Doctoral Theses (Mathematical & Computer Sciences)

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Accurate and efficient algorithms for the approximate solution of large hyperbolic problems
(Heriot-Watt University, 1992) Lynch, M.A.M.
Action semantics of unified modeling language
(Heriot-Watt University, 2009-07) Yang, Mikai; Pooley, Professor Rob; Michaelson, Professor Greg
The 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.
Actuarial applications of survival analysis in healthcare
(Mathematical and Computer Science, 2020-04) Duncan, Ian Gordon; Macdonald, Professor Angus; Streftaris, Professor George
Healthcare actuaries are increasingly responsible for advising their employers and clients in areas of managed care. Managed care links traditional health actuarial financial work to areas of medical practice, to address the fundamental question: what works? These relatively new responsibilities have required an expansion of actuarial techniques into non-traditional areas, and, in particular, epidemiology and biostatistics. This study is about a specific area of statistics, survival analysis, a topic of great potential application in non-traditional managed care actuarial practice. Survival analysis is used frequently in biostatistics to evaluate the efficacy of treatments and to identify factors that contribute to patient survival. In this study, we illustrate three applications of survival models to solve real-world problems in areas of health actuarial practice: the estimation of survival of permanently disabled workers receiving lifetime benefits for occupational illness and injury, the rate at which seriously ill hospice patients, at risk of polypharmacy, are weaned from non-life sustaining drugs, and the ability to predict, using a model incorporating drug dosage information and specifically changes in dosage, changes in expected future lifetimes of hospice patients. All three case studies are examples of practical models that can be applied within a business context. The study will serve a more important purpose, if it shows health actuaries the potential value of the application of a non-traditional technique within their evolving practice.
Actuarial investigations in Irish capital markets
(Heriot-Watt University, 2003) Whelan, Shane F.
Adaptive and high order methods for time domain boundary elements
(Heriot-Watt University, 2018-04) Stark, David; Gimperlein, Doctor Heiko
This thesis concerns eﬃcient and accurate time domain boundary element methods for the wave equation, with an emphasis on wave scattering in singular geometries and also towards higher frequencies in 3d. The work focuses on three approaches: Mesh reﬁnements, as obtained in adaptive boundary elements or with algebraically graded meshes; a p-version of the boundary element method; and generalized boundary elements based on enriching the approximation spaces with either singular functions or plane waves. An application to traﬃc noise addresses computations for the sound ampliﬁcation in the singular horn geometry between tyre and road. The thesis ﬁrst shows that algebraically graded meshes recover quasi-optimal convergence rates in polyhedral domains. For more general singularities of the solution, adaptive mesh reﬁnements based on residual and Zienkiewicz-Zhu a posteriori error indicators lead to improved convergence rates. In benchmark examples for wave scattering on screens the convergence rates recover the rates known for time-independent problems. Then a p-version of the time domain boundary element method is presented, based on increasing the polynomial degree on a ﬁxed coarse space-time mesh. Compared to the standard h-version the p-methods are shown to double the convergence rate on screens. Generalized boundary elements are studied for both screen and plane-wave scattering. For screens the ansatz and test functions are enriched with the singular functions known from the asymptotic expansion of the exact solution near edges and corners. For planewave scattering enrichments based on plane waves are presented. In examples we obtain a rapid convergence to engineering accuracy even on coarse meshes. The work is supplemented with the study of an eﬃcient preconditioner for the linear systems arising in the time domain method. It leads to eﬃcient computation times for a wide range of discretisations.
