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In Chapter 1, we are concerned with the number of lines a set S < ;;;; [n]d of a given size can contain. Here, a line in [n]d means a 'geometric line ', i.e. a set { x(ll, ... , x(n)} of n elements of [n]d such that for each 1 :::; i :::; d, the sequence x?), ... , x~n) is either strictly increasing from 1 to n, or strictly decreasing from n to 1, or constant. One of our aims in this chapter is to provide for every n ~ 3, a counterexample to the Ratio Conjecture of Patashnik, which states that the greatest average degree is attained when S = [n]d. Our other main aim is to prove the result (which would have been strongly suggested by the Ratio Conjecture) that the number of lines contained in S is at most [S[ 2 -c: for some c > 0. Our main aim in Chapter 2 is to provide a new proof of the Alon-Roichman Theorem. There are groups, for example Z2', such that their smallest generating set has size at least log [ G [. The Alon-Roichman Theorem theorem states that for any group G, if we pick clog [G[ elements of G uniformly at random, then not only do these elements form a generating set for the group, but in fact the Cayley graph of G with respect to these elements is highly connected, in the sense that it is an expander graph. Our proof of the Alon-Roichman Theorem gives an improvement to the known bounds. In Chapter 3, we study properties of random graphs arising from Latin squares. These include, as special cases, results on random Cayley graphs which were previously unknown. In Chapter 4, we provide asymptotically best possible bounds for a randomized version of the majority problem, extending a result of De 1/Iarco and Pelc. In this problem, we are given n balls coloured black and white. We are allowed to query whether two balls have the same colour or not and our task is to find a ball of majority colour in the minimal number of queries. Finally, in Chapter 5, we prove that the pair length of the cartesian product of two graphs is the sum of their pair lengths, answering a question of Chen.

Equivocation is a condition of language that runs riot in Hamlet, Othello, Macbeth, and King Lear. Whether as ambiguity or dissimulation, equivocation propels the plots of these plays to their tragic finales. The Doom as depicted in pre-Reformation churches is invoked in the plays as a force that could end both equivocation and tragedy. However, Shakespeare withholds this divine intervention, allowing the tragedy to play out. Chapter One outlines the thesis, explains the methodological approach, and locates the thesis in relation to the major fields of Shakespeare studies. Chapter Two focuses on the equivocal position of father-and-not-father occupied by Claudius and the Ghost in Hamlet, and the memento mori imagery in the play that reminds the audience of the inevitability of death and Judgement. Chapter Three on Othello examines Iago's equivocal mode of address, a blend of equivocations and lies that aims to move Othello from a valued insider to a detested outsider in Venice. Chapter Four argues that linguistic and temporal equivocations are the condition of Macbeth, where the trace of the future invades the present and the trace of vice invades virtue. In both Othello and Macbeth, the protagonists, in their darkest moments, summon images of apocalyptic damnation. Chapter Five proposes that the language of King Lear deconstructs the opposition between Christianity and paganism, and interprets Cordelia as both Lear's poison and remedy. Furthermore, it analyses the moment when Lear enters the stage carrying Cordelia's dead body as an equivocal invocation of the Doom. The methodological approach to this thesis draws on Derrida's conception of language as differential and without access to any divine guarantees that could anchor meaning. The tragedies, then, can be understood in relation to language: they are denied the divine force that could fix, resolve, and stabilize them.

The losses in a loaded induction motor are appreciably greater than the segregated losses based on the standard theory, but the precise causes of such losses were not fully understood. An investigation has been carried out into the nature of these additional losses and a theory is presented which explains their origins in detail. The proposed theory is based on the Fourier analysis of the stator and rotor mmf waveforms into a series of space harmonics. Each harmonic is then considered as if acting on its own; incremental paramotors being used when saturation is present. A full mathematical derivation is given of the losses produced by current flow between two adjacent squirrel cage bars, through the rotor iron, when the squirrel cage is not perfectly insulated from the rotor laminations. The theory also includes a calculation of the eddy-current and hysteresis losses in the stator and rotor teeth, caused by the high frequency harmonic fluxes that penetrate them. It shows how the eddy-currents in the rotor iron surface can reduce the value of the differential harmonic leakage of a bar, thus allowing more harmonic bar current to flow and hence more I2 R loss to be produced. It discusses how the effective skew differs from its geometrical value, depending on the width of the rotor bar. The effect of saturation on the load losses is investigated both theoretically and experimentally and proper saturation factors are derived for this purpose. Practical tests were carried out on eleven squirrel-cage induction motors and one slip-ring motor in order to verify the theoretical formulae. A new back-to-back testing technioue was developed, and by its use direct measurements of the load losses under normal operating conditions were made to a high degree of accuracy and reliability hitherto unobtainable. Other tests included measurements of the torque-slip characteristics both at reduced voltage using a swinging stator dynamometer, and at full voltage using an accelerometer. A special accelerometer, embodying a filter with time varying components to give a very high attenuation at the noise frequencies, was designed for use with this last test. Comparisons between theoretical calculations and experimental results from all the tests show a good agreement. Having established the validity of the theoretical formulae, the effect of variations in each machine parameter (skew, bar insulation, slot combination, and air gap length) on the load losses is investigated and ways of reducing these losses suggested.

