This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts. / Singapore-MIT Alliance (SMA)

This thesis is an investigation of the representation of the figure of the man who raped on the early modern stage. The early modern “man who raped” must be distinguished from the modern term “rapist” insofar as the modern term ascribes an ontological or sociological position to the individual male that was alien to the early modern world view. The shifting value of “rape” in the early modern period presaged more modern conceptions of rape as “an experience imposed on an embodied subject, a violent sexual assault that in its corporal nature destabilizes the intersubjective personhood of the victim” (Cahill 207). As such, the shifting values of the term also prefigured more modern conceptions of masculinity and the successful performance of masculine values. The figure of the man who raped on the early modern English stage often was not merely the monster against which successful forms of masculine behaviour could be contrasted – often such characters found a sympathetic audience. And often, that audience was encouraged and directed through paratextual and dramaturgical devices to see themselves in and identify with the man who raped, for he could be redeemed. This thesis uses the lens of the Roman play to investigate sexual assault because Roman plays clarified masculine ideals for the early moderns; Rome, civilization, manliness, stoic self-control and virtus on the early modern stage were all coincident terms that articulated sexual difference and therefore the construction of the male subject (Kahn 15). The first section looks extensively at the English inheritance of Roman and Anglo-Saxon laws on sexual assault, while the subsequent chapters turn to early modern drama more closely. The plays under study are Marston’s Wonder of Women, Heywood’s Rape of Lucrece, Shakespeare’s Titus Andronicus, Middleton’s Hengist, King of Kent, and Fletcher’s Bonduca. / SSHRC, School of English and Theatre Studies, College of Arts

A new neural network approach for performing matrix computations is presented. The idea of this approach is to construct a feed-forward neural network (FNN) and then train it by matching a desired set of patterns. The solution of the problem is the converged weight of the FNN. Accordingly, unlike the conventional FNN research that concentrates on external properties (mappings) of the networks, this study concentrates on the internal properties (weights) of the network. The present network is linear and its weights are usually strongly constrained; hence, complicated overlapped network needs to be construct. It should be noticed, however, that the present approach depends highly on the training algorithm of the FNN. Unfortunately, the available training methods; such as, the original Back-propagation (BP) algorithm, encounter many deficiencies when applied to matrix algebra problems; e. g., slow convergence due to improper choice of learning rates (LR). Thus, this study will focus on the development of new efficient and accurate FNN training methods. One improvement suggested to alleviate the problem of LR choice is the use of a line search with steepest descent method; namely, bracketing with golden section method. This provides an optimal LR as training progresses. Another improvement proposed in this study is the use of conjugate gradient (CG) methods to speed up the training process of the neural network. The computational feasibility of these methods is assessed on two matrix problems; namely, the LU-decomposition of both band and square ill-conditioned unsymmetric matrices and the inversion of square ill-conditioned unsymmetric matrices. In this study, two performance indexes have been considered; namely, learning speed and convergence accuracy. Extensive computer simulations have been carried out using the following training methods: steepest descent with line search (SDLS) method, conventional back propagation (BP) algorithm, and conjugate gradient (CG) methods; specifically, Fletcher Reeves conjugate gradient (CGFR) method and Polak Ribiere conjugate gradient (CGPR) method. The performance comparisons between these minimization methods have demonstrated that the CG training methods give better convergence accuracy and are by far the superior with respect to learning time; they offer speed-ups of anything between 3 and 4 over SDLS depending on the severity of the error goal chosen and the size of the problem. Furthermore, when using Powell's restart criteria with the CG methods, the problem of wrong convergence directions usually encountered in pure CG learning methods is alleviated. In general, CG methods with restarts have shown the best performance among all other methods in training the FNN for LU-decomposition and matrix inversion. Consequently, it is concluded that CG methods are good candidates for training FNN of matrix computations, in particular, Polak-Ribidre conjugate gradient method with Powell's restart criteria.

The purpose of this thesis is, first, to explore the presence and meaning of Foucault’s heterotopia within William Shakespeare’s “Hamlet”and Beaumont and Fletcher’s “The Knight of the Burning Pestle.” The heterotopia is a privileged space of self-reflection created by individuals or societies in crisis. In each play, the presence of crisis is explained though the metaphor of syphilis; to which individual characters respond by entering the reflective space of the heterotopia in order to countenance and “cure” their afflictions. The second purpose of this thesis is to examine the ways in which the crises acted upon the stage reflect pressing social anxieties of late – Elizabethan and early- Jacobean England: succession to the throne and shifting market structure. Both playwrights create heterotopic space for their audience through the structure of their dramatic work, and ask their audience to enter this reflective space, and consider –and learn from – their remarks upon the state of society.

