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This thesis presents a comprehensive study on the impacts of bank capital allocation practices on broader economic growth and sustainability with secondary effects on financial system performance. In completing the study, in Chapter 1 we begin by extending Schumpeter's theory (1934; 1939) on financial intermediation to account for the effects of capital allocation practices at banks. We uniquely demonstrate, in quasi-experimental settings through a bank-economy Agent-Based Model, that use of more comprehensive capital allocation practices at banks promotes more efficient credit allocations. Significantly, the gains in efficiencies result in positive real effects on industrial economic growth and loan performance, as well as financial system profitability and capital adequacy. In seeking to confirm Schumpeter's extended theory in real-world settings, in Chapter 2 we develop a novel lexical frontier analysis approach for measuring ex-ante banks' efficiency by assessing capital allocation capabilities. Comparing results from the novel approach to existing techniques, we demonstrate a link between the quality of capital allocation practices and bank production and economic (profit) efficiencies. In Chapter 3, we calculate US banks' profit efficiencies, as ex-post proxy for capital allocation efficiency, and demonstrate that US banks utilizing robust capital allocation practices that are economically efficient, promote growth of ESG sustainable industries while moderating growth of sectors with lower prospects. The collection of findings demonstrate that application of robust capital allocation practices by banks can be a major accelerator of the Schumpeterian credit intermediation channel for industrial growth, with significant positive effects on bank efficiency, capital adequacy, resiliency, and financial system stability.

Artificial intelligence (AI) methods are changing the sciences and scientific computing, in particular also in the field of inverse problems. In inverse problems, for example in imaging AI based methods seemingly achieve higher reconstruction accuracy than standard methods, such as compressed sensing. However, trustworthiness has become a serious issue as there is empirical evidence that deep learning (DL) may lead to unstable methods in inverse problems. Recently, in inverse problems in imaging, another phenomenon of DL decoders yielding false yet realistic looking artefacts, coined AI generated hallucinations, has been reported on. This thesis explores the use of DL in inverse problems and aims at providing a theoretical basis for assessing the stability and accuracy of such methods. In the second chapter, a fully learned neural network approach for image reconstruction, which was introduced in [192] and coined 'automated transform by manifold approximation', is examined. In particular, its potential benefits with respect to accuracy and disadvantages with respect to stability and robustness compared to standard methods for image reconstruction are investigated. We show that without further conditions on the sampling operator, such fully learned approaches to solving inverse problems become unstable. In the third chapter, we present a comprehensive mathematical analysis explaining different causes of AI generated hallucinations and the links to instabilities. Our results establish four crucial issues for AI methods in inverse problems. Firstly, overly accurate AI methods will wrongly transfer details from one image to another reconstructed image creating a hallucination. Secondly, there is an accuracy-hallucination trade-off. Thirdly, there is an accuracy-stability trade-off, and optimising these trade-offs through standard training processes is difficult. And lastly, hallucinations can occur due to any kind of noise model and probability distribution used on the training set. In the last chapter, we investigate how DL based methods for solving inverse problems can perform better than standard methods. Thus, we establish fundamental accuracy bounds for solving ill-posed inverse problems. This is achieved by obtaining upper and lower bounds on a universal optimality constant, that includes the best worst-case noise, the average and the statistical reconstruction error for the reconstruction of an ill-posed inverse problem. This framework encompasses non-linear and linear inverse problems with different noise models and allows to assess stability, accuracy and learning of approximate decoders for ill-posed inverse problems.

This thesis focuses on three-dimensional thermally-driven boundary layers with three distinct types of (steady) thermal forcing (i) a streamwise-aligned heat source that is spanwise localised, (ii) a spanwise and streamwise localised heat source and (iii) a non-localised globally driven natural convection problem. What ties these problems together is that the induced three-dimensionality is on a spanwise lengthscale commensurate with the boundary-layer thickness, and so their leading-order flow is governed by the 'boundary-region' equations, attributed to Kemp (1951). A lot of work has been undertaken within this boundary-region framework in an isothermal context, for example forced by injection or roughness, but presently there has been limited work in which temperature variation has been applied. In our first problem (i), we embed a streamwise-aligned spanwise-localised heated strip, which has an O(Re^(-1/2)) spanwise scale, in a horizontal semi-infinite flat plate. At large spanwise distances from the forcing region, the flow takes the form of the two-dimensional Falkner--Skan boundary layer (1930). The three-dimensional flow response is determined numerically and a robust streak-roll structure forms downstream. We undertake an asymptotic analysis at large streamwise coordinates, and obtain the downstream transverse growth of the nonlinear response. We also determine the flow over a streamwise-aligned injection slot, and make qualitative comparisons with the thermally forced problem. A localised heat source with an O(1) streamwise scale and an O(Re^(-1/2)) spanwise scale is then considered (ii), and the corresponding nonlinear problem is solved. For weak thermal forcing, the isolated heated region results in a downstream response which has an algebraically developing velocity field. By seeking a linear bi-global eigenvalue problem in terms of the downstream algebraic spatial growth, we show that there is a new class of linear spanwise-localised algebraically developing disturbances in the Falkner--Skan boundary layer when thermal effects are included. The velocity field of the dominant mode grows (algebraically) downstream, and is driven by a decaying (weak) temperature field. Above a critical pressure gradient the dominant mode decays, and we determine the critical Prandtl number and pressure gradient parameter for downstream algebraic growth. The linear algebraically growing response ultimately gives rise to a nonlinear spanwise-localised streak-roll response downstream. We assess the stability of the streak response to time-harmonic (viscous) disturbances and inviscid Rayleigh modes. Our third problem (iii) is the natural convection flow in a heated vertical corner. This is a globally driven, non-localised problem, however in a high Grashof number regime the flow in a region near to the corner is governed by the boundary-region equations. Two self-similar solutions are determined: (A) a solution first discussed by Riley and Poots (1972), and (B) a new solution which, at large spanwise coordinates, has a coupled linearly-developing crossflow component. We show that the streamwise velocity and temperature fields determined by Riley and Poots (1972) for solution A were surprisingly accurate, given that their computational resources were limited. However, they concluded that there is an in-plane flow away from the corner which is not present in the properly resolved solution. The non-parallel stability of the self-similar profiles is tackled with the parabolised stability equations (PSE).

