Doctoral Theses (Mathematical & Computer Sciences)
Permanent URI for this collectionhttps://dspace-upgrade.is.ed.ac.uk/handle/10399/37
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Item Interest rate models with non-gaussian driven stochastic volatility(Heriot-Watt University, 2009-10) Bi, Jiangchun; Cairns, Professor Andrew J.G.In this thesis, we consider some two-factor short rate models that incorporate stochastic volatility with jumps. The motivation for studying such kinds of model is to overcome the shortcomings of di usion-based stochastic models and to provide a more accurate description of the empirical characteristics of the short rates. In our rst model, a jump process for the short-rate volatility is described with jump times generated by a Poisson process and with jump sizes following exponential distribution. Secondly, we extend the volatility model further by taking a superposition of two independent jump processes. We present the corresponding Markov chain Monte Carlo estimation algorithm and provide estimation results of candidate model parameters, latent volatility processes and the jump processes using the 3- month U.S. Treasury Bill rates. Finally, we apply our models to price fixed-income products through Monte Carlo simulation.Item Interactive real-time three-dimensional visualisation of virtual textiles(Heriot-Watt University, 2009-12) Robb, Michael Stuart Alexander; Chantler, Professor MichaelVirtual textile databases provide a cost-efficient alternative to the use of existing hardcover sample catalogues. By taking advantage of the high performance features offered by the latest generation of programmable graphics accelerator boards, it is possible to combine photometric stereo methods with 3D visualisation methods to implement a virtual textile database. In this thesis, we investigate and combine rotation invariant texture retrieval with interactive visualisation techniques. We use a 3D surface representation that is a generic data representation that allows us to combine real-time interactive 3D visualisation methods with present day texture retrieval methods. We begin by investigating the most suitable data format for the 3D surface representation and identify relief-mapping combined with Bézier surfaces as the most suitable 3D surface representations for our needs, and go on to describe how these representation can be combined for real-time rendering. We then investigate ten different methods of implementing rotation invariant texture retrieval using feature vectors. These results show that first order statistics in the form of histogram data are very effective for discriminating colour albedo information, while rotation invariant gradient maps are effective for distinguishing between different types of micro-geometry using either first or second order statistics.Item Higher genus Abelian functions associated with algebraic curves(Heriot-Watt University, 2009-12) England, Matthew; Eilbeck, Professor ChrisWe investigate the theory of Abelian functions with periodicity properties defined from an associated algebraic curve. A thorough summary of the background material is given, including a synopsis of elliptic function theory, generalisations of the Weierstrass σ and 0functions and a literature review. The theory of Abelian functions associated with a tetragonal curve of genus six is considered in detail. Differential equations and addition formula satisfied by the functions are derived and a solution to the Jacobi Inversion Problem is presented. New methods which centre on a series expansion of the σ function are used and discussions on the large computations involved are included. We construct a solution to the KP equation using these functions and outline how a general class of solutions can be generated from a wider class of curves. We proceed to present new approaches used to complete results for the lower genus trigonal curves. We also give some details on the the theory of higher genus trigonal curves before finishing with an application of the theory to the Benney moment equations. A reduction is constructed corresponding to Schwartz-Christoffel maps associated with the tetragonal curve. The mapping function is evaluated explicitly using derivatives of the σ function.Item Developing semantic pathway comparison methods for systems biology(Heriot-Watt University, 2009-09) Gamalielsson, Jonas; Corne, David W.; Olsson, BjornSystems biology is an emerging multi-disciplinary field in which the behaviour of complex biological systems is studied by considering the interaction of many cellular and molecular constituents rather than using a “traditional” reductionist approach where constituents are studied individually. Systems are often studied over time with the ultimate goal of developing models which can be used to understand and predict complex biological processes, such as human diseases. To support systems biology, a large number of biological pathways are being derived for many different organisms, and these are stored in various databases. This pathway collection presents an opportunity to compare and contrast pathways, and to utilise the knowledge they represent. This thesis presents some of the first algorithms that are designed to explore this opportunity. It