Thesis (Ph.D.)--McMaster University, 2006. / Supervisor: Tamás Terlaky. Includes bibliographical references (p. 181-190).

<p>The Cell Broadband Engine processor is a powerful processor capable of over 220 GFLOPS. It is highly specialized and can be controlled in detail by the programmer. The Cell is significantly more complicated to program than a standard homogeneous multi core processor such as the Intel Core2 Duo and Quad. This thesis explores the possibility to abstract some of the complexities of Cell programming while maintaining high performance. The abstraction is achieved through a library of parallel skeletons implemented in the bulk synchronous parallel programming environment NestStep. The library includes constructs for user defined SIMD optimized data parallel skeletons such as map, reduce and more. The evaluation of the library includes porting of a vector based scientific computation program from sequential C code to the Cell using the library and the NestStep environment. The ported program shows good performance when compared to the sequential original code run on a high-end x86 processor. The evaluation also shows that a dot product implemented with the skeleton library is faster than the dot product in the IBM BLAS library for the Cell processor with more than two slave processors.</p><p> </p>

The appropriate separation of concerns is a fundamental engineering principle. A concern, for software developers, is that which must be represented by code in a program; by extension, separation of concerns is the ability to represent a single concern in a single appropriate programming language construct. Advanced separation of concerns is a relatively recent technique in software development for dealing with the complexity of systems that contain crosscutting concerns, namely those individual concerns that cut across programs. Aspect-oriented programming (AOP), which is the area of this dissertation, offers a form of advanced separation of concerns in which primary and crosscutting concerns can be separated during problem solving. An aspect gathers into one place a concern that is or would otherwise be scattered throughout an object-oriented program or system. The primary aim of this dissertation-the AOPy project-is to investigate the usefulness of advanced separation of concerns that aspect-oriented programming offers. In other words, the AOPy Project determines whether the potential usefulness of aspect-oriented programming is currently actualized in practice. In determining its current practical usefulness, this dissertation also determines characteristics of and obstacles to usefulness of aspect-orientation in software development. Perhaps the most important contribution to understanding and addressing the problem of complexity in software systems that this dissertation makes is that the AOPy research project establishes a definition of compatibility of aspect-orientation and provides an analysis of sample instances during problem solving that indicate evidence of compatibility between object-orientation and aspect-orientation. Compatibility, as defined by the AOPy Project, exists when aspect-oriented ideas, terminology, and techniques are appropriately employed in the experimental problem-solving session. The primary scientific contribution of this dissertation, therefore, is a narrative description of the actual use of aspect-oriented programming in a series of controlled, problem-solving scenarios. Theories describing the use of aspect-oriented ideas, terminology, and techniques are generated and refined by means of Grounded Theory, a qualitative data analysis technique. Because this dissertation 1) analytically explores areas of compatibility of aspect-orientation with object-orientation and 2) defines areas of compatibility thwarted in practice, this research project can serve as a foundation for the development of aspect-oriented programming-based design methodologies that encourage compatibility and discourage non-compatibility. Therefore, the AOPy Project establishes a foundation for future research in both its methodology and its results and for future software development in practice. By contributing a definition of aspect-oriented compatibility and a framework within which it can be understood, this dissertation fosters the progression toward a seamless use of aspect-orientation between developer and task. / Graduation date: 2005

Declarative visual programming languages (VPLs), including spreadsheets, make up a large portion of both research and commercial VPLs. Spreadsheets in particular enjoy a wide audience, including end users. Unfortunately, spreadsheets and most other declarative VPLs still suffer from some of the problems that have been solved in other languages, such as ad-hoc (cut-and-paste) reuse of code which has been remedied in object-oriented languages, for example, through the code-reuse mechanism of inheritance. We believe spreadsheets and other declarative VPLs can benefit from the addition of an inheritance-like mechanism for fine-grained code reuse. This dissertation first examines the opportunities for supporting reuse inherent in declarative VPLs, and then introduces similarity inheritance and describes a prototype of this model in the research spreadsheet language Forms/3. Similarity inheritance is very flexible, allowing multiple granularities of code sharing and even mutual inheritance; it includes explicit representations of inherited code and all sharing relationships, and it subsumes the current spreadsheet mechanisms for formula propagation, providing a gradual migration from simple formula reuse to more sophisticated uses of inheritance among objects. Since the inheritance model separates inheritance from types, we investigate what notion of types is appropriate to support reuse of functions on different types (operation polymorphism). Because it is important to us that immediate feedback, which is characteristic of many VPLs, be preserved, including feedback with respect to type errors, we introduce a model of types suitable for static type inference in the presence of operation polymorphism with similarity inheritance. / Graduation date: 1999

Lifting is a well known technique in resolution theorem proving, logic programming, and term rewriting. In this paper we formulate lifting as an efficiency-motivated program transformation applicable to a wide variety of nondeterministic procedures. This formulation allows the immediate lifting of complex procedures, such as the Davis-Putnam algorithm, which are otherwise difficult to lift. We treat both classical lifting, which is based on unification, and various closely related program transformations which we also call lifting transformations. These nonclassical lifting transformations are closely related to constraint techniques in logic programming, resolution, and term rewriting.

