Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the Bartels--Stewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite flexible way. They can handle the transposed equations and provide scaling to avoid overflow in the solution. Moreover, the Bartels--Stewart subroutine offers the optional estimation of the separation and the reciprocal condition number. A brief description of both algorithms is given. The performance of the software is demonstrated by numerical experiments.

This thesis considers elements of autobiography and autobiographical fiction in the writings of three female Modernists: Jean Rhys, Gertrude Stein and Djuna Barnes. In chapter 1, after drawing distinctions between male and female autobiographical writing, I discuss key male autobiographical fictions of the Modernist period by D.H. Lawrence, Marcel Proust and James Joyce, and their debt to the nineteenth century literary forms of the Bildungsroman and the Künstlerroman. I relate these texts to key European writers, Andre Gide and Colette, and to works by women based on two separate female Modernist aesthetics: first, the school of "lyrical transcendence"—Dorothy Richardson, Katherine Mansfield and Virginia Woolf—in whose works the self as literary subject dissolves into a renunciatory "female impressionism;" the second group—Rhys, Stein and Barnes--who as late-modernists, offer radically "objectified" self-portraits in fiction which act as critiques and revisions of both male and female Modernist fiction of earlier decades. In chapter 2, I discuss Jean Rhys' objectification of female self-consciousness through her analysis of alienation in two different settings: the Caribbean and the cities of Europe. As an outsider in both situations, Rhys presents an unorthodox counter-vision. In her fictions of the 1930's, she deliberately revises earlier Modernist representations, by both male and female writers, of female self-consciousness. In the process, she offers a simultaneous critique of both social and literary conventions. In chapter 3, I consider Gertrude Stein's career-long experiments with the rendering of consciousness in a variety of literary forms, noting her growing concern throughout the 1920's and 1930's with the role of autobiography in writing. In a close reading of The Autobiography of Alice B. Toklas, I examine Stein's parody and "deconstruction" of the autobiographical form and the Modernist conception of the self based on memory, association and desire. Her witty attack on the conventions of narrative produces a new kind of fictional self-portraiture, drawing heavily on the visual arts to create new prose forms as well as to dismantle old ones. Chapter 4 focuses on Djuna Barnes' metaphorical representations of the self in prose fiction, which re-interpret the Modernist notion of the self, by means of an androgynous fictional poetics. In her American and European fictions she extends the notion of the work of art as a formal, self-referential and self-contained "world" by subverting it with the use of a late-modern, "high camp" imagery to create new types of narrative structure. These women's major works, appearing in the 1930's, mark a second wave of Modernism, which revises and in certain ways subverts the first. Hence, these are studies in "late Modernism" and in my conclusion I will consider the distinguishing features of this transitional period, the 1930's, and the questions it provokes about the idea of periodization in general. / Arts, Faculty of / English, Department of / Graduate

The Rosetta Stone is one of the most important stone fragments in history. It is the most popular single object in London’s British Museum, has been the object of scholarly research and has had much written about it. Indeed, any account of the history of translation will at least mention the Rosetta Stone. Today, the name “Rosetta” is used metaphorically in the context of translation, foreign-language learning, and even space exploration. In the light of this, one would assume that all sources are in agreement on the facts but, surprisingly, this is not the case. This article shows that sources disagree even in the most obvious aspects, such as the material, colour, condition of the stone and, in particular, with respect to its discovery. Based on an excursion to Alexandria, Rashíd and the – in all likelihood – real discovery site in the Nile delta, this article provides facts and casts some doubt on the reliability of internet sources.

The aim of this study is to show how teachers plan for whole class discussions during problem solving lessons in years 4–6. The study has conducted interviews with five teachers who teach maths in years 4-6. The interviews were done both online and in person. To reach the goal of this study, I used five practices that Stein et.al has created to analyse my result and to come to a conclusion. In this study, I have used previous research about problem solving to help me understand my questions and to reach my aim. To help me analyse my results, I initially did a text analysis, and then, I did a content analysis. I used five practices by Stein et.al for my theory; these five practices can be used as a guideline for teachers when they are planning for problem solving lessons. The conclusion of this study is that teachers try to plan for whole class discussions during problem solving lessons, but they do not all the steps in the practice that Stein et.al has created. / <p>Matematik</p>