Adaptive architecture-transparent policy control in a distributed graph reducer
(Heriot-Watt University, 2019-05) Belikov, Evgenij; Loidl, Associate Professor Hans-Wolfgang; Michaelson, Professor Greg
The end of the frequency scaling era occured around 2005 as the clock frequency has stalled for commodity architectures. Thus performance improvements that could in the past be expected with each new hardware generation needed to originate elsewhere. Almost all computer architectures exhibit substantial and growing levels of parallelism, exploiting which became one of the key sources of performance and scalability improvements. Alas, parallel programming proved much more difficult than sequential, due to the need to specify coordination and parallelism management aspects. Whilst low-level languages place the burden on the programmers reducing productivity and portability, semi-implicit approaches delegate the responsibility to sophisticated compilers and run-time systems. This thesis presents a study of adaptive load distribution based on work stealing using history and ancestry information in a distributed graph reducer for a nonstrict functional language. The results contribute to the exploration of more flexible run-time-system-level parallelism control implementing a semi-explicit model of parallelism, which offers productivity and high level of abstraction by delegating the responsibility of coordination to the run-time system. After characterising a set of parallel functional applications, we study the use of historical information to adapt the choice of the victim to steal from in a work stealing scheduler. We observe substantially lower numbers of messages for data-parallel and nested applications. However, this heuristic fails in cases where past application behaviour is not resembling future behaviour, for instance for Divide-&-Conquer applications with a large number of very fine-grained threads and generators of parallelism that move dynamically across processing elements. This mechanism is not specific to the language and the run-time system, and applies to other work stealing schedulers. Next, we focus on the other key work stealing decision of which sparks that represent potential parallelism to donate, investigating the effect of Spark Colocation on the performance of five Divide-&-Conquer programs run on a cluster of up to 256 PEs. When using Spark Colocation, the distributed graph reducer shares related work resulting in a higher degree of both potential and actual parallelism, and more fine-grained and less variable thread size. We validate this behaviour by observing a reduction in average fetch times, but increased amounts of FETCH messages and of inter-PE pointers for colocation, which nevertheless results in improved load balance for three of the five benchmark programs. The results show high speedups and speedup improvements for Spark Colocation for the three more regular and nested applications and performance degradation for two programs: one that is excessively fine-grained and one exhibiting limited scalability. Overall, Spark Colocation appears most beneficial for higher numbers of PEs, where improved load balance and higher degree of parallelism have more opportunities to pay off. In more general terms, we show that a run-time system can beneficially use historical information on past stealing successes that is gathered dynamically and used within the same run and the ancestry information dynamically reconstructed at run time using annotations. Moreover, the results support the view that different heuristics are beneficial for applications using different parallelism patterns, underlining the advantages of a flexible architecture-transparent approach.
An adaptive educational system that caters for combination of two models of learning styles
(Heriot-Watt University, 2010-11) Alghamdi, Abdulrahaman A.; Rist, Doctor Roger; Ashton, Doctor Helen; Robertson, Doctor Judy; Marwiick, David
This thesis aimed to explore the affect of combining two models of learning styles (VARK, and Honey and Mumford) in terms of students‘ learning gains and satisfaction. VARK focuses on how the students perceive learning, while Honey and Mumford examines how an individual would like to learn. A web-based educational system was built to test the combination of the two models of learning styles. A study to examine the feasibility of the system was carried out on 129 participants to explore whether the system presented tutorials according to their individual learning styles. A second study to investigate learning gains and user satisfaction was carried out on 149 participants. Satisfaction was divided into three main concepts: usability, preference and perception of learning. Learning gains were tested by giving participants a pre-test, a post-test and a confirmatory test. Participants were divided into four groups and had the lesson presented according to one learning style of either the VARK or Honey & Mumford model, both of the participants‘ learning styles or with no personal customization. The results found that participants who used the two models of learning styles showed higher learning gains and had higher levels of satisfaction across all three factors; compared to those using only one or no learning style. Furthermore, those using only one learning style showed higher learning gains and had higher levels of satisfaction than those with no learning style. The application of these findings would be of benefit to educational institutions‘ decision makers, educators, students and e-learning designers. Adaptation is a key feature of the system of research. It is intended for future work; preliminary research has shown that the users profile and learning item will change over time. This important finding is worth exploring in future research.
Adaptive Milstein methods for stochastic differential equations
(Heriot-Watt University, 2023-02) Sun, Fandi; Lord, Professor Gabriel J.; Kelly, Doctor Conall
It was shown in [27] that the Euler-Maruyama (EM) method fails to converge with equidistant timesteps in the strong sense to the solutions of stochastic differential equations (SDEs) when either of the drift or diffusion coefficients is not globally Lipschitz continuous. Higher-order methods or schemes that are developed based on EM, e.g. Milstein method or EM with jumps, inherit the problem. We introduce an explicit adaptive Milstein method for SDEs with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method relies on a class of path-bounded time-stepping strategies which work by reducing the stepsize as solutions approach the boundary of a sphere, invoking a backstop method in the event that the timestep becomes too small. We prove that such schemes are strongly L2 convergent of order one. This order is inherited by an explicit adaptive EM scheme in the additive noise case. Moreover, we show that the probability of using the backstop method at any step can be made arbitrarily small. We compare our method to other fixed-step Milstein variants on a range of test problems. Secondly, we introduce a jump-adapted adaptive Milstein (JAAM) method for SDEs driven by Poisson random measure. With the conditions of drift and diffusion coefficients remaining the same as for the adaptive Milstein method, and the jump coefficient is globally Lipschitz continuous. The corresponding time-stepping strategies that we propose are hence path-bounded and also jump-adapted. We prove the L2 strong convergence of order one for JAAM and compare its computational efficiency with jump-adapted and fixed-step methods on test models.