is argued that the methods will be useful to biologists in order to assess the biological plausibility of derived pathways, compare different biological pathways for semantic similarities, and to derive putative pathways that are semantically similar to documented biological pathways. The methods will therefore extend the systems biology toolbox that biologists can use to make new biological discoveries.Item Some non-standard approaches to the study of sums of heavy-tailed distributions(Heriot-Watt University, 2009-09) Richards, Andrew WilliamHeavy-tailed phenomena arise whenever events with very low probability have sufficiently large consequences that these events cannot be treated as negligible. These are sometimes described as low intensity, high impact events. Sums of heavy-tailed random variables play a major role in many areas of applied probability, for instance in risk theory, insurance mathematics, financial mathematics, queueing theory, telecommunications and computing, to name but a few areas. The theory of the asymptotic behaviour of a sum of independent heavy-tailed random variables is well-understood. We give a review of known results in this area, stressing the importance of some insensitivity properties of the class of long-tailed distributions. We introduce the new concept of the Boundary Class for a long-tailed distribution, and describe some of its properties and uses. We give examples of calculating the boundary class. Geometric sums of random variables are a useful model in their own right, for instance in reliability theory, but are also useful because they model the maximum of a random walk, which is itself a model that occurs in many applications. When the summands are heavy-tailed and independent then the asymptotic behaviour has been known since the 1970s. The asymptotic expression for the geometric sum is often used as an approximation to the actual distribution, owing to the (usually) analytically intractable form of the exact distribution. However the accuracy of this asymptotic approximation can be very poor, as we demonstrate. Following and further developing work by Kalashnikov and Tsitsiashvili we construct an upper bound for the relative accuracy of this approximation. We then develop new techniques for the application of our analytical results, and apply these in practice to several examples. Source code viii for the computer algorithms used in these calculations is given. As we have said, the asymptotic behaviour of a sum of heavy-tailed random variables is well-understood when the random variables are independent, the main characteristic being the principle of the single big jump. However, the case when the random variables are dependent is much less clear. We study this case for both deterministic and random sums using a novel approach, by considering conditional independence structures on the random variables. We seek sufficient conditions for the results of the theory with independent random variables still to hold. We give several examples to show how to apply and check our conditions, and the examples demonstrate a variety of effects owing to the dependence, and are also interesting in their own right. All the results we develop on this topic are entirely new. Some of the examples also include results that are new and have not been obtainable through previously existing techniques. For some examples we study the asymptotic behaviour is known, and this allows us to contrast our approach with previous approaches.Item Action semantics of unified modeling language(Heriot-Watt University, 2009-07) Yang, Mikai; Pooley, Professor Rob; Michaelson, Professor GregThe Uni ed Modeling Language or UML, as a visual and general purpose modeling language, has been around for more than a decade, gaining increasingly wide application and becoming the de-facto industrial standard for modeling software systems. However, the dynamic semantics of UML behaviours are only described in natural languages. Speci cation in natural languages inevitably involves vagueness, lacks reasonability and discourages mechanical language implementation. Such semi-formality of UML causes wide concern for researchers, including us. The formal semantics of UML demands more readability and extensibility due to its fast evolution and a wider range of users. Therefore we adopt Action Semantics (AS), mainly created by Peter Mosses, to formalize the dynamic semantics of UML, because AS can satisfy these needs advantageously compared to other frameworks. Instead of de ning UML directly, we design an action language, called ALx, and use it as the intermediary between a typical executable UML and its action semantics. ALx is highly heterogeneous, combining the features of Object Oriented Programming Languages, Object Query Languages, Model Description Languages and more complex behaviours like state machines. Adopting AS to formalize such a heterogeneous language is in turn of signi cance in exploring the adequacy and applicability of AS. In order to give assurance of the validity of the action semantics of ALx, a prototype ALx-to-Java translator is implemented, underpinned by our formal semantic description of the action language and using the Model Driven Approach (MDA). We argue that MDA is a feasible