicit elements in black men's attainment of manhood in a comparative examination of the Sanitation Workers Strike (1968) and the Million Man March (1995)

Chiral Nonanalytic Behaviour: The Edinburgh Plot

The Edinburgh Plot is a scale independent way of presenting lattice QCD calculations over a wide range of quark masses. In this sense it is appealing as an indicator of how the approach to physical quark masses is progressing. The difficulty remains that even the most state of the art calculations are still at quark masses that are too heavy to apply dimensionally-regulated chiral perturbation theory. We present a method allowing predictions of the behaviour of the Edinburgh plot, in both the continuum, and on the lattice.Comment: 3 pages, 4 figures, Lattice2002(Spectrum

Baryon Mass Extrapolation

Consideration of the analytical properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct heavy-quark limit and have the advantage of containing information on the extended structure of hadrons. The forms involve only three unknown parameters which may be optimized by fitting to present lattice data. Recent dynamical fermion results from CP-PACS and UK-QCD are extrapolated using these new functional forms. We also use these functions to probe the limit of the chiral perturbative regime and shed light on the applicability of chiral perturbation theory to the extrapolation of present lattice QCD results.Comment: LATTICE99 (QCD Spectrum and Quark Masses