This thesis examines the validity of the cost of carry model for pricing FTSE100 futures contracts and the relationship between FTSE100 spot and futures markets during two sub-periods characterised by different market trading systems employed by the LSE and LIFFE. The empirical work is carried out using three approaches to econometric modeling: a basic VECM for spot and futures prices, a VECM extended with a DCCTGARCH framework to account for the conditional variance-covariance structure for spot and futures prices and a threshold VECM to capture regime-dependent spot-futures price dynamics. Overall, both the basic VECM and the DCC-TGARCH analysis suggest that there are deviations from the cost of carry relationship in the first sub-sample when transactions costs in both markets are relatively high but that the cost of carry relationship tends to be valid in the second sub-sample when transactions costs are lower. This is further confirmed by the evidence of higher conditional correlations between the two markets in the second sub-sample as compared with the first, using the DCC-TGARCH analysis. This implies that the no-arbitrage cost of carry relationship between spot and futures markets is more effectively maintained by index arbitrageurs in the second period when market conditions are closer to perfect market assumptions, and hence the cost of carry model could be more reasonably used as a benchmark for pricing stock index futures. The threshold VECM analysis depicts regime-dependent price dynamics between FTSE100 spot and futures markets and leads to some interesting and important findings: arbitrage may not be practicable under some market conditions, either because it is difficult to find counterparties for the arbitrage transactions, or because there is significant risk associated with arbitrage; as a result, the cost of carry model may not always be suitable for pricing stock index futures. Furthermore, the threshold values yielded from estimating the threshold VECM reflect the average transaction costs for most arbitrageurs that are more reliable and fair than subjective estimations.

This dissertation presents techniques for high-order simulation of electromagnetic fields, particularly for problems involving ships with ferromagnetic hulls and active corrosion-protection systems. A set of numerically constrained hexahedral basis functions for volume integral equation discretization is presented in a method-of-moments context. Test simulations demonstrate the accuracy achievable with these functions as well as the improvement brought about in system conditioning when compared to other basis sets. A general method for converting between a locally-corrected Nyström discretization of an integral equation and a method-of-moments discretization is presented next. Several problems involving conducting and magnetic-conducting materials are solved to verify the accuracy of the method and to illustrate both the reduction in number of unknowns and the effect of the numerically constrained bases on the conditioning of the converted matrix. Finally, a surface integral equation derived from Laplace’s equation is discretized using the locally-corrected Nyström method in order to calculate the electric fields created by impressed-current corrosion protection systems. An iterative technique is presented for handling nonlinear boundary conditions. In addition we examine different approaches for calculating the magnetic field radiated by the corrosion protection system. Numerical tests show the accuracy achievable by higher-order discretizations, validate the iterative technique presented. Various methods for magnetic field calculation are also applied to basic test cases.

The thesis deals with the numerical modeling of nonreactive and nonlinearly sorbing solutes in groundwater and analysis of the effect of heterogeneity resulting from spatial variation of physical and chemical parameters on the transport of solutes. For this purpose, a hy­brid flux corrected transport (FCT) and central difference method based on operator-split approach is developed for advection-dispersion solute transport equation. The advective transport is solved using the FCT technique, while the dispersive transport is solved using a conventional, fully implicit, finite difference scheme. Three FCT methods are developed and extension to multidimensional cases are discussed. The FCT models developed are anlaysed using test problems possessing analyt­ical solutions for one and two dimensional cases, while analysing advection and dispersion dominated transport situations. Different initial and boundary conditions, which mimic the laboratory and field situations are analysed in order to study numerical dispersion, peak cliping and grid orientation. The developed models are tested to study their relative merits and weaknesses for various grid Peclet and Courant numbers. It is observed from the one dimensional results that all the FCT models perform well for continuous solute sources under varying degrees of Courant number restriction. For sharp solute pulses FCT1 and FCT3 methods fail to simulate the fronts for advection dominated situations even for mod­erate Courant numbers. All the FCT models can be extended to multidimensions using a dimensional-split approach while FCT3 can be made fully multidimensional. It is observed that a dimensional-split approach allows use of higher Courant numbers while tracking the fronts accurately for the cases studied. The capability of the FCT2 model is demonstrated in handling situations where the flow is not aligned along the grid direction. It is observed that FCT2 method is devoid of grid orientation error, which is a common problem for many numerical methods