Motivated by the global need for greener energy, the exploration of renewable energies is on the rise. Due to their intermittent availability, inverters are increasingly used as interfaces to provide power conditioning. In contrast to the conventional power systems with fewer generators, numerous distributed inverter-interfaced renewable generation units must be connected to meet load demands. This fact requires a paradigmatic change in power system operation. One solution to facilitate this change are autonomous microgrids, which allow renewable powered systems to operate independent of the fossil-fuelled power grids. To achieve this, inverters must have grid-forming capabilities, operate in a synchronised manner and share power optimally. However, the absence of the stabilising inertia makes the control and stabilising of autonomous microgrids a complex problem. In this thesis, we consider the main control objectives associated with operating inverter-based microgrids in autonomous mode, which are frequency and voltage regulation, and power sharing. More precisely, we design grid-forming control policies which satisfy conditions for stability and achieve the aforementioned control objectives, and appropriate stability assessments are performed. This thesis is structured as follows. Considering the amount of literature on autonomous inverter-based microgrids, we start by reviewing models of different accuracy. In particular, an investigation of the accuracy of reduced models used to describe autonomous microgrids is performed relative to that of a detailed average model, and it is shown that various simplifications upon which the reduced models rely can impact their quality. Based on the findings, recommendations are given on the models to be used for microgrid stability assessment. The main results of the thesis are then presented and these are summarised below: (i) Passivity techniques are applied to the problem of stabilising an inverterbased microgrid. Representing the inverter and network models in the common reference frames, it is shown that microgrids can be described as the negative feedback interconnection of the two subsystems. Using the passivity framework, local conditions are imposed for stability at each inverter, the passivity properties of various existing control strategies for microgrids are assessed numerically, and improvement on these is discussed. Simulations on advanced inverter models verify the improved performance when the passivity property is satisfied. (ii) A new grid-forming control strategy is proposed, which satisfies a decentralised passivity condition that guarantees stability in the local reference frame. This proposed frequency scheme circumvents the nonlinearity in the feedback policy associated with active power-based frequency droop control, provides active power sharing without a communication link and strict passivity of the inverter model in the local reference frame. Associated conditions for power sharing, strict passivity and closed-loop asymptotic stability conditions are derived. DC and AC-side voltage control schemes which provide voltage regulation and allow the passivity properties of the inverter to be maintained are proposed. The benefit of the passivity-based design is demonstrated via the simulations of advanced inverter models. (iii) A new control architecture for frequency and voltage control with good scalability properties is proposed. At slower timescales, it allows to incorporate a distributed secondary control policy for which is provided an analytical stability result with line conductances taken into account. At faster timescales, it satisfies a passivity property in the common reference frame for a wide range of parameters. The voltage control scheme has a double loop structure that uses the DC voltage in the feedback control policy to improve performance through power imbalance elimination, and provides current limiting capability. The frequency control policy employs the inverter output current and angle to provide an improved angle droop policy. This scheme provides inverters with sufficient stabilising inertia and damping similar to the dynamical behaviour of synchronous generators. The performance of the control policy is illustrated via advanced simulations. (iv) The problem of synchronisation of droop-controlled inverters interconnected in lossy microgrids is considered by investigating conditions for which an equilibrium point exists for synchronisation. A reduced model of the interconnected inverters is derived via singular perturbation analysis and the behaviour of the boundary layer model is investigated. Using the reduced model sufficient conditions for the existence of an equilibrium point are derived. In particular, computable 2-norm and ∞-norm sufficient conditions are derived given that the bus angle differences are sufficiently small. These conditions take into account line conductances in contrast to those in the literature. Also, results on the worst synchronisation rate and the expanded Laplacian of the lossy network are presented. The conservativeness of the proposed 2-norm condition is compared to that of the ∞-norm condition numerically using IEEE test cases.

This thesis describes new methods in input/output systems theory. The first part of this thesis develops a novel graphical method for the stability analysis of feedback systems. The Scaled Relative Graph (SRG), a recent concept from monotone operator theory, is shown to generalize the classical Nyquist diagram of an LTI transfer function, and may be plotted for arbitrary nonlinear operators. Applying the SRG to the analysis of feedback interconnections leads to a graphical incremental stability theorem, which unifies and generalizes the Nyquist criterion, circle criterion, incremental passivity theorem, incremental small gain theorem and incremental secant condition. A novel special case of this theorem concerns systems which only violate the assumptions of the incremental passivity theorem when their incremental gains are small. This captures systems whose incremental passivity is destroyed by common effects such as delay and saturation. The second part of this thesis develops algorithmic methods for solving nonlinear circuits composed of monotone elements. Monotonicity is a generalization of the linear property of passivity, and is a fundamental property in the theory of large-scale convex optimization. Modern splitting methods, which invert sums of operators, are shown to correspond to the series or parallel interconnection of circuit elements which are monotone, and may be used to solve the steady-state behavior of such circuits. Consideration of circuits with arbitrary series/parallel interconnections leads to a new splitting algorithm, the nested forward-backward algorithm, which inverts operators composed of sums and inverses. Finally, these methods are extended to circuits composed of the difference of monotone elements. The steady-state behavior of such circuits can be solved via an adaptation of Difference of Convex (DC) Programming. Such circuits include the classical van der Pol oscillator and the FitzHugh-Nagumo model of an excitable neuron, which both consist of an LTI transfer function in parallel with monotone and anti-monotone nonlinear resistors. A new algorithm, the difference-of-monotone Douglas-Rachford algorithm, is proposed, which matches the mixed-feedback structure of these circuits.

Organic bioelectronics is an emerging field that utilizes electronic devices made from a large family of aromatic compounds (conjugated polymers and small molecules) for biological applications. Organic materials seem ideal candidates for bioelectronics due to their softness, biocompatibility, stretchability, and their ability to conduct both electrons and ions. Many fundamental studies have been conducted, utilizing devices such as the Organic Field Effect Transistor (OFET), the Electrolyte-Gated OFET (EG-OFET), and the Organic Electro-Chemical Transistor (OECT). However, water constitutes a key factor in charge trapping and device degradation in organic materials, due to its strong dipole moment, high dielectric constant, and its omnipresence in almost all processing, environmental, and operational conditions. In this dissertation, we used an additives-based approach to stabilize OFETs immersed in DI water and saline solution, for periods up to a month, making the first high-performance water-stable OFETs reported in the literature. We then repeated the long-term water stability experiments on EG-OFETs, and demonstrated that cleanly fabricated EG-OFETs can remain stable within the course of an overnight measurement (16 hours), without needing the additive stabilization process. By comparing the water stability of OFETs and EG-OFETs, we highlighted the different requirements involved in stabilizing these two architectures, challenging the notion that organic materials are intrinsically unstable in water.

Background: Not only have antibiotics saved countless patients' lives but they have also played a crucial role in supporting major advances in modern medicine. However, precipitously emerging resistant bacterial strains jeopardise the remarkable advances achieved with antibiotics. In the past, the development of new antibiotics was an effective strategy to combat resistant bacteria. However, with the discovery of new antibiotics diminishing, optimising the administration of currently available antibiotics has become a necessity. A strategy of particular interest involves applying pharmacokinetic and pharmacodynamic concepts to optimise time-dependant antibiotics dosing regimens. The latter is a growing area of interest for reducing the development of antibiotic resistance, and it involves differential dosing regimens such as prolonged or continuous infusions of beta-lactam antibiotics. Aim: The overarching aim of this research is to optimise antibiotic therapy for inpatient and outpatient use. This thesis consists of literature-based, practice-based, and laboratory-based research. Literature-based: The aim of the literature-based research category was to review existing literature to compare the clinical outcomes of continuous vs intermittent infusion beta-lactam antibiotics and appraise the strengths and the weaknesses of current evidence. Overall, literature-based research demonstrated a wealth of studies in terms of systematic reviews, meta-analysis as well as primary studies. Despite the literature exhibiting favourable outcomes towards prolonged/continuous infusions, the literature review and systematic reviews conducted support the need for better conducted, definitive trials and systematic reviews given the variability in scope of the available studies. Practice-based: The aim of the practice-based research category was to provide a snapshot of beta-lactam antibiotic use in clinical practice. The first study was single-centre retrospective cohort practice review conducted to Investigate the prescribing patterns of beta-lactam antibiotics in critical care wards. The second study was a cross sectional survey investigating nurse's knowledge, perceptions, and experiences regarding differential antibiotic dosing. Findings show that prolonged/continuous infusions as dosing strategies are implemented in practice to improve patient outcomes, however, healthcare XI professionals implementing this practice have not received sufficient training to support the administration of differential antibiotic dosing. This was evident from both practice based studies that disclose beta-lactam antibiotics are not used to their full potential or are inaccurately used. There is a need for tailored education and training to improve health care professional's knowledge of prolonged/continuous infusions. Laboratory-based: Despite the advantages that prolonged/continuous infusions beta-lactam antibiotics offer, in order to use these dosing regimens efficiently, infusion solutions should remain stable for the preparation, storage and infusion time. Concerns regarding stability present a challenge in practice as most stability information is based on administration via bolus injection or an intermittent infusion. Therefore, the aim of the laboratory-based research category was to determine the feasibility of prolonged/continuous infusion beta-lactam antibiotics for hospital and outpatient settings. Findings from the conducted studies aid in ameliorating current dosing regimens to optimise antibiotic efficacy. Results obtained from stability studies assist in resolving challenges experienced in practice in terms of preparation, storage, and administration as they indicate the effects of temperature, diluent, and pre-preparation of infusion solutions. Studies demonstrated that stability data generated in all studies are an improvement to the stability data presented in the British, American, and European pharmacopoeias. Conclusion: Findings of this PhD research are supportive of the beneficial role of differential antibiotic dosing. Overall, the gathered data indicate that prolonged/continuous infusions are feasible, advantageous and could potentially improve patient clinical outcomes.

