Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

What vs how : comparing students' testing and coding skills

The well-known difficulties students exhibit when learning to program are often characterised as either difficulties in understanding the problem to be solved or difficulties in devising and coding a computational solution. It would therefore be helpful to understand which of these gives students the greatest trouble. Unit testing is a mainstay of large-scale software development and maintenance. A unit test suite serves not only for acceptance testing, but is also a form of requirements specification, as exemplified by agile programming methodologies in which the tests are developed before the corresponding program code. In order to better understand students’ conceptual difficulties with programming, we conducted a series of experiments in which students were required to write both unit tests and program code for non-trivial problems. Their code and tests were then assessed separately for correctness and ‘coverage’, respectively. The results allowed us to directly compare students’ abilities to characterise a computational problem, as a unit test suite, and develop a corresponding solution, as executable code. Since understanding a problem is a pre-requisite to solving it, we expected students’ unit testing skills to be a strong predictor of their ability to successfully implement the corresponding program. Instead, however, we found that students’testing abilities lag well behind their coding skills.

Performance comparison of four power system stabilizer

The well-known power system stabilizer (PSS) is used to generate supplementary control signals for the excitation system of a generator so as to damp low frequency oscillations in the power system concerned. Up to now, various kinds of PSS design methods have been proposed and some of them applied in actual power systems with different degrees. Given this background, the small-disturbance eigenvalue analysis and large-disturbance dynamic simulations in the time domain are carried out to evaluate the performances of four different PSS design methods, including the Conventional PSS (CPSS), Single-Neuron PSS (SNPSS), Adaptive PSS (APSS) and Multi-band PSS (MBPSS). To make the comparisons equitable, the parameters of the four kinds of PSSs are all determined by the steepest descent method. Finally, an 8-unit 24-bus power system is employed to demonstrate the performances of the four kinds of PSSs by the well-established eigenvalue analysis as well as numerous digital simulations, and some useful conclusions obtained.

Bayesian computation via empirical likelihood

Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.

Multi-criteria ranking and source apportionment of airborne particulate matter

Particulate matter research is essential because of the well known significant adverse effects of aerosol particles on human health and the environment. In particular, identification of the origin or sources of particulate matter emissions is of paramount importance in assisting efforts to control and reduce air pollution in the atmosphere. This thesis aims to: identify the sources of particulate matter; compare pollution conditions at urban, rural and roadside receptor sites; combine information about the sources with meteorological conditions at the sites to locate the emission sources; compare sources based on particle size or mass; and ultimately, provide the basis for control and reduction in particulate matter concentrations in the atmosphere. To achieve these objectives, data was obtained from assorted local and international receptor sites over long sampling periods. The samples were analysed using Ion Beam Analysis and Scanning Mobility Particle Sizer methods to measure the particle mass with chemical composition and the particle size distribution, respectively. Advanced data analysis techniques were employed to derive information from large, complex data sets. Multi-Criteria Decision Making (MCDM), a ranking method, drew on data variability to examine the overall trends, and provided the rank ordering of the sites and years that sampling was conducted. Coupled with the receptor model Positive Matrix Factorisation (PMF), the pollution emission sources were identified and meaningful information pertinent to the prioritisation of control and reduction strategies was obtained. This thesis is presented in the thesis by publication format. It includes four refereed papers which together demonstrate a novel combination of data analysis techniques that enabled particulate matter sources to be identified and sampling site/year ranked. The strength of this source identification process was corroborated when the analysis procedure was expanded to encompass multiple receptor sites. Initially applied to identify the contributing sources at roadside and suburban sites in Brisbane, the technique was subsequently applied to three receptor sites (roadside, urban and rural) located in Hong Kong. The comparable results from these international and national sites over several sampling periods indicated similarities in source contributions between receptor site-types, irrespective of global location and suggested the need to apply these methods to air pollution investigations worldwide. Furthermore, an investigation into particle size distribution data was conducted to deduce the sources of aerosol emissions based on particle size and elemental composition. Considering the adverse effects on human health caused by small-sized particles, knowledge of particle size distribution and their elemental composition provides a different perspective on the pollution problem. This thesis clearly illustrates that the application of an innovative combination of advanced data interpretation methods to identify particulate matter sources and rank sampling sites/years provides the basis for the prioritisation of future air pollution control measures. Moreover, this study contributes significantly to knowledge based on chemical composition of airborne particulate matter in Brisbane, Australia and on the identity and plausible locations of the contributing sources. Such novel source apportionment and ranking procedures are ultimately applicable to environmental investigations worldwide.

