Parallel Solution of Diffusion Equations using Laplace Transform Methods with Particular Reference to Black-Scholes Models of Financial Options

Diffusion equations arise in areas such as fluid mechanics, cellular biology, weather forecasting, electronics, mechanical engineering, atomic physics, environmental science, medicine, etc. This dissertation considers equations of this type that arise in mathematical finance. For over 40 years traders in financial markets around the world have used Black-Scholes equations for valuing financial options. These equations need to be solved quickly and accurately so that the traders can make prompt and accurate investment decisions. One way to do this is to use parallel numerical algorithms. This dissertation develops and evaluates algorithms of this kind that are based on the Laplace transform, numerical inversion algorithms and finite difference methods. Laplace transform-based algorithms have faced a legitimate criticism that they are ill-posed i.e. prone to instability. We demonstrate with reference to the Black-Scholes equation, contrary to the received wisdom, that the use of the Laplace transform may be used to produce reasonably accurate solutions (i.e. to two decimal places), in a fast and reliable manner when used in conjunction with standard PDE techniques. To set the scene for the investigations that follow, the reader is introduced to financial options, option pricing and the one-dimensional and two-dimensional linear and nonlinear Black-Scholes equations. This is followed by a description of the Laplace transform method and in particular, four widely used numerical algorithms that can be used for finding inverse Laplace transform values. Chapter 4 describes methodology used in the investigations completed i.e. the programming environment used, the measures used to evaluate the performance of the numerical algorithms, the method of data collection used, issues in the design of parallel programs and the parameter values used. To demonstrate the potential of the Laplace transform based approach, Chapter 5 uses existing procedures of this kind to solve the one-dimensional, linear Black-Scholes equation. Chapters 6, 7, 8, and 9 then develop and evaluate new Laplace transform-finite difference algorithms for solving one-dimensional and two-dimensional, linear and nonlinear Black-Scholes equations. They also determine the optimal parameter values to use in each case i.e. the parameter values that produce the fastest and most accurate solutions. Chapters 7 and 9 also develop new, iterative Monte Carlo algorithms for calculating the reference solutions needed to determine the accuracy of the LTFD solutions. Chapter 10 identifies the general patterns of behaviour observed within the LTFD solutions and explains them. The dissertation then concludes by explaining how this programme of work can be extended. The investigations completed make significant contributions to knowledge. These are summarised at the end of the chapters in which they occur. Perhaps the most important of these is the development of fast and accurate numerical algorithms that can be used for solving diffusion equations in a variety of application areas

Magic, Mysticism, and Modern Medicine: The Influence of Alchemy on Seventeenth-Century England

In 1947, historian George Sarton questioned the place of alchemy in the history of science. He was not unlike many historians, who even attacked scholars of the subject, characterizing them as fabulous creatures who seem to be under the wrath of God themselves and who become tinctured with the kind of lunacy they set out to describe. For decades, critics fought hard to keep alchemy out of the history of science. Instead, the emphasis of the Scientific Revolution centered on the mathematical sciences, focusing mainly on the intellectual development from Copernicus to Newton and highlighting astronomy and the studies of motion at the expense of the biological and chemical sciences. It was not until 1945 that the positivism of the history of science was finally challenged by the German historian of medicine, Walter Pagel. In a short 4-page essay entitled, The Vindication of Rubbish, Pagel cautioned historians that interpretations based on the selection of material from the modern point of view, may endanger the presentation of historical truth. Instead of selecting data that \u27make sense\u27 to the acolyte of modern science, Pagel chose to focus on three very different historical figures of the Scientific Revolution; Paracelsus, van Helmont, and Harvey. Paracelsus (1493-1541), who is often recognized as the father of Renaissance alchemy and naturalism, became the focus of Pagel\u27s work. Through his research, Pagel was able to show that both the scientific and the non-scientific emerged not as simply juxtaposed or as having been conceived in spite of each other but as an organic whole in which they support and confirm each other. By the 1950s, Pagel laid the foundation for important future studies to be made in the history of alchemy and magic

Cell cycle control of endoplasmic reticulum structure and Ca2+ -release in the mouse oocyte and early embryo

In mammals, fertilisation triggers a series of intracellular Ca2+ transients which are responsible for egg activation and completion of meiosis. These oscillations are generated by InsP3-induced release of Ca2+ from the endoplasmic reticulum (ER). Ca2+ oscillations last for 3-4 hours in mouse, ceasing at the time of pronucleus formation. The subsequent breakdown of the pronuclei (NEBD) at mitosis entry is accompanied by the resumption of Ca2+ oscillations. The experiments presented in this thesis examine the relationship between ER structure and Ca2+ release in the mouse oocyte and early embryo, and investigate the role of Ca2+ release m mitosis. Using the ER-specific marker Dil, we report that germinal vesicle breakdown is associated with a dramatic microtubule-dependent redistribution of ER to the region surrounding the metaphase-I spindle. ER remains tightly packed around the spindle, during centro-cortical migration. The formation of clusters of ER in the oocyte cortex occurs around the time of polar body formation, and coincides with increased responsiveness of InsP3-mediated Ca2+ release. The decrease in cdkl-cyclin B activity which occurs following activation is both necessary and sufficient for the subsequent disappearance of ER clusters, and corresponds with diminished Ca2+ release in response to InsP3. Cortical ER clusters do not re-appear following NEBD, rather ER accumulates around the mitotic spindle. NEBD is associated with increased responsiveness of Ca2+ release both in fertilised and parthenogenetic embryos. The role of Ca2+ in mitosis was examined. Mitotic Ca2+ transients are dispensable since InsP3-receptor-downregulation and Ca2+ -chelators prohibit mitotic Ca2+ transients without affecting the first embryonic division. Microinjection of a fluorescent marker into one pronucleus reveals that nuclear membrane permeablisation begins prior to initiation of mitotic Ca2+ signals. The subsequent cessation of mitotic oscillations precedes the formation of nuclei in the two-cell embryo. No Ca transients are detected during the second mitotic division. These data demonstrate dynamic microtubule and cell cycle dependent ER reorganisations in meiosis and mitosis, in which clustering of ER in the cortex or around the spindle is associated with increased responsiveness of InsP3-releasable Ca2+ stores. Additionally, the results presented suggest that global mitotic Ca2+ transients are triggered by NEBD, rather than being the cause