The 2010s were a decade of transformation and conflict in the Middle East and North Africa (MENA). Throughout, most global and regional powers declared stability to be one of their main objectives in the region. This included Saudi Arabia, the United Arab Emirates (UAE), and Qatar, the three Arab states with the most ambitious and influential regional policies during the decade. Yet, observation of these policies suggests that instead of serving as a common denominator, the seemingly shared objective of stability obscured the differences between their competing agendas. Without a universally accepted definition of stability, the thesis develops an original analytical framework. It holds that states understand stability as a condition in their strategic environment, emerging from systems of order, that they consider favourable; and that their conceptions of this order derive from their perceptions of themselves and of what constitutes and drives instability. Drawing on qualitative data, the thesis analyses and compares Saudi Arabia, the UAE, and Qatar's perceptions of political developments in the MENA during the 2010s, and their conceptions of what constituted stability. The thesis finds that the three Gulf monarchies concurred that the region descended into unprecedented and dangerous instability following the 2010/11 Arab Uprisings. Yet, their assessments of what characterised and drove this instability diverged. This led them to formulate different - and, in some areas, contradictory - views of how the politics in and between regional states had to be organised, and what role external powers could play, in order to yield stability. The thesis concludes that examining states' conceptions of stability provides a useful lens to understand their foreign policy behaviour. It further establishes that the joint declaratory commitments to stability, often evoked by European and North American governments to frame relations with partners in the region, are insufficient as a basis for strategic alignments.

Among the techniques of forming the geometry of a reconfigurable and programmable matter, origami (the art of paper folding) and kirigami (paper folding with cutting) are especially appealing, as they are effective tools for transforming simple two-dimensional materials into complex three-dimensional structures. Rigid origami is the underpinning kinematics and dynamics of origami and kirigami engineering, which considers possible path between two complex structures through continuous folding. Rigid origami serves as suitable scale-independent mathematical models for both structures found in nature (e.g., molecules, crystals, proteins, biological materials) and man-made structures (e.g., biomedical devices, reconfigurable metamaterials, self-folding robotics, stretchable electronics, fold-core deployable structures, architectures, large space elements), even in multiple forms of art. My research focus is on the unsolved theoretical challenges when establishing systematic theories for rigid origami. These challenges can be classified into the "forward problem'', which is the useful sufficient and necessary condition for a rigid origami with certain crease pattern to be foldable; and the "inverse problem'', which is to systematically design a rigid origami based on some targets, such as approximating a surface or following a given path, meanwhile balancing the freedom of approximation and stability of folding motion. This thesis will report results on four topics associated with the theoretical challenges mentioned above. (1) We set up the definitions of key concepts for origami and rigid origami. The major difficulties are how to describe the contact between different parts of a paper while preventing self-intersection, and how to describe rigid origami as a realization of an underlying graph. This modelling could be used to connect rigid origami and its cognate areas, such as the rigidity theory, graph theory, linkage folding, abstract algebra and computer science. (2) We develop the rigidity theory for rigid origami under the folding angle description, including the generic rigidity and local rigidity. Generic rigidity studies how the rigidity is determined from the underlying graph of a rigid origami. Local rigidity includes: first and second order rigidity, which are defined from local differential analysis on the consistency constraint; static rigidity and prestress stability, which are defined after finding the form of internal force and load. We show there is a hierarchical relation among these local rigidity with examples representing different levels. (3) For the forward problem, progress is made from a thorough analysis on the compatibility condition, then new mathematical tools are applied to extend the current solution set. We discover several new classes of large foldable quadrilateral meshes, which are presented symbolically with numeric examples. (4) For the inverse problem, new design examples are adapted from the foldable quadrilateral meshes discovered above. Further, new algorithms that are applicable for more design targets are developed. We propose several algorithms on approximating a target surface from a planar rigid origami, which can be folded continuously. The folding motion will stop at the desired shape due to the clashing of panels. A discussion on future work concludes this thesis.

This thesis focusses on extremal graph theory, the study of how local constraints on a graph affect its macroscopic structure. We primarily consider the chromatic structure: whether a graph has or is close to having some (low) chromatic number. Chapter 2 is the slight exception. We consider an induced version of the classical Turán problem. Introduced by Loh, Tait, Timmons, and Zhou, the induced Turán number ex(n, {H, F-ind}) is the greatest number of edges in an n-vertex graph with no copy of H and no induced copy of F. We asymptotically determine ex(n, {H, F-ind}) for H not bipartite and F neither an independent set nor a complete bipartite graph. We also improve the upper bound for ex(n, {H, K_2,t-ind}) as well as the lower bound for the clique number of graphs that have some fixed edge density and no induced K_2,t. The next three chapters form the heart of the thesis. Chapters 3 and 4 consider the Erdős-Simonovits question for locally r-colourable graphs: what are the structure and chromatic number of graphs with large minimum degree and where every neighbourhood is r-colourable? Chapter 3 deals with the locally bipartite case and Chapter 4 with the general case. While the subject of Chapters 3 and 4 is a natural local to global colouring question, it is also essential for determining the minimum degree stability of H-free graphs, the focus of Chapter 5. Given a graph H of chromatic number r + 1, this asks for the minimum degree that guarantees that an H-free graph is close to r-partite. This is analogous to the classical edge stability of Erdős and Simonovits. We also consider the question for the family of graphs to which H is not homomorphic, showing that it has the same answer. Chapter 6 considers sparse analogues of the results of Chapters 3 to 5 obtaining the thresholds at which the sparse problem degenerates away from the dense one. Finally, Chapter 7 considers a chromatic Ramsey problem first posed by Erdős: what is the greatest chromatic number of a triangle-free graph on n vertices or with m edges? We improve the best known bounds and obtain tight (up to a constant factor) bounds for the list chromatic number, answering a question of Cames van Batenburg, de Joannis de Verclos, Kang, and Pirot.

Risk prediction models have become embedded into the health system. They are used to guide clinical decision making in a variety of settings: risk of death following surgery (should we operate?), diagnostic models for cancer (should we screen?), or the probability of having a clinical event over a certain time period (should we take preventative measures?). Despite clear guidelines on the development and reporting of models, features of models developed for the same purpose often differ. Furthermore, in the field of cardiovascular disease (CVD), risk thresholds for initiating statin therapy vary across England, Scotland, the US and Europe, despite a large body of evidence on when treatment becomes cost effective. This results in uncertainty when using these models to guide treatment for a patient, as using different models or clinical guidelines may result in a different decision for an individual. This thesis focused on identifying sources of uncertainty associated with both parts of this process, generating risk predictions, and making clinical decisions based on these risk predictions. Case studies consider the primary prevention of CVD, which was chosen due to the high incidence of CVD, the saturation of CVD risk prediction models in the literature, and the fierce debate over the last 10 years about the best approach for the primary prevention of CVD. Chapter 3 found the impact of covariate selection on the risks of individuals to be small, apart from a large secular trend. Chapter 4 identified high levels of instability in risk scores when using sample sizes of widely used models, and when derived from recently published sample size formula. Chapter 5 found that the secular trend in CVD (identified in Chapter 3) caused over prediction of risks for patients in the present day and was not driven by increasing statin use. Chapter 6 highlighted that a small number of extra CVD events could be prevented by delaying statin initiation to when patients are at risks higher than 10% (given the high statin discontinuation rates identified in practice). Chapter 7 showed that the reduction of the risk threshold for initiating statins for the primary prevention of CVD, from a 10-year CVD risk of 20% to 10%, had little impact on clinical practice in England. This finding is contrary to current evidence. The findings in this thesis are a mix of methodological findings of interest to those developing models, and those that have a direct impact on the prevention of CVD in the UK.

