Magnetic Resonance Imaging (MRI) is a widely used soft-tissue imaging modality that has evolved over the past several years into a powerful and versatile medical diagnostic tool capable of providing in-vivo diagnostic images of human and animal anatomies. Current research efforts in MRI system design are driven by the need to obtain detailed high resolution images with improved image signal-to-noise ratio (SNR) at a given magnetic field strength. Invariably, this requirement demands the development of high performance MRI radio frequency (RF) coils. However, the complexities and stringent requirements of modern clinical MRI systems necessitate the development of new modeling methodologies for the design of high performance RF coils. This dissertation addresses this need by developing a distinct Method of Moments (MoM) modeling approach suitable for the simulation of RF coils loaded with biological tissues. The unique implementation utilizes two distinct basis functions in order to collectively describe the surface current density on the RF coil, and the sum of the volume current density and the displacement current density in the associated biological tissue. By selecting basis functions with similar properties to the actual physical quantities they describe, we avoided spurious solutions normally associated with MoM based implementations. The validity of our modeling method was confirmed by comparisons with analytical solutions as well as physical measurements, yielding good agreement. Furthermore, we applied the MoM based modeling method in the design and development of a novel 4-channel receive-only RF coil for breast imaging in a clinical 1.5T system. The new coil design was inspired by the multi-channel array concept, where multiple conducting strips were arranged in an anatomically conforming profile with the intention of improving sensitivity and SNR. In addition, the coil structure featured an open breast coil concept in order to facilitate MRI-guided biopsy and patient comfort. A comparison of simulation results and actual physical measurements from the prototype RF coil demonstrated good agreement with one another. Also, imaging tests were conducted on a pair of MRI phantoms as well as on a human patient after obtaining proper authorization. The tests revealed good magnetic field homogeneity and a high SNR in the region of interest. In addition, performance comparisons between the prototype 4-channel RF coil and existing high end clinical 4-channel RF breast coils indicated an achievement of superior SNR in conjunction with very good magnetic field homogeneity. Currently, the prototype 4-channel RF coil has outperformed all existing high end clinical 4-channel RF coils used in comparison studies.

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Typically wire antenna structures are modeled by approximating curved structures with straight wire segments. The straight wire approximation yields accurate results, but often requires a large number of segments to adequately approximate the antenna geometry. The large number of straight wire segments or unknowns requires a large amount of memory and time to solve for the currents on the antenna. By using curved segments which exactly describe the contour of the antenna geometry the number of unknowns can be reduced, thus allowing for bigger problems to be solved accurately. This thesis focuses on the analysis of a helix antenna. The Method of Moments is used to solve for the currents on the antenna, and both the triangle basis and pulse testing functions exactly follow the contour of the helix antenna. The thin wire approximation is used throughout the analysis. The helix is assumed to be oriented along the z-axis with an optional perfect electric conductor (PEC) ground plane in the x-y plane. For simplicity, a delta gap source model is used. Straight feed wires may also be added to the helix, and are modeled similarly to the helix by the Method of Moments with triangular basis and pulse testing functions. The primary validation of the curved wire approach is through a comparison with MININEC and NEC of the convergence properties of the input impedance of the antenna versus the number of unknowns. The convergence tests show that significantly fewer unknowns are needed to accurately predict the input impedance of the helix, particularly for the normal mode helix. This approach is also useful in the analysis of the axial mode helix where the current changes significantly around one turn. Because of the varying current distribution, the improvement of impedance convergence with curved segments is not as significant for the axial mode helix. However, radiation pattern convergence improvement is found. Multiple feed structures for the axial mode helix are also investigated. In general, the many straight wire segments, and thus unknowns, that are needed to accurately approximate the current around one turn can be greatly reduced by the using the curved segment method. / Master of Science

In this thesis, the Method of Moments has been applied to calculate capacitance between two arbitrary 3D metal conductors or a capacitance matrix for a 3D multi-conductor system. Capacitance extraction has found extensive use for systems involving sets of long par- allel transmission lines in multi-dielectric environment as well as integrated circuit package including three-dimensional conductors located on parallel planes. This paper starts by reviewing fundamental aspects of transient electro-magnetics followed by the governing dif- ferential and integral equations to motivate the application of numerical methods as Method of Moments(MoM), Finite Element Method(FEM), etc. Among these numerical tools, the surface-based integral-equation methodology - MoM is ideally suited to address the prob- lem. It leads to a well-conditioned system with reduced size, as compared to volumetric methods. In this dissertation, the MoM Surface Integral Equation (SIE)-based modeling approach is developed to realize electrostatic capacitance extraction for 3D geometry. MAT- LAB is employed to validate its e?ciency and e?ectiveness along with design of a friendly GUI. As a base example, a parallel-plate capacitor is considered. We evaluate the accu- racy of the method by comparison with FEM simulations as well as the corresponding quasi-analytical solution. We apply this method to the parallel-plate square capacitor and demonstrate how far could the undergraduate result 0C = A ? "=d' be from reality. For the completion of the solver, the same method is applied to the calculation of line capacitance for two- and multi-conductor 2D transmission lines.