based on Cartesian co-ordinate system. The hybrid FCT2 numerical model which is observed to perform better among the three FCT models is extended to model transport of sorbing solutes. The present study analyses the case of nonlinear sorption with a view to extend the model for any reactive transport situation wherein the chemical reactions are nonlinear in nature. A two step approach is adopted in the present study for coupling the partial differential equation gov­erning the transport and the nonlinear algebraic equation governing the equilibrium sorp­tion. The suitability of explicit-implicit (EI - form) formulation for obtaining accurate solution coupling the transport equation with the nonlinear algebraic equation solved using a Newton-Raphson method is demonstrated. The performance of the numerical model is tested for a range of Peclet numbers for modelling self-sharpening and self-smearing con­centration profiles resulting from nonlinear sorption. It is observed that FCT2 model based on this formulation simulates the fronts quite accurately for both advection and dispersion dominated situations. The delay in the solute mobility and additional dispersion are anal­ysed varying the statistical parameters characterising the heterogeneity namely, correlation scale and variance during the transport of solutes and comparisons are drawn with invariant, cases. The impact of dispersion during the heterogeneous transport is discussed.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Many control techniques applied to converters with power factor correction (PFC) use cascaded control to compensate the output voltage and the input current. These techniques usually employ linear time-invariant (LTI) models and ignore the periodic output voltage oscillation by using compensator with low-pass characteristic. To ensure correlation between the rectifier and its LTI model, as well as power factor correction, these techniques reduce the crossing frequency, which result in a closed-loop voltage with poor dynamic response. Aiming to reduce the time-response designers have associated notch filters into the controller to increase the bandwidth. These filters increase the attenuation in ripple frequencies making possible to enlarge system bandwidth without compromising power factor correction. However, increasing the crossing frequency enhances the interaction between ac output components and the feedback system. In these cases, linear time-invariant (LTI) approach can not adequately represent the closed loop dynamics. As a result, LTI stability analysis based on LTI approach is no longer valid. On the other hand, a better dynamic representation can be achieved by using linear time-periodic models (LTP). These models include the modulation effects inherent in the output voltage dynamics. This work presents an alternative systematic methodology to perform the stability analysis for continuous-time closed-loop control systems using linear time-periodic (LTP) models. This methodology use an LTP representation in frequency domain called harmonic transfer function (HTF). This method extends the multi-variable LTI techniques for LTP approach. Finally is detailed the stability analysis of full-bridge and half-bridge single-phase PFC rectifiers. Theoretical, simulation and experimental results are presented to validate the proposed technique. / Muitas técnicas de controle aplicadas a retificadores monofásicos com correção do fator de potência (PFC) utilizam controladores em cascata para compensação da tensão de saída e da corrente de entrada. Essas técnicas, em geral, empregam modelos lineares e invariantes no tempo (LTI) e desconsideram as oscilações periódicas presentes nas tensões de saída, fazendo uso de leis de controle com características passa-baixa. Para garantir a correlação entre o modelo LTI e o retificador, bem como a correção do fator de potência, estas estratégias utilizam banda-passante reduzida, o que limita consideravelmente a resposta dinâmica da compensação da tensão. No intuito de reduzir o tempo de resposta da malha de tensão, sem comprometer a correção do fator de potência, projetistas têm associado filtros rejeita-banda à malha de controle. Esses filtros acentuam a atenuação nas frequências de interesse e, assim, possibilitam elevar a banda-passante sem comprometer a correção do fator de potência na entrada. Porém, a elevação da banda-passante aumenta a interação das componentes alternadas da tensão do lado cc com o sistema de compensação. Nestes casos, a abordagem LTI pode não representar adequadamente as dinâmicas de malha fechada e, consequentemente, não é válida para a análise da estabilidade. Por outro lado, uma melhor representação dinâmica da malha de compensação da tensão de retificadores PFC monofásicos pode ser obtida com a utilização de modelos lineares periódicos no tempo (LTP). Esses modelos dinâmicos incluem os efeitos de modulação inerentes da dinâmica da tensão de saída. Este trabalho apresenta uma metodologia sistemática alternativa para a análise da estabilidade de malha fechada de retificadores PFC monofásicos empregando-se modelos LTP em tempo contínuo. A metodologia de análise da estabilidade utiliza uma representação dos modelos LTP no domínio da frequência, denominado função de transferência harmônica (HTF). Esta representação estende as técnicas clássicas de análise da estabilidade de sistemas LTI multivariáveis para a abordagem LTP. Por fim, são detalhadas as análise de estabilidade dos retificadores monofásicos em ponte completa e meia ponte, considerando-se a operação com correção do fator de potência de entrada. Resultados teóricos, de simulação e experimentais são apresentados para validar a técnica de análise da estabilidade.