In this thesis, abstract bounds for the normal approximation of Poisson functionals are computed by the Malliavin-Stein method and used to derive central limit theorems for problems from stochastic geometry. As a Poisson functional we denote a random variable depending on a Poisson point process. It is known from stochastic analysis that every square integrable Poisson functional has a representation as a (possibly infinite) sum of multiple Wiener-Ito integrals. This decomposition is called Wiener-Itô chaos expansion, and the integrands are denoted as kernels of the Wiener-Itô chaos expansion. An explicit formula for these kernels is known due to Last and Penrose. Via their Wiener-Itô chaos expansions the so-called Malliavin operators are defined. By combining Malliavin calculus and Stein's method, a well-known technique to derive limit theorems in probability theory, bounds for the normal approximation of Poisson functionals in the Wasserstein distance and vectors of Poisson functionals in a similar distance were obtained by Peccati, Sole, Taqqu, and Utzet and Peccati and Zheng, respectively. An analogous bound for the univariate normal approximation in Kolmogorov distance is derived. In order to evaluate these bounds, one has to compute the expectation of products of multiple Wiener-Itô integrals, which are complicated sums of deterministic integrals. Therefore, the bounds for the normal approximation of Poisson functionals reduce to sums of integrals depending on the kernels of the Wiener-Itô chaos expansion. The strategy to derive central limit theorems for Poisson functionals is to compute the kernels of their Wiener-Itô chaos expansions, to put the kernels in the bounds for the normal approximation, and to show that the bounds vanish asymptotically. By this approach, central limit theorems for some problems from stochastic geometry are derived. Univariate and multivariate central limit theorems for some functionals of the intersection process of Poisson k-flats and the number of vertices and the total edge length of a Gilbert graph are shown. These Poisson functionals are so-called Poisson U-statistics which have an easier structure since their Wiener-Itô chaos expansions are finite, i.e. their Wiener-Itô chaos expansions consist of finitely many multiple Wiener-Itô integrals. As examples for Poisson functionals with infinite Wiener-Itô chaos expansions, central limit theorems for the volume of the Poisson-Voronoi approximation of a convex set and the intrinsic volumes of Boolean models are proven.

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Yes / This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

This thesis investigates the integration of Stein Variational Gradient Descent (SVGD) with Joint Energy Models (JEMs), comparing its performance to Stochastic Gradient Langevin Dynamics (SGLD). We incorporated a generative loss term with an entropy component to enhance diversity and a smoothing factor to mitigate numerical instability issues commonly associated with the energy function in energy-based models. Experiments on the CIFAR-10 dataset demonstrate that SGLD, particularly with Sharpness-Aware Minimization (SAM), outperforms SVGD in classification accuracy. However, SVGD without SAM, despite its lower classification accuracy, exhibits lower calibration error underscoring its potential for developing well-calibrated classifiers required in safety-critical applications. Our results emphasize the importance of adaptive tuning of the SVGD smoothing factor ($alpha$) to balance generative and classification objectives. This thesis highlights the trade-offs between computational cost and performance, with SVGD demanding significant resources. Our findings stress the need for adaptive scaling and robust optimization techniques to enhance the stability and efficacy of JEMs. This thesis lays the groundwork for exploring more efficient and robust sampling techniques within the JEM framework, offering insights into the integration of SVGD with JEMs. / Master of Science / This thesis explores advanced techniques for improving machine learning models with a focus on developing well-calibrated and robust classifiers. We concentrated on two methods, Stein Variational Gradient Descent (SVGD) and Stochastic Gradient Langevin Dynamics (SGLD), to evaluate their effectiveness in enhancing classification accuracy and reliability. Our research introduced a new mathematical approach to improve the stability and performance of Joint Energy Models (JEMs). By leveraging the generative capabilities of SVGD, the model is guided to learn better data representations, which are crucial for robust classification. Using the CIFAR-10 image dataset, we confirmed prior research indicating that SGLD, particularly when combined with an optimization method called Sharpness-Aware Minimization (SAM), delivered the best results in terms of accuracy and stability. Notably, SVGD without SAM, despite yielding slightly lower classification accuracy, exhibited significantly lower calibration error, making it particularly valuable for safety-critical applications. However, SVGD required careful tuning of hyperparameters and substantial computational resources. This study lays the groundwork for future efforts to enhance the efficiency and reliability of these advanced sampling techniques, with the overarching goal of improving classifier calibration and robustness with JEMs.