The stability problem plays an important role not only in industry but also in our everyday life. Unstable systems are dangerous and can cause financial losses or can lead to injuries and loss of human life. Starting with the 19th century, many methods were proposed for analysing the stability of linear dynamical systems, nonlinear dynamical systems, and for systems with uncertainties. This thesis proposes several methods to study the stability of nonlinear dynamic systems with uncertainties. The majority of existing methods can only be applied to nonlinear dynamical systems under some particular circumstances. New approaches are developed in this thesis by combining the existing theory with interval analysis. The new methods are used to analyse the stability of Sliding Mode Control (SMC) strategy, for generating automatic Lyapunov functions and for solving Ordinary Differential Equations (ODE) and ODE with uncertainties. New types of sliding mode control structures, able to cope with faults, are developed and tested on a differential drive robot. Suitable tuning parameters for the SMC when dealing with multiple uncertainties are found by using novel methods which employ interval analysis techniques. To the best of my knowledge, there is no analytical method for tuning and estimating the robustness for an SMC in the presence of uncertainties. Moreover, the stability of uncertain nonlinear dynamical systems was studied from a Lyapunov perspective. Lyapunov functions can be automatically generated for mechanical systems based on their energy. In the majority of the cases, the energy function does not guarantee an asymptotic convergence to the equilibrium point. LaSalle theorem solved this problem for systems without uncertainties. However, when the systems have uncertainty it is not possible to apply LaSalle invariant principle. In this thesis, this was solved by adding perturbation functions to the energy function of the system, and by using interval analysis, the asymptotic convergence for systems with uncertainties was proved. New guaranteed integration methods are proposed for solving nonlinear ODEs in the last part of the thesis. It was shown, that by using interval methods, we are able to bracket the boundary of the solution manifold. Two methods for generating a boundary approximation were proposed: the first method used radial basis function networks and the second method used linear interpolation for a mesh triangulation.

Averaging over fast phases reduces study of stability of quasi-periodic and periodic trajectories to study of stability of periodic trajectories and equilibria. The aim of the proposed research is to study stability properties in several averaged models of dynamics. Bifurcation analysis is the central tool in study of such properties. The first and second models that we study are the simple and the spherical pendulums {with vibrating suspension points}. We give a complete description of bifurcations of their phase portraits. Main part of the research is devoted to the restricted elliptic three body problem (ER3BP). This model with large eccentricities of the planet is of particular interest in relation to study of motion of exoplanets.

Perovskite solar cell (PSC) is one of the most promising next-generation photovoltaic technologies that can provide low-cost, alternative renewable energy. The main hindrances to the deployment of PSC panels are instability issues. Deterioration in the power conversion efficiency of PSCs over time greatly originates from perovskite light absorbers. Hence, in this thesis, the stability of lead and tin perovskites is investigated. Some key factors to improve the stability of perovskite materials are discussed, including processing, materials, and understanding degradation mechanisms in particular. I introduce a state-of-the-art characterisation technique, near-ambient pressure X-ray photoelectron spectroscopy (NAP-XPS), to investigate the surface stability and degradation process of perovskites. We propose the moisture-induced degradation behaviour of a prototypical halide perovskite, methylammonium lead iodide (MAPI): MAPI decomposes into lead iodide and hydrocarbon chains by releasing hydrogen iodide and ammonia gases. For processing, we find that MAPI films made by aerosol-assisted chemical vapour deposition (AACVD) generally have better stability in humid air than their spin-coated counterparts, which can be attributed to larger grain sizes. Moreover, surface passivation plays a crucial role in the improved stability against moisture. This can be achieved using excess CH3NH3I (to react with a Pb(SCN)2 precursor) or bulky ammonium iodides for MAPI films. Formamidinium (FA)-based mixed-cation mixed-halide perovskites and Cs2SnI6 double perovskite not only have better water resistance but also undergo different degradation routes compared to MAPI. Upon H2O vapour exposure, the FA cation transforms into CH3NH3+ first, whilst the degraded species of Cs2SnI6, CsI, remains at the surface. It will be shown that these insights can pave the way towards stable PSCs.

Nanofluids are advanced type of fluids that are produced by dispersing nanoparticles within a non-dissolving liquid. In heat transfer applications, these suspensions have shown to be superior to conventional heat transfer fluids in terms of thermal performance because of their enhanced effective thermal properties. The effective thermal conductivity of nanofluid depends on several factors, such as the preparation method employed, particles concentration, colloidal stability, thermal conductivities of both basefluid and solid particles used, ... etc. Furthermore, the suspension effective thermal conductivity can only have a value within the range of the added nanoparticles (highest) and the hosting fluid (lowest) thermal conductivities. Thus, to obtain an optimum effective thermal conductivity for a certain mixture with minimum degradation in the aforementioned property, the nanofluid needs to be homogeneously dispersed while sustaining its short and long-term stability. This is one of the main challenges seen today with such type of advanced fluids. Moreover, the nanofouling effect associated with these suspensions in operational conditions is another important factor that needs to be focused on, as it tends to change the surface wettability behaviour depending on the fluid and deposited surface properties, and hence can increase or decrease the heat transfer performance of the system. To address the previous challenges, the thesis at hand investigates the effect of nanofluid fabrication approach on its stability and pH value, and explores the influence of deposited particles of similar surface materials on the wettability behaviour of the surface. In order to achieve this, a two-step controlled temperature approach was used to fabricate the nanofluids at different set of fixed temperatures using a bath type ultrasonicator. The as- prepared suspensions were then characterised in terms of changes in pH value and stability using a pH meter and the sedimentation photograph capturing method, respectively. In addition, an electron beam physical vapour deposition technique was used to form nanoscaled layers on surfaces of similar materials to the evaporant source, so that a reflection of the nanofouling build-up on surfaces can be obtained, after which the wettability was examined, through a goniometer device, by varying the extracted liquid conditions. The results have shown that increasing the nanoparticles concentration had caused the fluid alkalinity level to increase, while the rise in nanofluid sonication temperature had led to a decrease in its pH value, and vice versa. Furthermore, a general correlation was developed to predict the changes in pH value for similar fabricated suspensions, which illustrated an overall accuracy of ~92% in its prediction capability. The shelving-life evaluation of aluminium - water dispersion has showed that the nanofluids fabricated via the two-step controlled temperature approach at 30ᴼC had better short and long-term stabilities than the ones produced by the conventional method. Moreover, the wettability behaviour of aluminium surfaces was seen to depend on the deposited aluminium film thickness, surface characteristics, and water properties; but in general, the water of pH 7 has demonstrated a tendency to enhance the hydrophilicity of the surface, while water of lower and higher pH values were seen to have the opposite outcome. On the other hand, the wettability behaviour of copper or stainless steel surfaces has shown to greatly depend on the surface topographical structure compared to the attached liquid properties.