An adaptive robot for sports and rehabilitation coaching
(Heriot-Watt University, 2024-01) Ross, Martin Keith; Broz, Frank; Baillie, Professor Lynne
This thesis investigates how, and to what extent, an adaptive robotic coach could be used to increase motivation to, and effectiveness of, long-term repetitive solo practice in squash and rehabilitation after stroke. Stroke is one of the leading causes of acquired adult disability with survivors commonly suffering permanent impairments such as fatigue and weakness in the arms and legs. Although past research strongly suggests that unsupervised rehabilitation practice is beneficial to the patient, it is often not adhered to due to (among other reasons) a lack of motivation. Squash, on the other hand, is an intermittent, high-intensity racket sport in which repetitive, solo drills are used frequently by many of the top professionals. However, they are used much less frequently by players of lower levels, indicating a lack of motivation when a coach is not present. These two use cases, from different domains, are considered in the same body of work due to the similarities in the individual, often unsupervised and repetitive nature of practice that helps in making long-term functional improvements after stroke and helps high performance sports players improve their skill level. This thesis contributes a cross-domain implementation of a robotic coach using the Pepper robot, which incorporates high-level personalisation to groups of users and low-level adaption to individuals over time. The development process combined quantitative data from systematic observations and qualitative recommendations from domain professionals during semi-structured interviews, with mathematical modelling and computation techniques to produce coaching policies usable for robotic control. Short-term evaluations in squash and stroke rehabilitation validated the novel cross-domain design and implementation process and revealed that the robotic coach was viewed by non-professional squash players as more interesting/enjoyable, more socially competent, and a more effective coach than a robot that didn’t offer any coaching behaviours. Finally, a long-term evaluation showed that Pepper was able to make solo squash sessions more interesting/enjoyable, gave users a higher sense of perceived choice, and allowed players to make larger technical improvements within sessions than during regular, unsupervised practice.
Age heaping in population data of emerging countries
(Heriot-Watt University, 2022-02) Barajas Paz, Andres; Cairns, Professor Andrew; Kleinow, Doctor Torsten
Mortality analyses have commonly focused on countries represented in the Human Mortality Database that have good quality mortality data. In this thesis, we address the challenge that, in many countries, population and deaths data can be somewhat unreliable. In many countries, for example, there is significant misreporting of age in both census and deaths data: referred to as “age heaping”. The purpose of our research is to develop Bayesian computational methods for fitting a new model for misreporting of age for countries where their population data and death counts have been affected by age heaping. The innovation of our model is that it allows us to detect misreporting, identify age preferences and estimate the true underlying distribution of ages.
Algebraic and geometric aspects of two-dimensional Artin groups
(Heriot-Watt University, 2023-04) Vaskou, Nicolas; Martin, Alexandre
In this thesis we study the algebra and the geometry of two-dimensional Artin groups under various aspects. First, we solve the problem of acylindrical hyperbolicity, by proving that all the two-dimensional Artin groups that are not trivially non-acylindrically-hyperbolic are acylindrically hyperbolic. In particular, we prove that every non-spherical Artin group of dimension 2 has trivial centre. Then, we study the structure of parabolic subgroups of large-type Artin groups, and prove various results about their combinatorial structure. We notably show that any intersection of parabolic subgroups is again a parabolic subgroup. Finally, we study the isomorphisms between Artin groups of large-type, and we prove that the family of large-type free-of-infnity Artin groups is rigid. We also fully describe the automorphism groups of these Artin groups.
Algebraic structures in stochastic differential equations
(Heriot-Watt University, 2014-10) Curry, Charles; Malham, Simon; Wiese, Anke
We define a new numerical integration scheme for stochastic differential equations driven by Levy processes with uniformly lower mean square remainder than that of the scheme of the same strong order of convergence obtained by truncating the stochastic Taylor series. In doing so we generalize recent results concerning stochastic differential equations driven by Wiener processes. The aforementioned works studied integration schemes obtained by applying an invertible mapping to the stochastic Taylor series, truncating the resulting series and applying the inverse of the original mapping. The shuffle Hopf algebra and its associated convolution algebra play important roles in the their analysis, arising from the combinatorial structure of iterated Stratonovich integrals. It was recently shown that the algebra generated by iterated It^o integrals of independent Levy processes is isomorphic to a quasi-shuffle algebra. We utilise this to consider map-truncate-invert schemes for Levy processes. To facilitate this, we derive a new form of stochastic Taylor expansion from those of Wagner & Platen, enabling us to extend existing algebraic encodings of integration schemes. We then derive an alternative method of computing map-truncate-invert schemes using a single step, resolving diffculties encountered at the inversion step in previous methods.