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La modélisation des interférences de raies dans des spectres de gaz moléculaires repose sur le concept de la matrice de relaxation dont les éléments diagonaux décrivent les raies isolées et les éléments non-diagonaux représentent le transfert d'intensité entre les raies. Ces éléments non-diagonaux sont modélisés en appliquant des lois d'échelle comme le modèle ECS (Energy-Corrected-Sudden). Nous avons considéré la molécule de CO2 car ce gaz joue un rôle important dans les atmosphères terrestre et planétaires. En plus, à cause de la petite valeur de sa constante de rotation, les raies se serrent et se chevauchent, donnant naissance à des interférences de raies. Grâce aux nouvelles valeurs des paramètres ajustés,nous avons réexaminé l'application de l'approche ECS non-Markovienne (déjà développée pour des spectres de diffusion Raman anisotrope de CO2) _a des spectres de diffusion Raman isotrope, spectre rotationnel pur et spectres ro-vibrationnels de la bande _1 et 2_2. Nous avons également présenté une généralisation de cette approche, aux bandes parallèles et perpendiculaires d'absorption infrarouge, pour les molécules linéaires avec des modes de flexion, accompagnée d'applications au cas de CO2. / Modeling of line mixing in the molecular gas spectra is based on the concept of the relaxation matrix whose diagonal elements describe the isolated lines and non-diagonal elements represent the transfer of intensity between the lines. Thesenon-diagonal elements are modeled by applying scaling laws such as ECS (Energy-Corrected Sudden) model. We considered the CO2 molecule due to its important role in the terrestrial and planetary atmospheres. In addition, because of the small value of the rotational constant, the lines over lap, giving rise to the line-mixing.Using the new values of the tted parameters, we reviewed the application of ECSnon-Markovian (already developed for an isotropic Raman scattering spectra ofCO2) approach to isotropic Raman scattering spectra, rotational spectrum andro-vibrational spectra of 1 and 2 2 band. We also presented a generalization of this approach for the parallel and perpendicular bands of infrared absorption for linear molecules with the bending modes, and their applications for CO2 molecule

Bright emitters with photoluminescence in the spectral region of 800–1600 nm are increasingly important as optical reporters for molecular imaging, sensing, and telecommunication and as active components in electrooptical and photovoltaic devices. Their rational design is directly linked to suitable methods for the characterization of their signal-relevant properties, especially their photoluminescence quantum yield (Φf ). Aiming at the development of bright semiconductor nanocrystals with emission >1000 nm, we designed a new NIR/IR integrating sphere setup for the wavelength region of 600–1600 nm. We assessed the performance of this setup by acquiring the corrected emission spectra and Φf of the organic dyes |trybe, IR140, and IR26 and several infrared (IR)-emissive Cd₁₋ₓHgₓTe and PbS semiconductor nanocrystals and comparing them to data obtained with two independently calibrated fluorescence instruments absolutely or relative to previously evaluated reference dyes. Our results highlight special challenges of photoluminescence studies in the IR ranging from solvent absorption to the lack of spectral and intensity standards together with quantum dot-specific challenges like photobrightening and photodarkening and the size-dependent air stability and photostability of differently sized oleate-capped PbS colloids. These effects can be representative of lead chalcogenides. Moreover, we redetermined the Φf of IR26, the most frequently used IR reference dye, to 1.1 × 10⁻³ in 1,2-dichloroethane DCE with a thorough sample reabsorption and solvent absorption correction. Our results indicate the need for a critical reevaluation of Φf values of IR-emissive nanomaterials and offer guidelines for improved Φf measurements.