way of implementing this source-to-source language translator because the cornerstone of MDA, UML, is adequate to specify the static aspect of programming languages, and MDA provides executable transformation languages to model mapping rules between languages. We also construct a translator using a commonly-used conventional approach, in i which a tool is employed to generate the lexical scanner and the parser, and then other components including the type checker, symbol table constructor, intermediate representation producer and code generator, are coded manually. Then we compare the conventional approach with the MDA. The result shows that MDA has advantages over the conventional method in the aspect of code quality but is inferior to the latter in terms of system performance.Item Data mining of many-attribute data : investigating the interaction between feature selection strategy and statistical features of datasets(Heriot-Watt University, 2009-06) Luo, Silang; Corne, Professor David W.In many datasets, there is a very large number of attributes (e.g. many thousands). Such datasets can cause many problems for machine learning methods. Various feature selection (FS) strategies have been developed to address these problems. The idea of an FS strategy is to reduce the number of features in a dataset (e.g. from many thousands to a few hundred) so that machine learning and/or statistical analysis can be done much more quickly and effectively. Obviously, FS strategies attempt to select the features that are most important, considering the machine learning task to be done. The work presented in this dissertation concerns the comparison between several popular feature selection strategies, and, in particular, investigation of the interaction between feature selection strategy and simple statistical features of the dataset. The basic hypothesis, not investigated before, is that the correct choice of FS strategy for a particular dataset should be based on a simple (at least) statistical analysis of the dataset. First, we examined the performance of several strategies on a selection of datasets. Strategies examined were: four widely-used FS strategies (Correlation, Relief F, Evolutionary Algorithm, no-feature-selection), several feature bias (FB) strategies (in which the machine learning method considers all features, but makes use of bias values suggested by the FB strategy), and also combinations of FS and FB strategies. The results showed us that FB methods displayed strong capability on some datasets and that combined strategies were also often successful. Examining these results, we noted that patterns of performance were not immediately understandable. This led to the above hypothesis (one of the main contributions of the thesis) that statistical features of the dataset are an important consideration when choosing an FS strategy. We then investigated this hypothesis with several further experiments. Analysis of the results revealed that a simple statistical feature of a dataset, that can be easily pre-calculated, has a clear relationship with the performance Silang Luo PHD-06-2009 Page 2 of certain FS methods, and a similar relationship with differences in performance between certain pairs of FS strategies. In particular, Correlation based FS is a very widely-used FS technique based on the basic hypothesis that good feature sets contain features that are highly correlated with the class, yet uncorrelated with each other. By analysing the outcome of several FS strategies on different artificial datasets, the experiments suggest that CFS is never the best choice for poorly correlated data. Finally, considering several methods, we suggest tentative guidelines for choosing an FS strategy based on simply calculated measures of the dataset.Item Solving key design issues for massively multiplayer online games on peer-to-peer architectures(Heriot-Watt University, 2009-05) Fan, Lu; Taylor, Doctor Hamish; Trinder, Doctor PhilMassively Multiplayer Online Games (MMOGs) are increasing in both popularity and scale on the Internet and are predominantly implemented by Client/Server architectures. While such a classical approach to distributed system design offers many benefits, it suffers from significant technical and commercial drawbacks, primarily reliability and scalability costs. This realisation has sparked recent research interest in adapting MMOGs to Peer-to-Peer (P2P) architectures. This thesis identifies six key design issues to be addressed by P2P MMOGs, namely interest management, event dissemination, task sharing, state persistency, cheating mitigation, and incentive mechanisms. Design alternatives for each issue are systematically compared, and their interrelationships discussed. How well representative P2P MMOG architectures fulfil the design criteria is also evaluated. It is argued that although P2P MMOG architectures are developing rapidly, their support for task sharing and incentive mechanisms still need to be improved. The design of a novel framework for P2P MMOGs, Mediator, is presented. It employs a self-organising super-peer network over a P2P overlay infrastructure, and addresses the six design issues in an integrated system. The Mediator framework is extensible, as it supports flexible policy