Allowing for insurance companies' liabilities in mean-variance models
(Heriot-Watt University, 1998) Berketi, Alexandra
Analysis and approximation of a nonlocal equation
(Heriot-Watt University, 2014-09) Alshomrani, Ali; Duncan, Professor Dugald; Carr, Professor Jack
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Analysis and massively parallel implementation of the 2-Lagrange multiplier methods and optimized Schwarz methods
(Heriot-Watt University, 2016-04) Karangelis, Anastasios; Loisel, Doctor Sebastien
The analysis and projection of mortality rates for annuity and pensions business
(Heriot-Watt University, 2012-02) Richards, Stephen J.; Macdonald, Professor Angus; Currie, Doctor Iain D.
Longevity risk is a major issue for the developed world. As both mortality rates and birth rates fall, the increasing burden of providing for retirees falls on a smaller working population. Under such circumstances, the accurate modelling and measurement of longevity risk becomes particularly important. Longevity risk is present in the annuity portfolios of insurance companies, and increasingly of reinsurers as well. However, the biggest concentration of longevity risk in the private sector in the United Kingdom is most often in the shape of de nedbene t pension promises by employers. This makes longevity risk of crucial interest to managers and investors, even if they think that their business has nothing to do with insurance. Actuaries handle longevity risk by breaking it into two components: the current (or period) rates of mortality, and the projection of future rates. In both areas actuaries have made signi cant advances in their modelling and understanding of longevity risk. This critical review outlines how methods have developed, and how the papers in the accompanying thesis have contributed to these advances.
Analysis of coupled PDE systems modelling micro-electro-mechanical systems
(Heriot-Watt University, 2021-09) He, Runan; Lacey, Professor Andrew; Gimperlein, Doctor Heiko
This thesis studies some mathematical models for a Micro-Electro-Mechanical System (MEMS) capacitor, consisting of a fixed plate and a flexible plate separated by a fluid. It investigates the wellposedness of solutions to the resulting quasilinear coupled systems, as well as the finite-time blow-up (quenching) of solutions. The models considered include a parabolic-dispersive system modelling the fluid flow under an elastic plate, a parabolic-hyperbolic system for a thin membrane, as well as an elliptic-dispersive system for quasistatic fluid flow under an elastic plate. Short-time existence, uniqueness and smoothness are obtained by combining wellposedness results for a single equation with an abstract semigroup approach for the system. Quenching is shown to occur, if the solution ceases to exist after a finite time. The thesis concludes with a study of self-similar quenching solutions and their stability for a simple hyperbolic membrane model for a MEMS capacitor.
Analysis of the availability of Infrastructure-as-a-Service-based cloud computing
(Heriot-Watt University, 2024-07) Ismail, Salih; Ragab, Doctor Hani
Cloud computing has become pervasive in organizations worldwide. A primary concern with the Cloud is security, especially the availability posed by Denial of Service (DoS) and Distributed Denial of Service attacks(DDoS). The evolving nature of this attack using reflectors and amplifiers eliminates the need for the attacker to have access to huge resources. We created a Cloud environment using Openstack and examined the availability of each building block component of the Cloud. Our experiments revealed vulnerabilities that led to availability issues in the Advanced Message Queuing Protocol (AMQP) message broker service, and the default one for Openstack is RabbitMQ. Our experimentation showed that it is possible to launch an amplification attack on RabbitMQ, which crashed the Cloud infrastructure. Our study showed that when the impact of a DoS attack is considered, only the network variables are considered in datasets. Hence, the resulting solutions to detect or prevent DoS attacks are built by testing them against these datasets. Using our infrastructure, we created a dataset with a series of systematic attacks in the Cloud that captured over 230 variables from seven different resource categories like processing, memory, and others. We studied the impact of DoS attacks (specifically TCP flood attacks) across different resource categories. We found attacks more impactful when the victim and attacker co-resides are in the same cloud. Additionally, our work allowed us to understand combinations of packets with flag and payload size that an attacker can devise for the maximum impact on the victim. Our results contain previously unknown insights, such as the fact that relatively smaller DoS packets could result in a larger impact on the victims. We also identified the most impacted system metrics, which would allow Cybersecurity software developers to build better and optimal (D)DoS monitoring and detection tools. We also proposed a metric to quantify the impact of a DoS attack considering the Cloud’s infrastructure and the various resource categories.
The analysis of woven fabric structure : a multidimensional approach to the analysis of 2-dimensional images of woven fabrics
(Heriot-Watt University, 2004) Taylor, C. D.
Analytic approximations to solitary waves on lattices
(Heriot-Watt University, 1993) Wattis, Jonathan A.D.