Monoclonal antibodies (mAbs) are now the most common protein therapeutics on the market. The therapeutic properties of mAbs originate from their inherent ability to specifically bind to a chosen target and the subsequent stimulation of effector functions as result of mAb glycosylation. Therefore mAbs are able to act as drug delivery systems, inhibitors or activators. Protein therapeutic characterisation possesses inherent analytical difficulties as mAbs are complex structures made up of multiple domains. The higher order structure of mAbs is essential for their specificity for targeted treatments. During the production of mAbs, the bioformulation process can induce structural perturbations that we separate into two main categories: Post-translational modifications (PTMs) and degradation. The most common PTMs are oxidation, deamidation and glycation. Degradation of mAbs covers general loss of structure through aggregation and fragmentation. Due to the wide variation and number of possible modifications to mAbs, monitoring, identification and quantification is difficult. Current analytical methods are dependent on sampling, are often destructive, and require time and expertise. Vibrational spectroscopic methods have been highlighted as possible analytical methods to overcome previous shortcomings. In particular, Raman spectroscopy has the potential to be developed into an in-line analytical tool due to being minimally invasive, non-destructive, information rich and rapid. Raman and FTIR are already utilised for in situ monitoring of pharmaceutical manufacturing, such as small molecules, but have not yet been extended into the quality control of mAbs. In this thesis we use a range of conditions to force the degradation and increase the PTM levels of three of the most common types of mAbs: IgG1, Fab and IgG4. We use circular dichroism (CD), peptide mapping, and size exclusion chromatography (SEC) to quantify and study the structural implications of the PTMs and degradation, and compare these to the information gained from Raman spectroscopy. Bioformulation parameters probed include: agitation, pH, temperature, sugar excipients, chemical stressors and UV light. Primarily, we explore the sensitivity of Raman spectroscopy to detect, quantify and provide a structural insight into the modifications. Additionally, we study the aggregation of mAbs to investigate the structural consequences on the protein, as well as identify spectral markers that could be used to monitor aggregation.

The long chain omega-3 polyunsaturated fatty acids (LC3PUFA) in human diets are mainly derived from oily fish and fish oil based supplements. Currently, the consumption of oily fish in the UK is far below the recommended level. LC3PUFA's non-fish sources such as algal oil with DHA (docosahexaenoic acid) are particularly important for vegetarians, non-fish eaters, and pregnant women. In previous work, high DHA vegetative algal oil load 50% w/w was successfully used to develop an oil-in-water nanoemulsion system suitable for functional food enrichment. The aims of this study included to investigate the effect of selected emulsifiers on oil-in-water nanoemulsions of algal oil prepared using ultrasonic technology. To improve the stability and digestibility of nanoemulsions within an In vitro digestion model. To examine the oxidation stability of nanoemulsions of algal oil and bulk algal oil with composition and droplet size changes during a 5 weeks storage trial at a temperature of 4 °C, 20 °C and 40 °C respectively. To evaluate sensory properties and consumer acceptability of food products with the incorporation of resulted nanoemulsion and find out possible relationship between the sensory profile of foods and the characteristics of added nanoemulsion. Nanoemulsion of LC3PUFA algal oil was developed with selected 6% w/w emulsifiers, including Lecithin (LN), Tween 40 (TN), Tween 60, equal ratio of Tween 40 and lecithin (LTN), 50% w/w Algal oil and 44%w/w water using a homogenizer and ultrasound processor. The results show that the nanoemulsion has been stabilised with selected emulsifiers (LN, TN & LTN) and the smallest droplet size of nanoemulsion was obtained using the combination of lecithin and Tween 40 at ratio 50:50. The In vitro digestion experiments were conducted with a model of fed state gastric and duodenal digestion using method of Lin et al (2014). The results show that the omega-3 oil nanoemulsion (LE/TW 50:50) were stable over 60 min in the gastric phase, in contrast omega-3 nanoemulsion (LE 100%) was destabilised at the gastric phase in 60 min, in which the droplet size diameter was significantly larger than at the beginning of gastric phase (P ≤ 0.05). The droplet size, fatty composition and oxidised compounds were measured to compare bulk algal oil and nanoemulsions stabilised with lecithin (LN) and Tween 40 (TN) solely and in combination (LTN) over a storage period of 5 weeks at temperatures of 4, 20 and 40°C. The results show the droplet size of nanoemulsions had no significant changes for samples stored at tested temperatures over 5 weeks storage. There were no significant differences in DHA composition within the weeks and temperatures used. For the GCHS analysed results, the increase in temperature to 40 ºC and storage time had a significant effect on the development of propanal for all samples (P≤0.05). Nanoemulsions prepared with lecithin alone had significantly higher development of propanal in week 1 at both 40 ºC and 20 ºC (P≤0.05). Lecithin (sole and combination with Tween 40) had more significant increases in oxidised volatiles at 40°C, which may be due to the instability of linoleic acid found in lecithin molecules which located in the outer layer of the oil droplets. There were no significant increase in oxidised compounds from the beginning to the end of storage for all tested samples stored at 4 °C. The sensory testing was also conducted on white sauce incorporated with omega-3 nanoemulsions with selected emulsifiers and bulk algal oil. The results show that the sensory attributes and overall acceptability of foods enriched with omega-3 nanoemulsion were statistically significantly lower than that of control sample (P≤ 0.05). Overall, the smallest droplet size of nanoemulsion was achieved with combination of lecithin and Tween 40 at a ratio of 50:50 by using ultrasonic processor. The stability and digestibility of nanoemulsion with the combination of lecithin and Tween 40 was improved in an In vitro digestion approach. A storage period of 5 weeks and temperature have no significant effect on the droplet size of tested nanoemulsion samples. However, there is a significant increase of the oxidised volatiles at 40 °C for all samples. Sensory testing show the white sauce with nanoemulsion has a stronger fishy taste and less overall liking than with bulk oil, indicating the smaller drop size is more ready to spread and reach the sensors of the mouth.

Solution processed organic semiconductors contain extrinsic environmental species that cause device instabilities as they are difficult to remove during low temperature processing and are able to penetrate into organic electronics after fabrication. This dissertation is centered on the search for and development of solid state molecular additives to improve device stability associated with atmospheric defects in organic field effect transistors. To achieve this, an extended study was undertaken of the influence of over 95 different molecular additives expected to improve the stability characteristics of organic field effect transistors based on the literature. This dissertation demonstrates that positive bias and light stress stability can be improved in both p-type diF-TES ADT and IDT-BT organic field effect transistors by incorporating solid state small molecular additives. Simulations predict that the additives improve stability by introducing a competitive recombination pathway in order to prevent the trapping of electrons in the LUMO of the semiconductor by atmospheric species. Improvements with the solid state molecular additives are achieved by controlling the LUMO and morphology of the additive polymer blend. Secondly, improvements in the environmental and negative bias stress stability of organic field effect transistors are also observed with molecular additives. The solid state small molecular additives that significantly improve device characteristics are limited to a subset of molecules with similar structure to tetracyanoquinodimethane. It is demonstrated that this subset of solid state molecular additives correlates with a chemical reaction between the molecules and water. The chemical reaction appears to change the molecular additives into a new chemical species, plausibly consuming water, modifying the pH and doping the semiconductor, resulting in improved organic field effect transistor characteristics. Thirdly, machine learning techniques are used to accurately predict which solid state additives are capable of improving device performance. The machine learning algorithm uses neural passing networks for feature generation, due to its ability to capture physical plausible features such as functional groups. The algorithm screened over 1.5 billion molecular structures and found plausible molecular structures based on expert knowledge. Fourthly, novel analogue neuromorphic computer architectures based on anti-ferromagnetic and analogue transistors are modeled. The proposed architecture presents both trainable anti-ferromagnetic based synapses for learning and non-trainable voltage controlled synapses for computationally demanding inferences. This dissertation suggests that combining both the fully controllable and trainable networks is a promising route forward for analog neuromorphic computers.