Cryptographic techniques for managing computational effort

Availability has become a primary goal of information security and is as significant as other goals, in particular, confidentiality and integrity. Maintaining availability of essential services on the public Internet is an increasingly difficult task in the presence of sophisticated attackers. Attackers may abuse limited computational resources of a service provider and thus managing computational costs is a key strategy for achieving the goal of availability. In this thesis we focus on cryptographic approaches for managing computational costs, in particular computational effort. We focus on two cryptographic techniques: computational puzzles in cryptographic protocols and secure outsourcing of cryptographic computations. This thesis contributes to the area of cryptographic protocols in the following ways. First we propose the most efficient puzzle scheme based on modular exponentiations which, unlike previous schemes of the same type, involves only a few modular multiplications for solution verification; our scheme is provably secure. We then introduce a new efficient gradual authentication protocol by integrating a puzzle into a specific signature scheme. Our software implementation results for the new authentication protocol show that our approach is more efficient and effective than the traditional RSA signature-based one and improves the DoSresilience of Secure Socket Layer (SSL) protocol, the most widely used security protocol on the Internet. Our next contributions are related to capturing a specific property that enables secure outsourcing of cryptographic tasks in partial-decryption. We formally define the property of (non-trivial) public verifiability for general encryption schemes, key encapsulation mechanisms (KEMs), and hybrid encryption schemes, encompassing public-key, identity-based, and tag-based encryption avors. We show that some generic transformations and concrete constructions enjoy this property and then present a new public-key encryption (PKE) scheme having this property and proof of security under the standard assumptions. Finally, we combine puzzles with PKE schemes for enabling delayed decryption in applications such as e-auctions and e-voting. For this we first introduce the notion of effort-release PKE (ER-PKE), encompassing the well-known timedrelease encryption and encapsulated key escrow techniques. We then present a security model for ER-PKE and a generic construction of ER-PKE complying with our security notion.

Metal ion levels post unilateral primary Exeter total hip replacement

There has been much discussion and controversy in the media recently regarding metal toxicity following large head metal on metal (MoM) total hip replacement (THR). Patients have been reported as having hugely elevated levels of metal ions with, at times, devastating systemic, neurolgical and/or orthopaedic sequelae. However, no direct correlation between metal ion level and severity of metallosis has yet been defined. Normative levels of metal ions in well functioning, non Cobalt-Chrome hips have also not been defined to date. The Exeter total hip replacement contains no Cobalt-Chrome (Co-Cr) as it is made entirely from stainless steel. However, small levels of these metals may be present in the modular head of the prosthesis, and their effect on metal ion levels in the well functioning patient has not been investigated. We proposed to define the “normal” levels of metal ions detected by blood test in 20 well functioning patients at a minimum 1 year post primary Exeter total hip replacement, where the patient had had only one joint replaced. Presently, accepted normal levels of blood Chromium are 10–100 nmol/L and plasma Cobalt are 0–20 nmol/L. The UK Modern Humanities Research Association (MHRA) has suggested that levels of either Cobalt or Chromium above 7 ppb (equivalent to 135 nmol/L for Chromium and 120 nmol/L for Cobalt) may be significant. Below this level it is indicated that significant soft tissue reaction and tissue damage is less likely and the risk of implant failure is reduced. Hips were a mixture of cemented and hybrid procedures performed by two experienced orthopaedic consultants. Seventy percent were female, with a mixture of head sizes used. In our cohort, there were no cases where the blood Chromium levels were above the normal range, and in more than 70% of cases, levels were below recordable levels. There were also no cases of elevated plasma Cobalt levels, and in 35% of cases, levels were negligible. We conclude that the implantation with an Exeter total hip replacement does not lead to elevation of blood metal ion levels.

Van der Waals-corrected density functional theory : benchmarking for hydrogen–nanotube and nanotube–nanotube interactions

Density functional theory (DFT) is a powerful approach to electronic structure calculations in extended systems, but suffers currently from inadequate incorporation of long-range dispersion, or Van der Waals (VdW) interactions. VdW-corrected DFT is tested for interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. The energy correction, based on an empirical London dispersion term with a damping function at short range, allows a reasonable physisorption energy and equilibrium distance to be obtained for H2 on a model graphite surface. The VdW-corrected DFT calculation for an (8, 8) nanotube bundle reproduces accurately the experimental lattice constant. For H2 inside or outside an (8, 8) SWCNT, we find the binding energies are respectively higher and lower than that on a graphite surface, correctly predicting the well known curvature effect. We conclude that the VdW correction is a very effective method for implementing DFT calculations, allowing a reliable description of both short-range chemical bonding and long-range dispersive interactions. The method will find powerful applications in areas of SWCNT research where empirical potential functions either have not been developed, or do not capture the necessary range of both dispersion and bonding interactions.