A new and attractive technique for reducing emissions by storing carbon dioxide geologically is to capture it within thermodynamically stable, carbonate solids, CaCO3. However, alkalinity is required to achieve favorable conditions for carbonate precipitation (pH >8) from aqueous streams containing dissolved CO2 (pH 97%) with magnesium and iron incorporation from produced water. A life cycle assessment was performed to analyze the net carbon emissions of the technology for two produced water compositions at various inlet CO2 partial pressures (pCO2 = 0.03 – 0.20 atm) which indicated a net CO2 reduction across most conditions studied (0.533 to -0.39 kg CO2e per kg precipitated calcium carbonate). Emissions were minimized under conditions utilizing concentrated produced waters and CO2 concentrations greater than 3 vol%. Nano filtration studies showed that the XN-45 membrane can be used to generate a sodium rich permeate stream and a calcium rich retentate stream that can be recycled in the system. The results from this study indicate the ion exchange process can be used to provide alkalinity for the precipitation of carbonate solids for most of the CO2 concentrations allowing for economic mineralization processes.

Les Œuvres Bâtardes: Gender, Sexuality, and Scandal in Nineteenth-Century French Women’s Writing offers an interdisciplinary consideration of three women of letters in nineteenth-century France. This study maps the novels of George Sand, the journalistic writing of Delphine de Girardin, and the poetry of Marceline Desbordes-Valmore in an exploration of the ways in which three very different authors push thematic and formal boundaries in their efforts to explore the nexus of gender and sexuality by engaging with or challenging their perceived social roles. Sand, Girardin, and Desbordes-Valmore employ varied techniques to negotiate legitimacy and inclusion in an environment that is openly hostile to women writers. Beginning with an investigation into the controversy surrounding George Sand’s ill-received third novel Lélia, my analysis illustrates how questions of literary form, authorial gender, and women’s sexuality are closely intertwined in the nineteenth-century French cultural landscape. I then examine Delphine de Girardin’s journalistic feuilleton, the Courrier de Paris, demonstrating how Girardin’s genre crossing and gender bending encourage us to question the relationship between gender and conceptions of modernity. Finally, turning to the works of the sole woman poète maudit, Marceline Desbordes-Valmore, I interrogate the relationship between gender and poetry in the nineteenth century, revealing how the poet’s unique manner of performing femininity complicate her position in the French literary canon.

Our central nervous system employs strict regulation of the trace element copper, and dysregulation is implicated in the neuropathology of many neurodegenerative and neurocognitive diseases. Recent interest into the contribution of copper dysregulation to neurological disease has exposed our limited understanding of neuronal copper homeostasis. For instance, known uptake mechanisms do not completely account for cellular copper concentrations, suggesting alternate mechanisms remain to be found. Past work has established that some neuropeptides can bind copper, with the tachykinin neuropeptide, Neurokinin B (NKB), able to form an unusual complex with copper. Other recent approaches focusing on NKB and its corresponding receptor NK3R, identified the endogenous ligand-induced translocation of NK3R to the nucleus. Further, the newly identified copper-NKB complex has been shown to not inhibit receptor uptake, however intracellular localisation and interactions are unknown. To identify copper-NKB complex induced changes intracellularly, we used Confocal microscopy, Spectral phasor analysis, and Inductively Coupled Plasma-Mass Spectrometry to determine receptor localisation and copper concentrations in human astrocyte cell line. Our results indicate that receptor–mediated endocytosis (RME), particularly of the [Cu(NKB)2]/NK3R complex contributes to cellular copper levels. Additionally, nuclear trafficking of the receptor and nuclear copper concentrations increase when exposed to the [Cu(NKB)2] complex. Furthermore, results illustrate that this process may be clathrin-mediated, but in the absence of clathrin, can utilise a clathrin-independent pathway. This is indicative of a novel CNS-specific copper trafficking pathway, due to the CNS-specific expression of NKB. This study establishes a foundation for future neurobiological research into the underlying role RME plays in copper regulation within the CNS.