From the alignment of magnets to the melting of ice, the transition between different phases of matter underpins our exploitation of materials. Both a quantum and a classical phase can undergo an instability into another state. In this thesis, we study the stability of matter in both contexts: topological states and crystalline solids. We start with the stability of fractional quantum Hall states on a lattice, known as fractional Chern insulators. We investigate, using exact diagonalization, fractional Chern insulators in higher Chern bands of the Harper-Hofstadter model, and examine the robustness of their many-body energy gap in the effective continuum limit. We report evidence of stable states in this regime; comment on two cases associated with a bosonic integer quantum Hall effect; and find a modulation of the correlation function in higher Chern bands. We next examine the stability of molecules using variational and diffusion Monte Carlo. By incorporating the matrix of force constants directly into the algorithms, we find that we are able to improve the efficiency and accuracy of atomic relaxation and eigenfrequency calculation. We test the performance on a diverse selection of case studies, with varying symmetries and mass distributions, and show that the proposed formalism outperforms existing restricted Hartree-Fock and density functional theory methods. Finally, we analyze the stability of three-dimensional crystals. We note that for repulsive Coulomb crystals of point nuclei, cubic systems have a zero matrix of force constants at second order. We investigate this by constructing an analytical model in the tight-binding approximation, and present a phase diagram of the most stable crystal structures, as we tune core and valence orbital radii. We reconcile our results with calculations in the nearly free electron regime, as well as current research in condensed matter and plasma physics.

The stability concept has been considered a shelter by international energy investors against unilateral host state actions. Investors constantly look for ways to ensure a stable legal environment in host states in order to be able to secure profit from their investments. Stability provisions, as found under investment contracts or domestic laws, are the main tools that international energy investors employ in this regard. Even though stabilisation clauses have been around for decades, the dispute regarding their efficiency is still ongoing. This thesis adds another perspective to the utilisation of the stability concept in investment treaty protection by assessing it through the prism of the legitimate expectations principle. The legitimate expectations principle, as the most important component of the Fair and Equitable Treatment Standard, plays a significant role in providing protection to the investments. Despite this, the contours of the principle have not been defined well under investment treaty jurisprudence. This thesis explores the relationship between the stability and legitimate expectations concepts in the field of international investment law. First, it analyses these concepts separately to identify their contours and then brings them together to illustrate the interplay between these two concepts. This thesis finds that there is a close link between these concepts, upon which investors might rely while arguing their cases before arbitral tribunals. The analysis in this thesis identifies three main sources of legitimate expectations: contractual commitments, administrative representations of host states, and the general legal framework prevailing in host states. It has been argued in this work that each of these sources, when analysed in conjunction with stability commitments, provide a stronger and more efficient protection framework to investors under investment treaties. The thesis shows that while stabilisation provisions create legitimate expectations to be protected, there is also a requirement arising from investment treaty law for host states to provide a stable investment environment, even in the absence of an explicit stability assurance.

Fixed Series Compensation (FSC) is quick to deploy, reliable, has a low environmental impact and is scalable in the event of future capacity expansion. Particularly, when compared to building new transmission lines, which often suffer from right of way issues and long lead times. FSC also helps enhance transient stability limits and enhance voltage stability by providing dynamic reactive power. Networks across the UK and Europe are now turning to series compensation as a solution; for example, FSC banks have been installed for the first time in 2015 by Scottish Power Transmission to increase the power flow capacity from Scotland to England. However, the presence of series capacitors can induce subsynchronous frequency current components that can interact with power system elements. The interaction with the turbine-generator rotor in the form of Subsynchronous Resonance (SSR) can cause dangerous amounts of shaft stress and fatigue and has been cited as a barrier to FSC deployment by some operators. Furthermore, the interaction with Type 3 wind turbines in the form of Subsynchronous Control Interactions (SSCI) can cause serious overvoltages, which are dangerous for both the wind turbine converter as well as the system. The goal of this thesis is to develop novel mitigation solutions for such subsynchronous interactions. The solutions proposed exploit existing resources and incur minimum additional costs for both operation and installation. The thesis presents an exhaustive literature survey of existing SSR analytical techniques, modelling, and mitigation methods to develop a clear understanding of the underlying assumptions and identify relevant gaps. The thesis studies the impact of including dynamic load modes on SSR damping, which has traditionally been neglected in SSR studies, and uses these findings to propose a novel mitigation solution using Variable Frequency Drive (VFD) interfaced auxiliary power plant induction motors. Next, the thesis looks at how Battery Energy Storage System (BESS) controls in a dispatchable wind farm interact with SSCI. With increasing penetration of wind power displacing synchronous generation, wind farms are expected to follow dispatch schedules by using BESS. The thesis proves how a dispatchable wind farm is inherently able to damp SSCI. The SSR studies use PowerFactory while the SSCI studies use MATLAB/Simulink.

In this dissertation, I examine the contingent link of CSR and employee work-related attitudes (e.g. staff affective commitment and job satisfaction). Based on Weiner's (1986) stability theory, I identify two types of CSR attribution: self-centred CSR attribution and other-centred CSR attribution. I have developed two arguments and use survey data to test them. Firstly, I argue that a positive link of corporate social responsibility (CSR) and employee work-related attitudes is more likely to occur when the level of self-centred CSR attribution is high or the level of other-centred CSR attribution is high. Secondly, based on organization theory, I argue that the link of CSR and staff affective commitment and job satisfaction will be positively mediated by employee work-meaningfulness. Results using a longitudinal study justify both arguments. I find that: (1) CSR has a positive link with staff affective commitment and job satisfaction ; (2) employee work-meaningfulness positively mediates the link of CSR and employee work-related attitudes; (3) the link of CSR and employee work-related attitudes is positively moderated by self-centred CSR attribution and other-centred CSR attribution; (4) CSR is positively related with employee work-related attitudes when both self-centred CSR attribution and other-centred CSR attribution are high; (5) the mediation role of employee work-meaningfulness on the link of CSR and staff affective commitment and job satisfaction is moderated by self-centred CSR attribution and other-centred CSR attribution respectively and jointly. These findings contribute to our knowledge of how CSR can have a positive effect on employee work-related attitudes. Theoretical and managerial implications are discussed.

In this thesis I make extensive use of the Lyapunov analysis formalism to unravel fundamental mechanisms of instability in two different systems : the Kuramoto model of globally coupled phase-oscillators and the Lorenz 96 (L96) atmospheric "toy" model, portraying the evolution of a physical quantity along a latitude circle. I start by introducing the relevant theoretical background, with special attention on the main tools I have been using throughout this work : Lyapunov Exponents (LEs), which quantify the asymptotic growth rates of infinitesimal perturbations in a system, and by extension, its degree of chaoticity, and Covariant Lyapunov Vectors (CLVs), which indicate the phase space direction (or the geometry) associated with these growth rates. The Kuramoto model is central in the study of synchronization among oscillatory units characterized by their various natural frequencies, but little is known on its chaotic dynamics in the unsynchronized state. I thus investigate the scaling behavior of the first LE, upon different assumptions on the natural frequencies, and make use of educated structural simplifications to analyze the origin of chaos in the finite size model. On the other hand, the L96 model has been devised to gather the main dynamical ingredients of atmospheric dynamics, namely advection, damping, external (solar) forcing and transfers across different scales of motion, in a minimalist and functional way. It features two coupled dynamical layers : the large scale variables, representing synoptic scale atmospheric dynamics, and the small scale variables, faster and more numerous, associated with convective scale dynamics. The core of the study revolves around geometrical properties of CLVs, in the aim of understanding the processes underlying the observed multiscale chaoticity, and an exhaustive study of a non-trivial ensemble of CLVs featuring relevant projection on the slow subspace.