Australian Tax Analysis : Cases, Commentary, Commercial Applications and Questions [9th Ed.]

Now in its ninth edition, Australian Tax Analysis: Cases, Commentary, Commercial Applications and Questions has a proven track record as a high-level work for students of taxation law written by a team of authors with many years experience. Taking into account the fact that the volume of material needed to be processed by today’s taxation student can be overwhelming, the well-chosen extracts and thought-provoking commentary in Australian Tax Analysis, 9th edition, provide readers with the depth of knowledge, and reasoning and analytical skills which will be required of them as practitioners. In addition to the carefully selected case extracts and the helpful commentary, each chapter is supplemented by engaging practice questions involving problem solving, commercial decision-making, legal analysis and quantitative application. All these elements combined make Australian Tax Analysis an invaluable aid to the understanding of a subject which can be both technical and complex.

Wrongful birth : assessment of damages in 2013

More than 10 years have passed since the High Court of Australia confirmed the recoverability of damages for the cost of raising a child, in the well-known decision in Cattanach v Melchior. Yet a number of aspects of the assessment of such “wrongful birth” damages had not been the subject of a comprehensive court ruling. The recent decision in Waller v James was widely anticipated as potentially providing a comprehensive discussion of the principles relevant to the assessment of damages in wrongful birth cases. However, given a finding on causation adverse to the plaintiffs, the trial judge held that it was unnecessary to determine the quantum of damages. Justice Hislop did, however, make some comments in relation to the assessment of damages. This article focuses mostly on the argued damages issues relating to the costs of raising the child and the trial judge’s comments regarding the same. The Waller v James claim was issued before the enactment of the Health Care Liability Act 2001 (NSW) and the Civil Liability Act 2002 (NSW). Although the case was therefore decided according to the “common law”, as explained below, his Honour’s comments may be of relevance to more recent claims governed by the civil liability legislation in New South Wales, Queensland and South Australia.

Multiple sclerosis susceptibility-associated SNPs do not influence disease severity measures in a cohort of Australian MS patients

Recent association studies in multiple sclerosis (MS) have identified and replicated several single nucleotide polymorphism (SNP) susceptibility loci including CLEC16A, IL2RA, IL7R, RPL5, CD58, CD40 and chromosome 12q13–14 in addition to the well established allele HLA-DR15. There is potential that these genetic susceptibility factors could also modulate MS disease severity, as demonstrated previously for the MS risk allele HLA-DR15. We investigated this hypothesis in a cohort of 1006 well characterised MS patients from South-Eastern Australia. We tested the MS-associated SNPs for association with five measures of disease severity incorporating disability, age of onset, cognition and brain atrophy. We observed trends towards association between the RPL5 risk SNP and time between first demyelinating event and relapse, and between the CD40 risk SNP and symbol digit test score. No associations were significant after correction for multiple testing. We found no evidence for the hypothesis that these new MS disease risk-associated SNPs influence disease severity.

Graphyne and graphdiyne : versatile catalysts for dehydrogenation of light metal complex hydrides

The interaction between new two-dimensional carbon allotropes, i.e. graphyne (GP) and graphdiyne (GD), and light metal complex hydrides LiAlH4, LiBH4, and NaAlH4 was studied using density functional theory (DFT) incorporating long range van der Waals dispersion correction. The light metal complex hydrides show much stronger interaction with GP and GP than that with fullerene due to the well defined pore structure. Such strong interactions greatly affect the degree of charge donation from the alkali metal atom to AlH4 or BH4, consequently destabilizing the Al-H or B-H bonds. Compared to the isolated light metal complex hydride, the presence of GP or GD can lead to a significant reduction of the hydrogen removal energy. Most interestingly, the hydrogen removal energies for LiBHx on GP and with GD are found to be lowered at all the stages (x from 4 to 1) whereas the H-removal energy in the third stage is increased for LiBH4 on fullerene. In addition, the presence of uniformly distributed pores on GP and GD is expected to facilitate the dehydrogenation of light metal complex hydrides. The present results highlight new interesting materials to catalyze light metal complex hydrides for potential application as media for hydrogen storage. Since GD has been successfully synthesized in a recent experiment, we hope the present work will stimulate further experimental investigations in this direction.

