Thesis (doctoral)--Bonn, 1998. / Includes bibliographical references (p. [273]-[274]).

In this thesis, we investigate the integrability of a class of multicomponent super integrable Korteweg-de Vries (KdV) systems in (1 + 1) dimensions in the context of recursion operator formalism. Integrability conditions are obtained for the system with arbitrary number of components. In particular, from these conditions we construct two new subclasses of multicomponent super integrable KdV systems.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Truth and falsehood, questions and answers, construction and deconstruction; most things come in dual pairs. Duality is a mirror that reveals the new from the old via opposition. This idea appears pervasively in logic, where duality inverts "true" with "false" and "and" with "or." However, even though programming languages are closely connected to logics, this kind of strong duality is not so apparent in practice. Sum types (disjoint tagged unions) and product types (structures) are dual concepts, but in the realm of programming, natural biases obscure their duality. To better understand the role of duality in programming, we shift our perspective. Our approach is based on the Curry-Howard isomorphism which says that programs following a specification are the same as proofs for mathematical theorems. This thesis explores Gentzen's sequent calculus, a logic steeped in duality, as a model for computational duality. By applying the Curry-Howard isomorphism to the sequent calculus, we get a language that combines dual programming concepts as equal opposites: data types found in functional languages are dual to co-data types (interface-based objects) found in object-oriented languages, control flow is dual to information flow, induction is dual to co-induction. This gives a duality-based semantics for reasoning about programs via orthogonality: checking safety and correctness based on a comprehensive test suite. We use the language of the sequent calculus to apply ideas from logic to issues relevant to program compilation. The idea of logical polarity reveals a symmetric basis of primitive programming constructs that can faithfully represent all user-defined data and co-data types. We reflect the lessons learned back into a core language for functional languages, at the cost of symmetry, with the relationship between the sequent calculus and natural deduction. This relationship lets us derive a pure lambda calculus with user-defined data and co-data which we further extend by bringing out the implicit control-flow in functional programs. Explicit control-flow lets us share and name control the same way we share and name data, enabling a direct representation of join points, which are essential for tractable optimization and compilation.

Traditional recursion theory is the study of computable functions on the natural numbers. This thesis considers recursion theory in first-order arithmetical theories and categories, thus expanding the work of Ritchie and Young, Lambek, Scott, and Hofstra. We give a complete characterisation of the representability of computable functions in arithmetical theories, paying attention to the differences between intuitionistic and classical theories and between theories with and without induction. When considering recursion theory from a category-theoretic perspective, we examine syntactic categories of arithmetical theories. In this setting, we construct a strong parameterised natural numbers object and give necessary and sufficient conditions to construct a Turing category associated to an intuitionistic arithmetical theory with induction.

For my MA thesis I propose to examine a series of novels that combine motifs of the body with structural and linguistic experimentation that parallels the state of the bodies within the text. Using Tsitsi Dangarembga's 1988 "bodybildungsroman" Nervous Conditions, Sherley Anne Williams' 1986 neo -slave narrative Dessa Rose, Samuel Beckett's 1938 existential novel Murphy, Vikram Seth's 1986 poetic novel Golden Gate, and Vladimir Nabokov's 1962 poetic novel Pale Fire, I will argue that these texts portray the body as a readable space of culture, a legible site of conflict or creation. I contend that these novels depict the body as either open or contained: osmotically interacting with and creatively responding to its environment, or recursively closed, interacting cancerously only with itself. In addition, using the words of the respective author when available, I will examine the form around the human form-the osmotic openness or recursiveness of the text itself: its structure, genre, and handling of language, as well as the author's deliberate unsettling of reader expectation and conscious cultivation of physical response from the audience.