The physical and chemical properties of orally inhaled powders in capsule-based dry powder inhalers (DPI) are crucial in maintaining a stable and functioning product during its shelf-life. The process history of a material has been known to directly influence formulation structure, performance, thermodynamic stability and shelf-life of a DPI product. It is also well-known that size-reduction processes, such as air-jet micronisation, activate an otherwise stable crystalline form of a material due to the high energy attrition the materials are subjected to. Process-induced structural defects upon particle comminution, which appear almost exclusively at the surface of a processed material, inevitably lead to an unstable, activated state. This energetic state will undergo mechanical relaxation post-micronisation. Relaxation is a thermodynamically driven and a time-dependant process where a material is driven to revert to a more stable form. Certain materials, including micronised lactose monohydrate, may succumb to degradation in the presence of a partial water vapour pressure, and can be rendered unusable during this period of relaxation. It is, therefore, crucial to understand the underlying processes dictating relaxation to achieve better control and a quality-led design of an orally inhaled drug product. This study focused on characterising the inherent disorder associated with micronised α-lactose monohydrate, and identifying methods and mechanisms by which material stability can be restored. An array of physical and chemical characterisation techniques were used to assess the material properties of micronised lactose before and upon conditioning using well-defined conditions of relative humidity and liquefied propellants. These studies indicated that air-jet micronisation can introduce profound changes to the distribution of crystal-bound water within micronised lactose monohydrate. The laagering effects of freshly micronised lactose monohydrate under ambient conditions were also investigated, and suggested an apparent but insignificant amount of dissipation of the energy associated with the mechanical activation process. Studies using controlled environmental conditioning to stabilise micronised lactose monohydrate showed no significant changes in the material's physical properties. However, results showed an unprecedented thermal behaviour in the material. Drastic changes in the distribution of freely-bound water and in the material's lattice were observed. In another study, a novel technique assessing the degradation of freshly micronised and conditioned lactose was undertaken over a six-month period under stressed stability conditions. A volatile degradation molecule was suppressed upon conditioning, suggesting a more stable form of micronised lactose monohydrate may have formed. A study was also undertaken to understand the effect of intense ball milling for size-reduction of primary crystals of lactose monohydrate. With a lower energy input during comminution, ball milling did not induce similar thermal changes observed for micronised lactose whilst its physical character was comparable. In establishing that freely available water under ambient conditions is a major issue for controlling metastable pharmaceutical powders, investigations into the stability and conditioning of commercially available capsule-based DPI products was commenced using water activity measurements. A novel method developed to assess the influence of water activity and equilibrium relative humidity in the headspace surrounding hermetically sealed capsule-based products, suggested that pre-equilibration appears to play a defining role in the successful shelf-life of capsule-based inhaler products. Finally, a study on the stability of a tiotropium formulation was investigated at elevated temperatures across a wide range of relative humidities with time. Results indicated that a relationship between the formulation and the material properties of the capsule may readily degrade the formulation and severely affect shelf-life and product performance.

This thesis addresses two crucial questions of contemporary political theory: why do we disagree about value and how should we respond politically to that disagreement? I make three major arguments that correspond to each of the three sections. I outline and analyse two theories of moral pluralism in Section I, value pluralism and epistemic pluralism, which offer explanations of disagreement about value. Value pluralism is a widely held metaphysical doctrine that makes a claim about the plural nature of value. Epistemic pluralism is a less widely known theory that makes a claim about the difficulty of reasoning about value. I argue that epistemic pluralism is the appropriate form of moral pluralism for political theory because, unlike value pluralism, it does not rely on controversial metaphysical ideas. In Section II I analyse two theories of public reason liberalism, John Rawls's political liberalism and Gerald Gaus's justificatory liberalism, both of which develop an account of political legitimacy in light of epistemic pluralism. I reject both theories on the basis that they are incompatible with a commitment to epistemic pluralism. In Section III I develop a political theory of modus vivendi which accords with my account of epistemic pluralism. Building on the work of other modus vivendi theorists I outline a theory of legitimacy that depends on two political conditions, peace and acceptance. In the final chapter I defend my conception of modus vivendi from various criticisms in order to show that a theory of modus vivendi is not a counsel of despair.

People's explanations for why team events occur (i.e., team-referent attributions) are instrumental in subsequent cognitive, affective, and behavioural responses. The nature of these relationships is likely dependent on the contexts in which they occur. The purpose of this PhD was to examine the extent to which contextual factors structure the relationships between attributions and sport outcomes. Chapters 1 and 2 provide an introduction and detail three team contextual factors that could structure the relationships between team-referent attributions and sport outcomes. The subsequent three chapters detail empirical investigations examining if these contextual factors moderate team-referent attribution-sport outcome relationships. In Chapter 3 the moderating roles of dispositional team- referent attributions on the relationships between situational team-referent attributions and collective efficacy were examined. Results indicated that adaptive dispositional attributions might buffer against the negative effects of maladaptive situational attributions. In Chapter 4, two studies were used to examine the moderating role of social identity on the relationships between team-referent attributions and sport outcomes. Results indicated that relationships between attributions and collective efficacy vary at different levels of social identity. In Chapter 5, the effect of team-referent attributions and attributional consensus on interpersonal outcomes and performance were examined. Two experiments in which participants were led to believe their teammate agreed or disagreed with their personal team-referent attribution revealed that high attributional consensus led to more positive interpersonal and performance outcomes. Chapter 6 provides a summary and theoretical explanation for the findings, as well as strengths, limitations, and future directions relevant to the research conducted. At a specific attribution level, the results of this thesis indicate that athletes' teams might help structure the way they think about their attributions. At a broad level, the results of this thesis highlight the importance of considering contextual factors when exploring group level constructs within sport.

Defects in the functional oxides play an important role in electronic devices like metal oxide semiconductor field effect transistors (MOSFETs) and resistive random-access memories (ReRAMs). The continuous scaling of CMOS has brought the Si MOSFET to its physical technology limit and the replacement of Si channel with Ge channel is required. However, the performance of Ge MOSFETs suffers from Ge/oxide interface quality and reliability problems, which originates from the charge traps and defect states in the oxide or at the Ge/oxide interface. The sub-oxide layers composed of GeII states at the Ge/GeO2 interface seems unavoidable with normal passivation methods like hydrogen treatment, which has poor electrical properties and is related to the reliability problem. On the other hand, ReRAM works by formation and rupture of O vacancy conducting filaments, while how this process happens in atomic scale remains unclear. In this thesis, density functional theory is applied to investigate the defect behaviours in oxides to address existing issues in these electronic devices. In chapter 3, the amorphous atomic structure of doped GeO2 and Ge/GeO2 interface networks are investigated to explain the improved MOSFET reliability observed in experiments. The reliability improvement has been attributed to the passivation of valence alternation pair (VAP) type O deficiency defects by doped rare earth metals. In chapter 4, the oxidation mechanism of GeO2 is investigated by transition state simulation of the intrinsic defect diffusion in the network. It is proposed that GeO2 is oxidized from the Ge substrate through lattice O interstitial diffusion, which is different from SiO2 which is oxidized by O2 molecule diffusion. This new mechanism fully explains the strange isotope tracer experimental results in the literature. In chapter 5, the Fermi level pinning effect is explored for metal semiconductor electrical contacts in Ge MOSFETs. It is found that germanides show much weaker Fermi level pinning than normal metal on top of Ge, which is well explained by the interfacial dangling bond states. These results are important to tune Schottky barrier heights (SBHs) for n-type contacts on Ge for use on Ge high mobility substrates in future CMOS devices. In chapter 6, we investigate the surface and subsurface O vacancy defects in three kinds of stable TiO2 surfaces. The low formation energy under O poor conditions and the +2 charge state being the most stable O vacancy are beneficial to the formation and rupture of conducting filament in ReRAM, which makes TiO2 a good candidate for ReRAM materials. In chapter 7, we investigate hydrogen behaviour in amorphous ZnO. It is found that hydrogen exists as hydrogen pairs trapped at oxygen vacancies and forms Zn-H bonds. This is different from that in c-ZnO, where H acts as shallow donors. The O vacancy/2H complex defect has got defect states in the lower gap region, which is proposed to be the origin of the negative bias light induced stress instability.

