The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

The economic ecology of small businesses in Oxfordshire

Report by the Oxfordshire Economic Observatory (OEO) for the Federation of Small Businesses (FSB), Oxfordshire Branch

Buckling without bending: a new paradigm in morphogenesis

A curious feature of organ and organoid morphogenesis is that in certain cases, spatial oscillations in the thickness of the growing "film" are out-of-phase with the deformation of the slower-growing "substrate," while in other cases, the oscillations are in-phase. The former cannot be explained by elastic bilayer instability, and contradict the notion that there is a universal mechanism by which brains, intestines, teeth, and other organs develop surface wrinkles and folds. Inspired by the microstructure of the embryonic cerebellum, we develop a new model of 2d morphogenesis in which system-spanning elastic fibers endow the organ with a preferred radius, while a separate fiber network resides in the otherwise fluid-like film at the outer edge of the organ and resists thickness gradients thereof. The tendency of the film to uniformly thicken or thin is described via a "growth potential". Several features of cerebellum, +blebbistatin organoid, and retinal fovea morphogenesis, including out-of-phase behavior and a film thickness amplitude that is comparable to the radius amplitude, are readily explained by our simple analytical model, as may be an observed scale-invariance in the number of folds in the cerebellum. We also study a nonlinear variant of the model, propose further biological and bio-inspired applications, and address how our model is and is not unique to the developing nervous system.Comment: version accepted by Physical Review

Emission Measures and Emission-measure-weighted Temperatures of Shocked ISM and Ejecta in Supernova Remnants

A goal of supernova remnant (SNR) evolution models is to relate fundamental parameters of a supernova (SN) explosion and progenitor star to the current state of its SNR. The SNR hot plasma is characterized by its observed X-ray spectrum, which yields electron temperature, emission measure and abundances. Depending on their brightness, the properties of the plasmas heated by the SNR forward shock, reverse shock or both can be measured. The current work utilizes models which are spherically symmetric. One dimensional hydrodynamic simulations are carried out for SNR evolution prior to onset of radiative losses. From these, we derive dimensionless emission measures and emission-measure-weighted temperatures, and we present fitting formulae for these quantities as functions of scaled SNR time. These models allow one to infer SNR explosion energy, circumstellar medium density, age, ejecta mass and ejecta density profile from SNR observations. The new results are incorporated into the SNR modelling code SNRPy. The code is demonstrated with application to three historical SNRs: Kepler, Tycho and SN1006.Comment: 50 pages, 10 figures, 5 table

Bantu pottery of Southern Africa

Includes bibliographical references.The Bantu people of Southern Africa entered this region from the North in successive migratory waves and advanced to the regions which they, now inhabit. The first of the immigrants crossed the Zambezi at about the beginning of the Christian era. Pottery of a type belonging to the earliest Iron Age traditions, and found north of the Zambezi (Clark 1959), has been found at Zimbabwe where it has, been dated 330 A.D. by radio carbon tests (Robinson 1961b). Contact with different people and new environments resulted in changes in the way of life and material culture of the migrants. These changes became more pronounced and permanent with the settlement of the European in South Africa and are very evident in regard to pottery. We know from the observations of early travellers and anthropologists that pottery used to be made in large quantities throughout Southern Africa

The Function of Religion in Selected Novels of George Gissing

ABSTRACT George Gissing has experienced a fluctuating reputation among critics in the period of over one hundred years since his death in 1903. Curiously, during the last decade of his life, many critics put Gissing on a par with Thomas Hardy and George Meredith among writers living at that time. Early in his career, however, his reputation suffered from the notion that Gissing was simply a naturalist with a pessimistic, atheistic streak. To some extent, this appraisal has some merit. Gissing pronounced himself an unbeliever to family and to acquaintances such as Fredrick Harrison as early as 1880. Nonetheless, Gissing maintained an interest in religion throughout his life, a fact made plain by his use of religious material in his novels. Furthermore, he was far from merely dismissing religion, nor did he adopt a uniformly unsympathetic view of belief. My dissertation will demonstrate that, starting with his first published novel, Gissing made extensive use of religious subject matter in the form of imagery, symbolism, plot elements, and characterization. More significantly, he also examined the relationship between religion and capitalism. Often, one detects in Gissing’s work a sense of what I will call economic Calvinism, an idea that has received extensive explication by Max Weber and others. I will show that Gissing’s characters are often divided into class and economic lines, a fact not in itself particularly novel, but one which finds expression in Gissing in terms very evocative of the Christian division of humanity into categories of damned and saved. I will also reveal patterns in Gissing’s work that depict the ongoing dialogue between religious issues and other social concerns such as feminism, philanthropy, poverty, church affiliation, philosophy, and marriage. The dissertation covers selected novels from roughly the first half of Gissing’s career in an attempt to bring to light the pervasiveness of religious reference in a representative assortment of Gissing’s work. My paper will show that more concentrated attention to the use of religion in Gissing will contribute to a greater understanding of him as an artist. It will also suggest that more study in this area needs to be done

Downscaled Tropical Cyclones in Simulations of the Last Glacial Maximum

A prominent area of current study is how tropical cyclone (TC) behavior will respond to future changes in global climate. One way to complement this research is by analyzing TC characteristics in simulations of past climates. In this project, we analyze the properties of TCs statistically downscaled from several climate simulations using the Coupled Hurricane Intensity Prediction System (CHIPS). This is done utilizing climate simulations of the Last Glacial Maximum (LGM) and 20th Century from three members of the Paleoclimate Modelling Intercomparision Project Phase III (PMIP3). We compare changes in large-scale tropical cyclone genesis factors to that of atmospheric circulations to better understand underlying sources of inter-model variability. Results from all three models depict a higher proportion of TCs reaching high (Category 4 and 5) intensities in the 20th Century climate compared to the colder LGM climate. Changes in TC annual frequency are more variable, with two models producing increased annual frequency with LGM to 20th Century warming and one model producing the opposite. This analysis provides insight on how tropical cyclones may have behaved during the LGM and can be compared to future projections of TC response to anthropogenic climate change

Enhancing Farm Profitability through Portfolio Analysis: The Case of Spatial Rice Variety Selection

This study applies portfolio theory to rice varietal selection decisions to find profit maximizing and risk minimizing outcomes. Results based on data from six counties in the Arkansas Delta for the period 1999–2006 suggest that sowing a portfolio of rice varieties could have increased profits from 3 to 26% (depending on the location) for rice producers in the Arkansas Delta. The major implication of this research is that data and statistical tools are available for rice producers to improve the choice of rice varieties to plant each year in specific locations. Specifically, there are large potential gains from combining varieties that are characterized by inverse yield responses to growing conditions such as drought, pest infestation, or the presence of a specific disease.optimal variety selection, portfolio analysis, rice, Agribusiness, Crop Production/Industries, Farm Management, Production Economics, Productivity Analysis, Risk and Uncertainty, G11, Q15, Q12,