This thesis investigates the reasons for Greenberg's aesthetic intransigence, that is, his adherence to a formalist/purist stance, and his refusal to countenance non-purist twentieth century avant-garde trends evident in the art he ignored or denigrated, and in the art he promoted. The most substantial body of work challenged is Cold War revisionism (exemplified by the scholarship of Francis Frascina, Serge Guilbaut, and John O'Brian) which casts Greenberg as a politically expedient party to the imperialist agendas of various CIA-funded organisations. The major conclusions reached are that: Greenberg's aesthetic intransigence was driven by a similarly intransigent ethico-political position, and that his critical method reflected patterns of argumentation set up in 'Avant-Garde and Kitsch' (1939). This essay, and Greenberg's ethico-political position, derived, not least, from his direct encounter with American Nazism and anti-Semitism which led him to realise that America (with what he saw as its decadence, cultural apathy, and low-level mass taste) was as vulnerable to the threat of totalitarianism as Europe and Russia. Reflecting this fear, 'Avant-Garde and Kitsch' had juxtaposed a stagnant, impure culture with a vigorous avant garde culture of impeccable vintage, in the process infusing politics into a formalist, historical conception of modernism Greenberg first devised in the early 1930s and then augmented, during 1938-9, with Hans Hofmann's theories and others. Thus established, this rudimentary paradigm for Greenberg's art writing was elaborated upon and made canonical in 'Towards a Newer Laocoon' (1940), and entrenched after the war concurrent with the entrenchment of his ethico-political position. In the face of a Stalinist/capitalist war of wills, continuing anti-Semitism, and what Greenberg perceived as increasing decadence, he continued to argue for a serious, professionally-skilled (predominantly abstract) art, which would be resistant to the ersatz, yet not dehumanized by excluding the natural. By promoting this as the only genuine avant-garde art (while ignoring or denigrating playful, humorous and anarchic avant-garde tendencies), and by reiterating in the 1950s his pre-war Marxist sympathies, Greenberg was effectively demonstrating his continued hope for a utopian culture (luxuriant, formal, informed and socialist) first visualised in the late 1930s.

An American option is a type of option that can be exercised at any time up to its expiration. American options are generally hard to value, as there is no closed-form solution for the price of an American option. When there are multiple stochastic factors in the equation, the usual solution methods – binomial trees and finite difference approaches – become infeasible. Therefore, only estimators based on Monte Carlo simulation can provide good quality results. The Least-square Monte Carlo method (LSM) is the most widely used Monte Carlo-based algorithm in the financial industry. In this thesis, the LSM algorithm and associated literature are reviewed and analysed. The first major contribution is the identification of the basic powers polynomial of 4th order as the most efficient basis polynomial for the least-squares regression within the LSM simulation. The conclusion is also drawn that the performance of LSM depends on both the number of time-steps and the number of simulated paths. Another significant finding in this thesis is that, for every option being valued with a predetermined number of paths, an 'optimal' number of time-steps exists for which the estimator's mean is closest to the exact value of the option. It is proved that, in the case of the LSM algorithm, the general belief that Monte Carlo simulations become more and more efficient with the increase in the number of iterations within the simulation does not necessarily hold. The proposed Average of Batch of LSM Estimates (ABO-LSME) approach calculates the average of multiple optimal LSM estimates within the same or less time than needed for the original LSM estimate and, surprisingly, yields more precise results than the original LSM approach. The basis of the newly introduced Bundled LSM (BLSM) algorithm is an LSM algorithm in which all of the in-the-money paths at each time-step are sorted (similar to Tilley's bundling algorithm, except only in-the-money paths are sorted) and divided into a predetermined number of bundles, to which separate least-squares regressions are applied. This method provides much more stable and precise results than the original LSM algorithm. When optimal BLSM is compared to the optimal LSM algorithm, the superiority of the BLSM estimator becomes clear. BLSM provides results with lower relative errors and RMSEs, around two times faster than optimal LSM.