Quantum information technologies include secure quantum communications and ultra precise quantum sensing that are significantly more efficient than their classical counterparts. To enable such technologies, we need a scalable quantum platform in which qubits are con trollable. Color centers provide controllable optically-active spin qubits within the coherence time limit. Moreover, the nearby nuclear spins have long coherence times suitable for quantum memories. In this thesis, I present a theoretical understanding of and control protocols for various color centers. Using group theory, I explore the wave functions and laser pumping-induced dynamics of VSi color centers in silicon carbide. I also provide dynamical decoupling-based high-fidelity control of nuclear spins around the color center. I also present a control technique that combines holonomic control and dynamically corrected control to tolerate simultaneous errors from various sources. The work described here includes a theoretical understanding and control techniques of color center spin qubits and nuclear spin quantum memories, as well as a new platform-independent control formalism towards robust qubit control. / Doctor of Philosophy / Quantum information technologies promise to offer efficient computations of certain algorithms and secure communications beyond the reach of their classical counterparts. To achieve such technologies, we must find a suitable quantum platform to manipulate the quantum information units (qubits). Color centers host spin qubits that can enable such technologies. However, it is challenging due to our incomplete understanding of their physical properties and, more importantly, the controllability and scalability of such spin qubits. In this thesis, I present a theoretical understanding of and control protocols for various color centers. By using group theory that describes the symmetry of color centers, I give a phenomenological model of spin qubit dynamics under optical control of VSi color centers in silicon carbide. I also provide an improved technique for controlling nuclear spin qubits with higher precision. Moreover, I propose a new qubit control technique that combines two methods - holonomic control and dynamical corrected control - to provide further robust qubit control in the presence of multiple noise sources. The works in this thesis provide knowledge of color center spin qubits and concrete control methods towards quantum information technologies with color center spin qubits.

Dans cette thèse, nous étudions deux problèmes d'apprentissage automatique : (I) la détection des communautés et (II) l'appariement adaptatif. I) Il est bien connu que beaucoup de réseaux ont une structure en communautés. La détection de ces communautés nous aide à comprendre et exploiter des réseaux de tout genre. Cette thèse considère principalement la détection des communautés par des méthodes spectrales utilisant des vecteurs propres associés à des matrices choisiesavec soin. Nous faisons une analyse de leur performance sur des graphes artificiels. Au lieu du modèle classique connu sous le nom de « Stochastic Block Model » (dans lequel les degrés sont homogènes) nous considérons un modèle où les degrés sont plus variables : le « Degree-Corrected Stochastic Block Model » (DC-SBM). Dans ce modèle les degrés de tous les nœuds sont pondérés - ce qui permet de générer des suites des degrés hétérogènes. Nous étudions ce modèle dans deux régimes: le régime dense et le régime « épars », ou « dilué ». Dans le régime dense, nous prouvons qu'un algorithme basé sur une matrice d'adjacence normalisée réussit à classifier correctement tous les nœuds sauf une fraction négligeable. Dans le régime épars il existe un seuil en termes de paramètres du modèle en-dessous lequel n'importe quel algorithme échoue par manque d'information. En revanche, nous prouvons qu'un algorithme utilisant la matrice « non-backtracking » réussit jusqu'au seuil - cette méthode est donc très robuste. Pour montrer cela nous caractérisons le spectre des graphes qui sont générés selon un DC-SBM dans son régime épars. Nous concluons cette partie par des tests sur des réseaux sociaux. II) Les marchés d'intermédiation en ligne tels que des plateformes de Question-Réponse et des plateformes de recrutement nécessitent un appariement basé sur une information incomplète des deux parties. Nous développons un modèle de système d'appariement entre tâches et serveurs représentant le comportement de telles plateformes. Pour ce modèle nous donnons une condition nécessaire et suffisante pour que le système puisse