Can We Calculate Fairness and Reasonableness? Determining What Satisfies the Fair Cross-Section Requirement of the Sixth Amendment

The Impartial Jury Clause of the Sixth Amendment requires that the venire from which the state and the defendant draw a twelve-person petit jury be a fair cross-section of the community. The Supreme Court announced a three-prong test in Duren v. Missouri to help courts determine whether there has been a Sixth Amendment violation: (1) whether a distinctive group in the community was excluded; (2) whether the venire was not a fair and reasonable representation of the county population as a whole; and (3) whether that underrepresentation was the result of systematic exclusion. When evaluating the second prong, courts routinely turn to statistical measurements. The four statistical tests that courts have used, including the disparity-of-risk test that the Michigan Supreme Court recently employed in People v. Bryant, fall short of adequately addressing the second prong. This Note proposes two solutions. First, courts should consider the comparative-disparity-of-risk test, borrowed from the medical malpractice loss-of-chance doctrine, as the best measure of whether underrepresentative venires are not fair and reasonable in relation to the community. Second, judges should consider whether a distinctive group in the community has systematically been excluded before turning to the question of whether an underrepresentative venire is fair and reasonable in a given community. After considering whether a distinctive group has been excluded, courts may employ the statistical tests as part of their analysis but should not use thresholds to determine what is fair and reasonable

Compositional techniques in Thomas Kerr, Jr.\u27s Anguished American Easter, 1968 and their application to the theme of African American theology

Thomas Kerr, Jr. (1915-1988), African-American organist, produced works for organ, piano, and choir. His most significant organ work, Anguished American Easter, 1968, was a musical reaction to the assassination of Martin Luther King, Jr. Powerful and dramatic, the work draws on all the forces of the modern pipe organ. Anguished American Easter, 1968, based on the spiritual He\u27 Rose expresses the sorrow and horror of death and the power and hope of the resurrection. A profound composition, it reflects the anguish of an oppressed race. The purpose of this monograph is to examine the compositional techniques Thomas Kerr, Jr. used in developing the spiritual He\u27 Rose in Anguished American Easter, 1968. Kerr\u27s piano composition, Easter Monday Swagger Scherzino, 1970, based on the spiritual Walk Together Chillen, which expresses African-American unity, will also be discussed in analyzing Thomas Kerr, Jr.\u27s utilization of the spiritual. The examination will include analyses of how Thomas Kerr, Jr. artistically interpreted the anguished African-American and the theology of Martin Luther King, Jr.\u27s message. The value of this study is to provide insight into Thomas Kerr, Jr.\u27s Anguished American Easter, 1968, as well as the struggle and oppression of the African-American race and their resulting legacy of faith as expressed through the genre of the spiritual. Chapter 1 provides biographical information and an introduction to Kerr\u27s musical style; Chapter 2 examines Kerr\u27s application of the spiritual; Chapter 3 analyzes African-American oppression as evidenced in Anguished American Easter, 1968. The conclusion summarizes Kerr\u27s musical style and the historical and theological messages inherent in Anguished American Easter, 1968

Nucleus downscaling in mouse embryos is regulated by cooperative developmental and geometric programs

Maintaining appropriate nucleus size is important for cell health, but the mechanisms by which this is achieved are poorly understood. Controlling nucleus size is a particular challenge in early development, where the nucleus must downscale in size with progressive reductive cell divisions. Here we use live and fixed imaging, micromanipulation approaches, and small molecule analyses during preimplantation mouse development to probe the mechanisms by which nucleus size is determined. We find a close correlation between cell and nuclear size at any given developmental stage, and show that experimental cytoplasmic reduction can alter nuclear size, together indicating that cell size helps dictate nuclear proportions. Additionally, however, by creating embryos with over-sized blastomeres we present evidence of a developmental program that drives nuclear downscaling independently of cell size. We show that this developmental program does not correspond with nuclear import rates, but provide evidence that PKC activity may contribute to this mechanism. We propose a model in which nuclear size regulation during early development is a multi-mode process wherein nucleus size is set by cytoplasmic factors, and fine-tuned on a cell-by-cell basis according to cell size

MINNESOTA AGRICULTURAL GROWTH, 1880-1970

The growth of Minnesota's agricultural sector, 1880-1970, was quite considerable. More important than providing a history, this study provides the necessary background for examination of the agricultural research system of Minnesota. Here, the record will be detailed. This study examines, in turn, the record of: output and production; the factors of production; relative output and input prices changes; and the structural changes in the sectorCommunity/Rural/Urban Development,

PUBLIC INSTITUTIONS AND AGRICULTURAL GROWTH: THE MINNESOTA EXPERIENCE

This chapter examines the origins and development of the agricultural research system in Minnesota. That systems encompasses the University of Minnesota's Agricultural Experiment Station; Agricultural Extension Service; and the Colleges of Agriculture, Forestry, and Home Economics.Teaching/Communication/Extension/Profession,

MINNESOTA AGRICULTURAL GROWTH, 1880-1970: APPENDIX

Community/Rural/Urban Development,