This thesis presents a detailed study of the numerical errors and the associated accuracy-efficiency tradeoffs encountered in the solution of frequency- and time-domain integral equations. For frequency-domain integral equations, the potential integrals contain singular Green’s function kernels and the resulting singular and near-singular integrals must be carefully evaluated, using singularity extraction or cancellation techniques, to ensure the accuracy of the method-of-moments impedance matrix elements. This thesis presents a practical approach based on the progressive Gauss-Patterson quadrature rules for implementing the radial-angular-transform singularity-cancellation method such that all singular and near-singular integrals are evaluated to an arbitrary pre-specified accuracy. Numerical results for various scattering problems in the high- and low-frequency regimes are presented to quantify the efficiency of the method and contrast it to the singularity extraction method. For time-domain integral equations, the singular Green’s function kernels are functions of space and time and sub-domain temporal basis functions rather than entire-domain sinusoidal/Fourier basis functions are used to represent the time variation of currents/fields. This thesis also investigates the accuracy-efficiency tradeoff encountered when choosing sub-domain temporal basis functions by contrasting two prototypical ones: The causal piecewise polynomial interpolatory functions, sometimes called shifted Lagrange interpolants, and the band-limited interpolatory functions based on approximate prolate spheroidal wave functions. It is observed that the former is more efficient for low to moderate accuracy levels and the latter achieves higher, but extrapolation-limited, accuracy levels. / text

abstract: Schennach (2007) has shown that the Empirical Likelihood (EL) estimator may not be asymptotically normal when a misspecified model is estimated. This problem occurs because the empirical probabilities of individual observations are restricted to be positive. I find that even the EL estimator computed without the restriction can fail to be asymptotically normal for misspecified models if the sample moments weighted by unrestricted empirical probabilities do not have finite population moments. As a remedy for this problem, I propose a group of alternative estimators which I refer to as modified EL (MEL) estimators. For correctly specified models, these estimators have the same higher order asymptotic properties as the EL estimator. The MEL estimators are obtained by the Generalized Method of Moments (GMM) applied to an exactly identified model. The simulation results provide promising evidence for these estimators. In the second chapter, I introduce an alternative group of estimators to the Generalized Empirical Likelihood (GEL) family. The new group is constructed by employing demeaned moment functions in the objective function while using the original moment functions in the constraints. This designation modifies the higher-order properties of estimators. I refer to these new estimators as Demeaned Generalized Empirical Likelihood (DGEL) estimators. Although Newey and Smith (2004) show that the EL estimator in the GEL family has fewer sources of bias and is higher-order efficient after bias-correction, the demeaned exponential tilting (DET) estimator in the DGEL group has those superior properties. In addition, if data are symmetrically distributed, every estimator in the DGEL family shares the same higher-order properties as the best member.   / Dissertation/Thesis / Ph.D. Economics 2013

In estimating econometric time series models, it is assumed that the parameters remain constant over the period examined. This assumption may not always be valid when using data which span an extended period, as the underlying relationships between the variables in these models are exposed to various exogenous shifts. It is therefore imperative to examine the stability of models as failure to identify any changes could result in wrong predictions or inappropriate policy recommendations. This research proposes a method of estimating the location of break points in linear econometric models with endogenous regressors, estimated using Generalised Method of Moments (GMM). The proposed estimation method is based on Wald, Lagrange Multiplier and Difference type test statistics of parameter variation. In this study, the equation which sets out the relationship between the endogenous regressor and the instruments is referred to as the Jacobian Equation (JE). The thesis is presented along two main categories: Stable JE and Unstable JE. Under the Stable JE, models with a single and multiple breaks in the Structural Equation (SE) are examined. The break fraction estimators obtained are shown to be consistent for the true break fraction in the model. Additionally, using the fixed break approach, their $T$-convergence rates are established. Monte Carlo simulations which support the asymptotic properties are presented. Two main types of Unstable JE models are considered: a model with a single break only in the JE and another with a break in both the JE and SE. The asymptotic properties of the estimators obtained from these models are intractable under the fixed break approach, hence the thesis provides essential steps towards establishing the properties using the shrinking breaks approach. Nonetheless, a series of Monte Carlo simulations conducted provide strong support for the consistency of the break fraction estimators under the Unstable JE. A combined procedure for testing and estimating significant break points is detailed in the thesis. This method yields a consistent estimator of the true number of breaks in the model, as well as their locations. Lastly, an empirical application of the proposed methodology is presented using the New Keynesian Phillips Curve (NKPC) model for U.S. data. A previous study has found this NKPC model is unstable, having two endogenous regressors with Unstable JE. Using the combined testing and estimation approach, similar break points were estimated at 1975:2 and 1981:1. Therefore, using the GMM estimation approach proposed in this study, the presence of a Stable or Unstable JE does not affect estimations of breaks in the SE. A researcher can focus directly on estimating potential break points in the SE without having to pre-estimate the breaks in the JE, as is currently performed using Two Stage Least Squares.