This work is concerned with the study of nonlinear nonconvex stochastic programming, in particular in the context of trust-region approaches. We first explore how to exploit the structure of multistage stochastic nonlinear programs with linear constraints, in the framework of primal-dual interior point methods. We next study consistency of sample average approximations (SAA) for general nonlinear stochastic programs. We also develop a new algorithm to solve the SAA problem, using the statistical inference information to reduce numercial costs, by means of an internal variable sample size strategy. We finally assess the numerical efficiency of the proposed method for the estimation of discrete choice models, more precisely mixed logit models, using our software AMLET, written for this purpose.

Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip stocks and well-established companies have folded and filed for bankruptcy, an event that might have thought to been absurd two years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for investment problems of the 21st century. Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of managing constraints that are coupled to general historic risk and return models. We identify three well-known portfolio problems and add an array of practical managing constraints that form three different types of Mixed-Integer Programs. The product is advanced mathematical models related to risk-return portfolios, index tracking portfolios, and an integrated stock-bond portfolio selection model. The numerous sources of uncertainty are captured in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We minimize trade-offs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market. Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.

Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip stocks and well-established companies have folded and filed for bankruptcy, an event that might have thought to been absurd two years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for investment problems of the 21st century. Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of managing constraints that are coupled to general historic risk and return models. We identify three well-known portfolio problems and add an array of practical managing constraints that form three different types of Mixed-Integer Programs. The product is advanced mathematical models related to risk-return portfolios, index tracking portfolios, and an integrated stock-bond portfolio selection model. The numerous sources of uncertainty are captured in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We minimize trade-offs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market. Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.

This study explored the development of student’s conceptual understanding of limit and derivative when specific computational tools were utilized. Fourteen students from a secondary Advanced Placement Calculus AB course explored the limit and derivative concepts from calculus using computational tools in the Maple computer algebra system. Students worked in pairs utilizing the pair-programming collaborative model. Four groups of student pairs constructed computational tools and used them to explore the limit and derivative concepts. The remaining four student pairs were provided similar tools and asked to perform identical explorations. A multiple embedded case design was utilized to explore ways students in two classes, a programming class P and a non-programming class N, constructed understandings focusing upon their interactions with each other and with the computational tools. The Action-Process-Object-Schema (APOS) conceptual model and Constructionist framework guided design and construction of the tools, outlined developmental goals and milestones, and provided interpretive context for analysis. Results provided insights into the effective design and use of computational tools in fostering conceptual understanding. The study found the additional burden of programming redirected students’ attention away from the intended conceptual understandings. The study additionally found, however, that pre-constructed tools effectively promote conceptual understanding of the limit concept when coupled with a mature conceptual model of development. Four themes influencing development of these understandings emerged: An instructional focus on skills over concepts, the instructional sequence, the willingness and ability of students to adopt and utilize computational tools, and the ways cognitive conflict was mediated.

Based on the recent successes in stochastic linear programming and mixed integer programming, in this thesis we combine these two important areas of mathematical programming; specifically we study stochastic integer programming. We first study a simple and important stochastic integer programming problem, called stochastic uncapacitated lot-sizing (SLS), which is motivated by production planning under uncertainty. We describe a multi-stage stochastic integer programming formulation of the problem and develop a family of valid inequalities, called the (Q, S) inequalities. We establish facet-defining conditions and show that these inequalities are sufficient to describe the convex hull of integral solutions for two-period instances. A separation heuristic for (Q, S) inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the inequalities as cuts. Then, motivated by the polyhedral study of (Q, S) inequalities for SLS, we analyze the underlying integer programming scheme for general stochastic integer programming problems. We present a scheme for generating new valid inequalities for mixed integer programs by taking pair-wise combinations of existing valid inequalities. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some special cases, we identify combination sequences that lead to a manageable set of all non-dominated inequalities. For the general scenario tree case, we identify combination sequences that lead to non-dominated inequalities. We also analyze the conditions such that the inequalities generated by our approach are facet-defining and describe the convex hull of integral solutions. We illustrate the framework for some deterministic and stochastic integer programs and we present computational results which show the efficiency of adding the new generated inequalities as cuts.