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Sweet Briar House is one of the best documented sites in Virginia, with sources ranging from architectural drawings and extensive archives to original furnishings. Sweet Briar House was purchased by Elijah Fletcher, a prominent figure in Lynchburg, Virginia, in 1830. Thirty years later it passed into the possession of his daughter Indiana Fletcher Williams, and remained her home until her death in 1900. In her will, Williams left instructions for the founding of Sweet Briar Institute, an educational institution for women that exists today as Sweet Briar College. This dissertation examines Sweet Briar House in three distinct phases, while advancing three theses. The first thesis proposes that the double portico motif introduced by Palladio at the Villa Cornaro in the sixteenth century became the fundamental motif of Palladianism in Virginia architecture, generating a line of offspring that proliferated in the eighteenth century and beyond. The Palladian plantation (Sweet Briar House I, c. 1800) featured this double portico. In 1851, following the return of the Fletcher children from an extended Grand Tour of Europe, the house was remodeled as an Italianate villa (Sweet Briar House II, 1851-52). The second thesis advances the contention that by renovating their Palladian house into an asymmetrical Italianate villa, the Fletcher family implemented an ideal solution between the balanced façade that characterized the Palladian Sweet Briar House I and the fashion for the Picturesque that dominated American building in the second half of the nineteenth century. In 1876, the Williams family traveled to the Centennial Exhibition in Philadelphia, where visitors were presented with an unimaginable array of artistic possibilities from countless eras and nations, exactly the conditions that the Aesthetic Movement needed to flourish in America. The third thesis maintains that the Williams family’s decision to transform Sweet Briar House into an Aesthetic Movement retreat was inspired by their reaction to the Centennial, and in particular by their appreciation for the Japanese objects presented there.

‘The Ophelia Versions: Representations of a Dramatic Type from 1600-1633’ interrogates early modern drama’s use of the Ophelia type, which is defined in reference to Hamlet’s Ophelia and the behavioural patterns she exhibits: abandonment, derangement and suicide. Chapter one investigates Shakespeare’s Ophelia in Hamlet, finding that Ophelia is strongly identified with the ballad corpus. I argue that the popular ballad medium that Shakespeare imports into the play via Ophelia is a subversive force that contends with and destabilizes the linear trajectory of Hamlet’s revenge tragedy narrative. The alternative space of Ophelia’s ballad narrative is, however, shut down by her suicide which, I argue, is influenced by the models of classical theatre. This ending conspires with the repressive legal and social restrictions placed upon early modern unmarried women and sets up a dangerous precedent by killing off the unassimilated abandoned woman. Chapter two argues that Shakespeare and Fletcher’s The Two Noble Kinsmen amplifies Ophelia’s folk and ballad associations in their portrayal of the Jailer’s Daughter. Her comedic marital ending is enabled by a collaborative, communal, folk-cure. The play nevertheless registers a proto-feminist awareness of the peculiar losses suffered by early modern women in marriage and this knowledge deeply troubles the Jailer’s Daughter’s happy ending. Chapter three explores the role of Lucibella in The Tragedy of Hoffman arguing that the play is a direct response to Hamlet’s treatment of revenge and that Lucibella is caught up in an authorial project of disambiguation which attempts to return the revenge plot to its morality roots. Chapters four and five explore the narratives of Aspatia in The Maid’s Tragedy and Penthea in The Broken Heart, finding in their very conformism to the behaviours prescribed for them, both by the Ophelia type itself and by early modern society in general, a radical protest against the limitations and repressions of those roles. This thesis is consistently invested in the competing dialectics and authorities of oral and textual mediums in these plays. The Ophelia type, perhaps because of Hamlet’s Ophelia’s identification with the ballad corpus, proves an interesting gauge of each play’s engagement with emergent notions of textual authority in the early modern period.

Franklin Delano Roosevelt (FDR) was the longest serving president in the history of the United States, and he served during the U.S.’s worst economic crisis. During his tenure, approximately 80,000 public school teachers were left unemployed and 145,700 students had their schools closed. Furthermore, public schools and their teachers were under attack for the large number of unemployed and illiterate people. Despite these public school challenges, the literature rarely mentions FDR’s reactions or thoughts; instead, the literature focuses on the Civilian Conservation Corps (CCC) and the National Youth Administration (NYA), two New Deal youth programs. The New Deal assisted many institutions, and educators assumed public schools would also receive assistance. Under FDR, the federal government became increasingly involved in the lives of its citizens in terms of housing, food, transportation, and employment, but it did not increase its involvement in education. In this dissertation, I decipher FDR’s educational policies by analyzing his administrative actions that supported or hindered education from 1933-1940. In particular, did FDR’s governmental programs emphasize or encourage the education of youth? Did his administrative decisions support public schools? What was FDR’s policy towards federal aid to education and why? Additionally, by analyzing how educational policies were developed within FDR’s administration, educators today will better discern how they can influence policies during each step of the policymaking process. In doing so, educators will be better prepared and positioned to support American schools.

<div>When, each holiday season, William Shakespeare’s newest plays were presented for King James I of England and his court, they shared the stage with propagandistic performances and ceremonies intended to glorify the monarch and legitimate his political ideals. Between 1608 and 1613, however, the King’s son, Prince Henry Frederick, sought to use the court stage to advance his own, oppositional ideology. By examining the entertainments through which James and Henry openly competed to control this crucial mythmaking mechanism, the present investigation recreates the increasingly unstable conditions surrounding and transforming each of Shakespeare’s last plays as they were first performed at court. I demonstrate that, once read in their original courtly contexts, these plays speak directly to each stage of that escalating rivalry and interrogate the power of ceremonial display, the relationship between fiction and statecraft, and the destabilization of monarchically imposed meaning, just as they would have then.<br></div>