gérer un certain flux de tâches. Nous introduisons également une politique de « back-pressure » sous lequel le débit gérable par le système est maximal. Nous prouvons que cette politique atteint un débit strictement plus grand qu'une politique naturelle « gloutonne ». Nous concluons en validant nos résultats théoriques avec des simulations entrainées par des données de la plateforme Stack-Overflow. / In this thesis, we study two problems of machine learning: (I) community detection and (II) adaptive matching. I) It is well-known that many networks exhibit a community structure. Finding those communities helps us understand and exploit general networks. In this thesis we focus on community detection using so-called spectral methods based on the eigenvectors of carefully chosen matrices. We analyse their performance on artificially generated benchmark graphs. Instead of the classical Stochastic Block Model (which does not allow for much degree-heterogeneity), we consider a Degree-Corrected Stochastic Block Model (DC-SBM) with weighted vertices, that is able to generate a wide class of degree sequences. We consider this model in both a dense and sparse regime. In the dense regime, we show that an algorithm based on a suitably normalized adjacency matrix correctly classifies all but a vanishing fraction of the nodes. In the sparse regime, we show that the availability of only a small amount of information entails the existence of an information-theoretic threshold below which no algorithm performs better than random guess. On the positive side, we show that an algorithm based on the non-backtracking matrix works all the way down to the detectability threshold in the sparse regime, showing the robustness of the algorithm. This follows after a precise characterization of the non-backtracking spectrum of sparse DC-SBM's. We further perform tests on well-known real networks. II) Online two-sided matching markets such as Q&A forums and online labour platforms critically rely on the ability to propose adequate matches based on imperfect knowledge of the two parties to be matched. We develop a model of a task / server matching system for (efficient) platform operation in the presence of such uncertainty. For this model, we give a necessary and sufficient condition for an incoming stream of tasks to be manageable by the system. We further identify a so-called back-pressure policy under which the throughput that the system can handle is optimized. We show that this policy achieves strictly larger throughput than a natural greedy policy. Finally, we validate our model and confirm our theoretical findings with experiments based on user-contributed content on an online platform.

The pursuit of high quality, large area graphene has been a major research focus of contemporary materials science research, in the wake of the discovery of the multitude of exceptional properties exhibited by the material. The DPhil project was undertaken with the objective of developing an understanding of the growth of large graphene sheets by chemical vapour deposition (CVD), and also in the subsequent characterisation of their material properties. By conducting atmospheric pressure CVD growth at high methane flow rates, it was found that few-layered graphene (FLG) could be deposited on a copper catalyst. It is demonstrated that the self-limiting property of a copper catalyst is not universal to all deposition conditions, and shown that FLG grows in a terrace-like configuration. In depth transmission electron microscopy (TEM) studies were carried out on FLG. By selective image reconstruction from the inverse power spectrum of the TEM images, it was possible to elucidate the inter-grain connectivity of few-layer graphenes. It was determined that there were two possible inter-grain configurations possible; specifically an overlap of graphene layers or a discrete atomic bonding edge. The perturbation of the few-layer structure when subject to an out of plane distortion was found to incur a shift in the conventional AB-Bernal stacking of FLG. By utilising the aberration corrected TEM (AC-TEM) at Oxford it was possible to resolve atomic detail in CVD synthesised monolayer films, including atomic bond rotations and vacancies. The use of a high current density at low accelerating voltage (80 kV) was demonstrated to allow for the controlled defect creation in graphene sheets. This permitted the creation of monovacancies and iron doped vacancy complexes suitable for further study. The behaviour of these two defect types under electron beam irradiation was subsequently studied.