Recursion is one of the most important and hardest topics in lower division computer science courses. As it is an advanced programming skill, the best way to learn it is through targeted practice exercises. But the best practice problems are hard to grade. As a consequence, students experience only a small number of problems. The dearth of feedback to students regarding whether they understand the material compounds the difficulty of teaching and learning CS2 topics. We present a new way for teaching such programming skills. Students view examples and visualizations, then practice a wide variety of automatically assessed, small-scale programming exercises that address the sub-skills required to learn recursion. The basic recursion tutorial (RecurTutor) teaches material typically encountered in CS2 courses. The advanced recursion in binary trees tutorial (BTRecurTutor) covers advanced recursion techniques most often encountered post CS2. It provides detailed feedback on the students' programming exercise answers by performing semantic code analysis on the student's code. Experiments showed that RecurTutor supports recursion learning for CS2 level students. Students who used RecurTutor had statistically significant better grades on recursion exam questions than did students who used a typical instruction. Students who experienced RecurTutor spent statistically significant more time on solving programming exercises than students who experienced typical instruction, and came out with a statistically significant higher confidence level. As a part of our effort in enhancing recursion learning, we have analyzed about 8000 CS2 exam responses on basic recursion questions. From those we discovered a collection of frequently repeated misconceptions, which allowed us to create a draft concept inventory that can be used to measure student's learning of basic recursion skills. We analyzed about 600 binary tree recursion programming exercises from CS3 exam responses. From these we found frequently recurring misconceptions. The main goal of this work is to enhance the learning of recursion. On one side, the recursion tutorials aim to enhance student learning of this topic through addressing the main misconceptions and allow students to do enough practice. On the other side, the recursion concept inventory assesses independently student learning of recursion regardless of the instructional methods. / Ph. D.

No description available.

Stock market volatility has been an important subject in the finance literature for which now an enormous body of research exists. Volatility modelling and forecasting have been in the epicentre of this line of research and although more than a few models have been proposed and key parameters on improving volatility forecasts have been considered, finance research has still to reach a consensus on this topic. This thesis enters the ongoing debate by carrying out empirical investigations by comparing models from the current pool of models as well as exploring and proposing the use of further key parameters in improving the accuracy of volatility modelling and forecasting. The importance of accurately forecasting volatility is paramount for the functioning of the economy and everyone involved in finance activities. For governments, the banking system, institutional and individual investors, researchers and academics, knowledge, understanding and the ability to forecast and proxy volatility accurately is a determining factor for making sound economic decisions. Four are the main contributions of this thesis. First, the findings of a volatility forecasting model comparison reveal that the GARCH genre of models are superior compared to the more ‘simple' models and models preferred by practitioners. Second, with the use of backward recursion forecasts we identify the appropriate in-sample length for producing accurate volatility forecasts, a parameter considered for the first time in the finance literature. Third, further model comparisons are conducted within a Value-at-Risk setting between the RiskMetrics model preferred by practitioners, and the more complex GARCH type models, arriving to the conclusion that GARCH type models are dominant. Finally, two further parameters, the Volatility Index (VIX) and Trading Volume, are considered and their contribution is assessed in the modelling and forecasting process of a selection of GARCH type models. We discover that although accuracy is improved upon, GARCH type forecasts are still superior.