Default correlation modelling is becoming the most popular problem in the field of credit derivatives pricing. An increase in default risk would cause the recovery rate to change correspondingly. Correlation between default and recovery rates has a noticeable effect on risk measures and credit derivatives pricing. After an introduction, we review the most recent literature covering default correlation and the relationship between default and recovery rates. We adopt the copula methodology to focus on estimating the default correlations rather than focus on modelling probabilities of default, we then use stress testing to compare the distributions of the probability of default under different copula functions. We develop a Gamma-Beta model to link the recovery rate directly with the individual probability of default, this is instead of an extended one factor model to relate them by a systematic common factor. One factor models are re-examined to explore correlated recovery rates under three distributions: the Logit-normal, the Normal and the Log-normal. By analyzing the results respectively obtained from these two classes of modelling scheme, we argue that the direct dependence (Gamma-Beta) model behaves better, in estimating the recovery rate given individual probability of default and in suggesting a better indication of their relationship. Finally, we apply default correlation and the correlated recovery rate to portfolio risk modelling. We conclude that if the recovery rates are independent stochastic variables, the expected losses in a large portfolio might be underestimated because the uncorrelated recovery risks can be diversified, so the correlation between default rate and recovery risk can not be neglected in the applications. Here, we believe the first time, the recovery rate depends on individual default probability by means of a closed formula.

Since its initial publication the SABR model has gained widespread use across asset classes and it has now become the standard pricing framework used in the market to quote interest rate products sensitive to the non flat strike-structure of the market implied volatility. While very simple, the modelÂ’s use has always been based on the original study of its authors who derive a formula for pricing European options through a few approximating assumptions which are at times severely violated in the market. This thesisÂ’ main theoretical goal is to set the path for a generalization of the SABR model which possesses a closed form solution free from assumptions about the magnitude of the modelÂ’s parameters. We propose such model and derive a closed form solution for the particular case in which the underlying forward rate and its volatility are uncorrelated. After using the solution for pricing caplets within a LIBOR Market Model framework we simplify an approximation for the swap rate developed by Piterbarg in order to use the same solution for the pricing of swaptions. We conduct the modelÂ’s calibration for short maturities using a computationally efficient approach which derives an approximation for the modelÂ’s implied volatility and uses it to fit the model to market quotes. Finally, we study the properties of the greeks of our model in comparison with those of the classical Black model.

This thesis presents an approach for company valuation by a replication portfolio of traded assets in discrete time. The model allows us to value companies with an uncertain cash flow stream without having to revert to any discount rates including premia. Modelling of asset values can be achieved in two steps: (i) Choosing a suitable stochastic process and calibrating its parameters to fit the historical asset time series behaviour, and (ii) generating a state space transition graph to implement the stochastic process dynamics in discrete time. For company valuation, a selected number of "assets" (economic, financial, and other factors) should be captured that may reasonably be assumed to influence future cash flows of the company. Each vertex of the transition graph represents a "state of the world" and is accompanied with a corresponding cash flow caused by the sales (or other company activities) at that vertex. These possible future company cash flows can be "replicated" (without the existence of the company) by investing in a self-financing portfolio of non-company assets at the beginning, and trading this portfolio as the future evolves. The minimum cost of such a self-financing portfolio equals the value of the company. A dynamic programming algorithm for this valuation problem has been derived in discrete time. Due to the fact that an exact duplication is not possible for all cases, the replication strategy will be generated by minimising the deviations in each state to approximate an exact replication. The company valuation algorithm in discrete time is based on two main ideas: The replication approach for arbitrage-free valuation as it is known for the valuation of contingency claims (Cox, Rubinstein 1985) as well as an optimisation to compute the least value replication portfolio following an approach originally established by Alexander Christofides (Christofides A. 2004). The research results derived in this thesis contribute to the further integration of some methodologies for contingent claim valuation and optimisation techniques. The derived algorithm has been applied for the valuation of companies with a high uncertainty in their expected cash flows (like start-up companies), and gives further insight in the valuation of non-traded companies. With the application of the derived company valuation algorithm, the limitations and shortcomings of determining the companies' weighted average cost of capital (WACC) can be by-passed. In a further step, the algorithm has been extended to calculate the potential value contribution of the companies' real options. Part of the contribution is the generalisation of the algorithm in the way that decision-making strategies from the capital markets, as well as strategic decisions from inside corporates can be implemented and evaluated. The optimal timing of the additional investment can be computed, and the attached additional value of the "optimal" execution of these investment options is calculated. The implementation of the algorithm is performed in C++. The extended algorithm has been applied for two high growth companies in the area of Life Sciences, confirming the applicability of the algorithm. Results will be reported for Qiagen and GPC Biotech.