Malnutrition in Parkinson's disease and an individualised approach to its management

It has been reported that poor nutritional status, in the form of weight loss and resulting body mass index (BMI) changes, is an issue in people with Parkinson's disease (PWP). The symptoms resulting from Parkinson's disease (PD) and the side effects of PD medication have been implicated in the aetiology of nutritional decline. However, the evidence on which these claims are based is, on one hand, contradictory, and on the other, restricted primarily to otherwise healthy PWP. Despite the claims that PWP suffer from poor nutritional status, evidence is lacking to inform nutrition-related care for the management of malnutrition in PWP. The aims of this thesis were to better quantify the extent of poor nutritional status in PWP, determine the important factors differentiating the well-nourished from the malnourished and evaluate the effectiveness of an individualised nutrition intervention on nutritional status. Phase DBS: Nutritional status in people with Parkinson's disease scheduled for deep-brain stimulation surgery The pre-operative rate of malnutrition in a convenience sample of people with Parkinson's disease (PWP) scheduled for deep-brain stimulation (DBS) surgery was determined. Poorly controlled PD symptoms may result in a higher risk of malnutrition in this sub-group of PWP. Fifteen patients (11 male, median age 68.0 (42.0 – 78.0) years, median PD duration 6.75 (0.5 – 24.0) years) participated and data were collected during hospital admission for the DBS surgery. The scored PG-SGA was used to assess nutritional status, anthropometric measures (weight, height, mid-arm circumference, waist circumference, body mass index (BMI)) were taken, and body composition was measured using bioelectrical impedance spectroscopy (BIS). Six (40%) of the participants were malnourished (SGA-B) while 53% reported significant weight loss following diagnosis. BMI was significantly different between SGA-A and SGA-B (25.6 vs 23.0kg/m 2, p<.05). There were no differences in any other variables, including PG-SGA score and the presence of non-motor symptoms. The conclusion was that malnutrition in this group is higher than that in other studies reporting malnutrition in PWP, and it is under-recognised. As poorer surgical outcomes are associated with poorer pre-operative nutritional status in other surgeries, it might be beneficial to identify patients at nutritional risk prior to surgery so that appropriate nutrition interventions can be implemented. Phase I: Nutritional status in community-dwelling adults with Parkinson's disease The rate of malnutrition in community-dwelling adults (>18 years) with Parkinson's disease was determined. One hundred twenty-five PWP (74 male, median age 70.0 (35.0 – 92.0) years, median PD duration 6.0 (0.0 – 31.0) years) participated. The scored PG-SGA was used to assess nutritional status, anthropometric measures (weight, height, mid-arm circumference (MAC), calf circumference, waist circumference, body mass index (BMI)) were taken. Nineteen (15%) of the participants were malnourished (SGA-B). All anthropometric indices were significantly different between SGA-A and SGA-B (BMI 25.9 vs 20.0kg/m2; MAC 29.1 – 25.5cm; waist circumference 95.5 vs 82.5cm; calf circumference 36.5 vs 32.5cm; all p<.05). The PG-SGA score was also significantly lower in the malnourished (2 vs 8, p<.05). The nutrition impact symptoms which differentiated between well-nourished and malnourished were no appetite, constipation, diarrhoea, problems swallowing and feel full quickly. This study concluded that malnutrition in community-dwelling PWP is higher than that documented in community-dwelling elderly (2 – 11%), yet is likely to be under-recognised. Nutrition impact symptoms play a role in reduced intake. Appropriate screening and referral processes should be established for early detection of those at risk. Phase I: Nutrition assessment tools in people with Parkinson's disease There are a number of validated and reliable nutrition screening and assessment tools available for use. None of these tools have been evaluated in PWP. In the sample described above, the use of the World Health Organisation (WHO) cut-off (≤18.5kg/m2), age-specific BMI cut-offs (≤18.5kg/m2 for under 65 years, ≤23.5kg/m2 for 65 years and older) and the revised Mini-Nutritional Assessment short form (MNA-SF) were evaluated as nutrition screening tools. The PG-SGA (including the SGA classification) and the MNA full form were evaluated as nutrition assessment tools using the SGA classification as the gold standard. For screening, the MNA-SF performed the best with sensitivity (Sn) of 94.7% and specificity (Sp) of 78.3%. For assessment, the PG-SGA with a cut-off score of 4 (Sn 100%, Sp 69.8%) performed better than the MNA (Sn 84.2%, Sp 87.7%). As the MNA has been recommended more for use as a nutrition screening tool, the MNA-SF might be more appropriate and take less time to complete. The PG-SGA might be useful to inform and monitor nutrition interventions. Phase I: Predictors of poor nutritional status in people with Parkinson's disease A number of assessments were conducted as part of the Phase I research, including those for the severity of PD motor symptoms, cognitive function, depression, anxiety, non-motor symptoms, constipation, freezing of gait and the ability to carry out activities of daily living. A higher score in all of these assessments indicates greater impairment. In addition, information about medical conditions, medications, age, age at PD diagnosis and living situation was collected. These were compared between those classified as SGA-A and as SGA-B. Regression analysis was used to identify which factors were predictive of malnutrition (SGA-B). Differences between the groups included disease severity (4% more severe SGA-A vs 21% SGA-B, p<.05), activities of daily living score (13 SGA-A vs 18 SGA-B, p<.05), depressive symptom score (8 SGA-A vs 14 SGA-B, p<.05) and gastrointestinal symptoms (4 SGA-A vs 6 SGA-B, p<.05). Significant predictors of malnutrition according to SGA were age at diagnosis (OR 1.09, 95% CI 1.01 – 1.18), amount of dopaminergic medication per kg body weight (mg/kg) (OR 1.17, 95% CI 1.04 – 1.31), more severe motor symptoms (OR 1.10, 95% CI 1.02 – 1.19), less anxiety (OR 0.90, 95% CI 0.82 – 0.98) and more depressive symptoms (OR 1.23, 95% CI 1.07 – 1.41). Significant predictors of a higher PG-SGA score included living alone (β=0.14, 95% CI 0.01 – 0.26), more depressive symptoms (β=0.02, 95% CI 0.01 – 0.02) and more severe motor symptoms (OR 0.01, 95% CI 0.01 – 0.02). More severe disease is associated with malnutrition, and this may be compounded by lack of social support. Phase II: Nutrition intervention Nineteen of the people identified in Phase I as requiring nutrition support were included in Phase II, in which a nutrition intervention was conducted. Nine participants were in the standard care group (SC), which received an information sheet only, and the other 10 participants were in the intervention group (INT), which received individualised nutrition information and weekly follow-up. INT gained 2.2% of starting body weight over the 12 week intervention period resulting in significant increases in weight, BMI, mid-arm circumference and waist circumference. The SC group gained 1% of starting weight over the 12 weeks which did not result in any significant changes in anthropometric indices. Energy and protein intake (18.3kJ/kg vs 3.8kJ/kg and 0.3g/kg vs 0.15g/kg) increased in both groups. The increase in protein intake was only significant in the SC group. The changes in intake, when compared between the groups, were no different. There were no significant changes in any motor or non-motor symptoms or in "off" times or dyskinesias in either group. Aspects of quality of life improved over the 12 weeks as well, especially emotional well-being. This thesis makes a significant contribution to the evidence base for the presence of malnutrition in Parkinson's disease as well as for the identification of those who would potentially benefit from nutrition screening and assessment. The nutrition intervention demonstrated that a traditional high protein, high energy approach to the management of malnutrition resulted in improved nutritional status and anthropometric indices with no effect on the presence of Parkinson's disease symptoms and a positive effect on quality of life.