Made available in DSpace on 2016-04-29T14:23:33Z (GMT). No. of bitstreams: 1 Gustavo Rick Amaral.pdf: 3226318 bytes, checksum: a3a2077e0753d164a9e77f4062405484 (MD5) Previous issue date: 2014-12-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis addresses the type of definition or characterisation used by Peirce to formulate a central concept within his semiotics: the concept of representation. Analyses carried out to support this thesis are limited to Peirce's texts from the end of the 1860s, an era in which Peirce's thinking begins to detach itself from his Kantian matrix and take on its own features. The focus of all research conducted in support of this thesis is the logical element of Charles S. Peirce s philosophical system, i.e. the argumentative structuring developed by the philosopher to validate the theories offered as responses to philosophical problems. Differently from dyadic approaches developed to explain the workings of a representation process, the conception of representation elaborated by Peirce within semiotics is triadic and such difference is far from merely numerical. Our thesis is that, with the introduction of this third element (the interpretant), characterisation of the concept of representation (elaborated within Peircean semiotics) becomes recursive by necessity and such characterisation is an in-built requirement of the theory that Peirce intends to offer as an answer to what he considered to be the central issue of philosophy: how is synthetic (i.e. ampliative) reasoning possible or, from another angle, how is it possible for knowledge to grow? With a view to proving our thesis in respect of the necessity for this type of conceptual characterisation within the Peircean philosophical project, we have dedicated a significant part of this text to the task of establishing not only that semiotics is central to such a project, but also to demonstrating that some central semiotic theses are a direct result of the fact that the concept of representation has been defined or characterised in a recursive manner. These central theses were termed elementary theses (of semiotics): "there is no first sign (in an interpretative process)" and there is no last sign (in an interpretative process)". Therefore, to render the theoretical solution found by Peirce sustainable for the (what he considered to be) central issue of philosophy, the two elementary theses referred to above must be established within semiotic theory (developed by Peirce himself), and their establishment depends on the recursion found within the concept of a sign or of a representative process (and introduced by the concept of interpretant). Our thesis is, therefore, precisely that the characterisation or definition of the concept of representation at the heart of the Peircean semiotics sign concept is necessarily recursive, because without such recursion it would simply be impossible to derive the two elementary theses of semiotics / Esta tese versa sobre o tipo de definição ou caracterização que Peirce utilizou para construir um conceito central dentro de sua semiótica: o conceito de representação. As análises que foram desenvolvidas para sustentar esta tese se limitam aos escritos peirceanos do final da década de 1860, época em que o pensamento de Peirce começa a se afastar de sua matriz kantiana e ganhar contornos próprios. O foco de toda a pesquisa realizada para a sustentação desta tese é o elemento lógico do sistema filosófico de Charles S. Peirce, i.e., a estruturação argumentativa desenvolvida pelo filósofo para validar as teorias que são oferecidas como respostas a problemas filosóficos. De modo diverso das abordagens diádicas desenvolvidas para explicar o funcionamento de um processo de representação, a concepção de representação elaborada por Peirce dentro da semiótica é triádica e esta diferença está longe de ser meramente numérica. Nossa tese é que, com a introdução desse terceiro elemento (o interpretante), a caracterização do conceito de representação (elaborado dentro da semiótica peirceana) torna-se necessariamente recursiva e este tipo de caracterização é uma exigência interna da teoria que Peirce planeja oferecer como resposta ao que considerou ser o problema central da filosofia: como são possíveis os raciocínios sintéticos (i.e., ampliativos) ou, sob outro ângulo, como é possível haver crescimento do conhecimento? Com intuito de provar esta (nossa) tese a respeito da necessidade deste tipo de caracterização conceitual dentro do projeto filosófico peirceano, dedicamos parte considerável deste texto à tarefa de estabelecer não apenas que a semiótica é central para tal projeto, mas também estabelecer que algumas teses centrais dentro da semiótica são decorrência direta do fato do conceito de representação ter sido definido ou caracterizado de forma recursiva. Estas teses centrais foram denominadas de teses elementares da semiótica: "não há primeiro signo (num processo interpretativo)" e "não há último signo (num processo interpretativo)". Então, para que seja sustentável a solução teórica encontrada por Peirce para o (que considera o) problema central da filosofia, estas duas teses elementares acima referidas têm que ser estabelecidas dentro da teoria semiótica (desenvolvida pelo próprio Peirce), e o estabelecimento destas teses depende da recursividade que é encontrada dentro da concepção de signo ou de processo representativo (e é introduzida pelo conceito de interpretante). Portanto, a nossa tese é justamente que a caracterização ou definição do conceito de representação que está no coração do conceito de signo da semiótica peirceana é necessariamente recursiva, pois sem esta recursividade, simplesmente não seria possível derivar as duas teses elementares da semiótica