This work considers the three-dimensional laminar boundary layer on a semi-infinite plate aligned with a uniform oncoming stream or driven by a favourable pressure gradient of power-law type. The three dimensionality is induced by a wall injection that exists over a finite spanwise scale that is comparable to the boundary-layer thickness. These short-scale disturbances require the inclusion of spanwise and transverse diffusion in the boundary layer. As the spanwise extent of the disturbances maintains a constant ratio with the boundary-layer thickness a self-similar formulation is used. This self-similar formulation is later extended to allow for downstream variation in the injection profile. In the absence of a pressure gradient, classical two-dimensional theory predicts separation when an injection into the boundary layer is of sufficient strength; injection over short spanwise scales leads to qualitatively different flow responses where no separation occurs. The flow exists in one of three distinct regimes depending upon the magnitude of the surface injection rate. These regimes take the form of low-speed streaks where the amplitude and spanwise width of the injection determines the geometry of the streaks. An asymptotic description in the limit of a large injection slot width and a fixed injection velocity is presented, this provides information on critical injection rates which distinguish the three regimes. Applying a favourable pressure gradient reduces the extent of the streaks and removes the delineation between the three flow regimes. For sufficiently strong pressure gradients the Falkner--Skan solution is recovered throughout the domain, albeit with an injection boundary condition in the slot region. Near the centreline of the injection slot the asymptotic description does not agree with the full numerical calculations due to the presence of spatially unstable eigenmodes. These local spatial (cross-flow) eigenmodes are associated with a cross-flow collisional process at the centre of the injection slot. The stability of the streak flow to a travelling wave disturbance is considered, both in terms of the fixed Reynolds number viscous stability and the inviscid limit. The inviscid analysis produces a two-dimensional analogue of the Rayleigh stability equation which forms a critical layer where the streak velocity is equal to the wave speed. The inviscid equations are well approximated by a two-dimensional analogue of the Orr-Sommerfeld equation when the Reynolds number is sufficiently large. The stability of the streak flow at various injection rates, pressure gradients, wavenumbers and Reynolds numbers is examined.

A method is proposed to infer stability properties for non-linear switching under continuous state feedback. Continuous-time systems which are dissipative in the multiple storage function sense are considered. A partition of the state space, induced by the cross-supply rates and the feedback function, is used to derive a restriction on switching. Then, conditions are proposed, under which, systems controlled by the feedback function and switching according to the rule are stable. In particular, Lyapunov and asymptotic stability are proved, both in a local and in a global context. Further, it is shown that the approach can be extended when one uses multiple controllers, and, therefore, is able to construct multiple partitions; conditions for this case are also presented. Finally, it is shown that, for the switching families that satisfy the switching rule posited by the results, one is able to find elements (that is, stabilising switching laws for the system) which are non-Zeno. Additional rule-sets that allow this are provided. It is argued that the conditions proposed here are easier to verify and apply, and that they offer additional flexibility when compared to those proposed by other approaches in the literature. The same infrastructure is used in the study of hybrid systems. For a general class of non-linear hybrid systems, a new property is proposed, that retains some of the properties of dissipativity, but it differs from it, crucially in the fact that it is not purely input-output. For systems having this property, it is shown that the partition used in the switching case can also be used. This, along with a set of conditions allows for the characterisation of the system behaviour in two scenaria. First, when the continuous behaviours and the jumping scheme act co-operatively, leading the system to lower energy levels (from the dissipativity point of view). Second, when the continuous behaviours are allowed to increase the stored energy, but the jumping is able to 6 compensate this increase. In the first case, it is shown that the equilibrium point under study is stable; in the second, it is shown that the system exhibits a type of attractivity, and, under additional conditions, it is asymptotically stable. Besides stability, a collection of stabilisation results are given for the case of dissipative switching systems. It is shown that one may design state feedback functions (controllers) with the objective that they satisfy the conditions of the stability theorems in this work. Then, systems under the designed controllers are shown to be stable, provided that the switching adheres to a specific switching rule. This problem is approached using a variety of tools taken from analysis, multi-valued functions and the space of non-switching stabilisation. In addition to the main results, an extensive overview of the literature in the area of switching and hybrid systems is offered, with emphasis on the topics of stability and dissipativity. Finally, a collection of numerical examples are given, validating the results presented here.

Feature Selection is central to modern data science, from exploratory data analysis to predictive model-building. The "stability"of a feature selection algorithm refers to the robustness of its feature preferences, with respect to data sampling and to its stochastic nature. An algorithm is "unstable" if a small change in data leads to large changes in the chosen feature subset. Whilst the idea is simple, quantifying this has proven more challenging---we note numerous proposals in the literature, each with different motivation and justification. We present a rigorous statistical and axiomatic treatment for this issue. In particular, with this work we consolidate the literature and provide (1) a deeper understanding of existing work based on a small set of properties, and (2) a clearly justified statistical approach with several novel benefits. This approach serves to identify a stability measure obeying all desirable properties, and (for the first time in the literature) allowing confidence intervals and hypothesis tests on the stability of an approach, enabling rigorous comparison of feature selection algorithms.

When receiving a negative outcome (e.g., rejection in a job interview), people tend to attribute it to different causes. For members of stigmatised groups, discrimination is a plausible cause for a negative outcome. However, because discrimination has become relatively subtle (Ellemers & Barreto, 2015), members of stigmatised groups always live in an attributional ambiguity where they constantly wonder whether discrimination was the cause of the received negative outcome. Some researchers argue that this attributional ambiguity leads members of stigmatised groups to make attributions to discrimination. In doing so, individuals would protect themselves by discounting their own role in the negative outcome they received. In other words, in order to protect their sense of competence, members of stigmatised groups prefer to make attributions to discrimination rather than their lack of deservingness (i.e., attributions to lack of ability; Crocker & Major, 1989; Major, Kaiser, & McCoy, 2003). On the other hand, other researchers argue that making attributions to discrimination is not necessarily self-protective as perceived discrimination can have negative consequences for individuals. It has been suggested that attributional stability plays a key role in determining the extent to which attributions to discrimination and to lack of ability are perceived as a threat to individuals (Branscombe & Schmitt, & Harvey, 1999; Schmitt & Branscombe, 2002; Dweck & Leggett, 1988). In three studies, I examined the extent to which attributions to discrimination and to lack of ability are threatening/challenging as a function of stability of those attributions. Threat and challenge were measured both via self-reported data and cardiovascular markers. The results confirmed the role of attributional stability in perceived threat/challenge. In addition, in another study I examined whether attributional stability influences the extent to which attributions to discrimination and to lack of ability are made. However, the results of this study did not confirm my expectations, instead, participants consistently made more attributions to their lack of ability irrespective of information about attributional stability.