Analysis of nonlinear sequences and streamciphers

Streamciphers are common cryptographic algorithms used to protect the confidentiality of frame-based communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation. The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the state-update and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's state-update function, output function, or both. The first contribution of this thesis relates to nonlinear sequences produced by the well-known Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multi-year project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear state-update and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Trivium-like streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's state-update function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium. Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Trivium-like ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of Bivium-A.The attack complexity for Bivium-B and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack. The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear state-update and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the state-update function used in its initialisation process is not one-to-one. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator. The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.

Self excitation in equity indices

A "self-exciting" market is one in which the probability of observing a crash increases in response to the occurrence of a crash. It essentially describes cases where the initial crash serves to weaken the system to some extent, making subsequent crashes more likely. This thesis investigates if equity markets possess this property. A self-exciting extension of the well-known jump-based Bates (1996) model is used as the workhorse model for this thesis, and a particle-filtering algorithm is used to facilitate estimation by means of maximum likelihood. The estimation method is developed so that option prices are easily included in the dataset, leading to higher quality estimates. Equilibrium arguments are used to price the risks associated with the time-varying crash probability, and in turn to motivate a risk-neutral system for use in option pricing. The option pricing function for the model is obtained via the application of widely-used Fourier techniques. An application to S&P500 index returns and a panel of S&P500 index option prices reveals evidence of self excitation.