plug-ins and can accommodate the introduction of new superpeer roles. Key components of this framework have been implemented and evaluated with a simulated P2P MMOG. As the Mediator framework relies on super-peers for computational and administrative tasks, membership management is crucial, e.g. to allow the system to recover from super-peer failures. A new technology for this, namely Membership-Aware Multicast with Bushiness Optimisation (MAMBO), has been designed, implemented and evaluated. It reuses the communication structure of a tree-based application-level multicast to track group membership efficiently. Evaluation of a demonstration application shows i that MAMBO is able to quickly detect and handle peers joining and leaving. Compared to a conventional supervision architecture, MAMBO is more scalable, and yet incurs less communication overheads. Besides MMOGs, MAMBO is suitable for other P2P applications, such as collaborative computing and multimedia streaming. This thesis also presents the design, implementation and evaluation of a novel task mapping infrastructure for heterogeneous P2P environments, Deadline-Driven Auctions (DDA). DDA is primarily designed to support NPC host allocation in P2P MMOGs, and specifically in the Mediator framework. However, it can also support the sharing of computational and interactive tasks with various deadlines in general P2P applications. Experimental and analytical results demonstrate that DDA efficiently allocates computing resources for large numbers of real-time NPC tasks in a simulated P2P MMOG with approximately 1000 players. Furthermore, DDA supports gaming interactivity by keeping the communication latency among NPC hosts and ordinary players low. It also supports flexible matchmaking policies, and can motivate application participants to contribute resources to the system.Item Two-loop string theory and the DVV Vertex(Heriot-Watt University, 2008-12) Cove, Henry C.D.; Szabo, Professor RichardWe compute the two-loop contributions to the free energy in the null compacti¯cation of perturbative string theory at ¯nite temperature. The cases of bosonic, Type II and heterotic strings are all treated. The calculation exploits an explicit reductive parametrization of the moduli space of in¯nite-momentum frame string worldsheets in terms of branched cover instantons. Various arithmetic and physical properties of the instanton sums are described. Applications to symmetric product orbifold conformal ¯eld theories and to the matrix string theory conjecture are investigated by analyzing the correspondence be- tween the two-loop thermal partition function of DLCQ strings in °at space and the integrated two-point correlator of twist ¯elds in a symmetric product orbifold con- formal ¯eld theory at one-loop order. This is carried out by deriving combinatorial expressions for generic twist ¯eld correlation functions in permutation orbifolds us- ing the covering surface method, by deriving the one-loop modi¯cation of the twist ¯eld interaction vertex, and by relating the two-loop ¯nite temperature DLCQ string theory to the theory of Prym varieties for genus two covers of an elliptic curve. The case of bosonic Z2 orbifolds is worked out explicitly and precise agreement between both amplitudes is found. We use these techniques to derive explicit expressions for Z2 orbifold spin twist ¯eld correlation functions in the Type II and heterotic string theories.Item The influence of cognitive styles on the design of adaptive web-based learning materials(Heriot-Watt University, 2009-05) Uruchurtu Cruz, Elizabeth; Rist, Dr Roger; MacKinnon, Professor LachlanThis research addresses the issues of adaptation and personalisation of the computer interface for Web-based learning materials taking into consideration key characteristics of learners and particularly their cognitive style. The thesis examines main concerns driving learning towards individualisation. Different approaches to adaptation and personalisation are analysed, as are a range of adaptive systems. The need for further research regarding individual differences is identified; it is argued that cognitive styles should be allowed for in designing adaptive learning materials. A comprehensive review of cognitive style classifications is presented, from which key defining attributes and advantageous instructional conditions are identified and a number of adaptive variables derived. LEARNINT, a prototype based on these variables was developed and used in two experimental studies. Results show a relationship between Interface Affect and learning outcomes and also between the variables underpinning the interface style used and variation in user reactions and performance; however, little interaction is observed between these variables and cognitive style. It is suggested that for most learners using Web-based learning materials performance may improve if they experience positive affect towards the interface; also, that the proposed variables stand as good candidates for providing adaptivity. A methodological approach is presented that extends the functionality of LEARNINT. The generic aspects of the research are further elaborated offering guidance on future directions for the design of adaptive Web-based learning materials.