This thesis consists of three parts. The first part is an introduction and referencessome recent work on 2D electromagnetic scattering problems at high frequencies. It alsopresents the basic integral equation types for impenetrable objects. A brief discussionof the standard elements of the method of moments is followed by summaries of thepapers.Paper I presents an accurate implementation of the method of moments for a perfectlyconducting cylinder. A scaling for the rapid variation of the solution improves accuracy.At high frequencies, the method of moments leads to a large dense system of equations.Sparsity in this system is obtained by modifying the integration path in the integralequation. The modified path reduces the accuracy in the deep shadow.In paper II, a hybrid method is used to handle the standing waves that are prominentin the shadow for the TE case. The shadow region is treated separately, in a hybridscheme based on a priori knowledge about the solution. An accurate method to combinesolutions in this hybrid scheme is presented.

<p>Sedan årsskiftet 2006/2007 har antalet medlemmar i arbetslöshetskassorna minskat drastiskt. Under samma period har ett flertal reformer genomförts på arbetslöshetsförsäkringens område som bland annat resulterat i höjda medlemsavgifter för de flesta a-kassorna. Syftet med denna uppsats är att undersöka huruvida det över tid går att finna något samband mellan förändringar i medlemsantal och medlemsavgifter. För att undersöka detta måste man förutom avgifterna även ta hänsyn till andra variabler kopplade till arbetslöshetsförsäkringen. Dessa övriga variabler är grundbelopp, högsta dagpenning, ersättningsgrad och arbetslöshet. Vi formulerar en modell för sambandet mellan medlemsantal och dessa variabler och skattar denna genom metoden Generalized Method of Moments med hjälp av data från 2000-2009. Våra resultat visar i enlighet med teori och tidigare forskning på ett negativt samband mellan medlemsavgifter och antalet medlemmar i a-kassan. Detta samband visar sig vara starkt, särskilt på lång sikt. För att tydigare se hur avgiftsförändringar påverkar olika typer av individer i olika grad har vi även undersökt huruvida medlemsantalet i a-kassor kopplade till tjänstemanna- respektive arbetarförbund är olika känsliga för förändringar i avgiften. Våra resultat visar i kontrast till tidigare studier att a-kassorna kopplade till tjänstemannaförbunden (TCO och Saco) är mer känsliga för förändringar jämfört med arbetarförbunden (LO). Detta skapar anledning att tro att det finns andra faktorer än avgifter och de övriga variablerna som inkluderats i vår modell vilka påverkar anslutningsgraden och som kan förklara skillnaden mellan de olika grupperna.</p>

Recent years have seen a growing interest in a new kind of periodic structures called ``metamaterials'. These new artificial materials exhibit many new appealing properties, not found in nature, and open many new possibilities in the domain of antenna design. This thesis describes efficient numerical tools and methods for the analysis of infinite and finite periodic structures. A numerical simulation code based on the Method of Moments has been developed for the study of both large phased arrays and periodic metamaterials made of metal and/or dielectrics. It is shown how fast infinite-array simulations can be used in a first instance to approximately describe the fields radiated by large antenna arrays or compute transmission and reflection properties of metamaterials. These infinite-array simulations rely on efficient computation schemes of the doubly periodic Green’s function and of its gradient. A technique based on eigenmode analysis is also described, that allows to efficiently compute the dispersion curves of periodic structures. Accounting for the finiteness of real structures is possible in good approximation thanks to a finite-by-infinite array approach. Moreover, the excitation of large finite periodic structures by a single (non periodic) source can be studied by using a combination of the Array Scanning Method with a windowing technique. All these techniques were validated numerically on several examples and it is finally shown how they can be combined to design high gain antennas, based on metamaterial superstrates excited by a slotted waveguide. The proposed design method relies on the separation of the whole structure in two different problems. An interior problem is used to optimize the input impedance of the antenna, while the radiation pattern can be optimized in the exterior problem.