The confinement properties of fusion plasmas are affected bymagnetic and electrostatic fluctuations. The determination ofthe plasma confinement properties requires the measurement ofseveral global and local quantities such as the ion andelectron temperatures, the electron and neutral densityprofiles, the radiation emissivity profiles, the ohmic inputpower and the particle and heat diffusivities. The focus ofthis thesis is the study of the plasma confinement propertiesbased on measurements of these quantities under differentexperimental conditions. The studies have been carried out on the reversed fieldpinch experiments EXTRAP T2 and T2R at the AlfvénLaboratory, Royal Institute of Technology (KTH) in Stockholm.Studies carried out in EXTRAP T2 were focused on dynamoactivity and on the effect of phase alignment and locking tothe wall of magnetic instabilities. These were observed with adedicated imaging system. The experimental studies in EXTRAPT2R were focused on the measurement of the confinementproperties of different configurations. To this aim, a set ofdiagnostics were used some of which were upgraded, such as theinterferometer, while others were newly installed, such as aneutral particle energy analyser and a bolometer array. The dynamo, which is responsible for the plasma sustainment,involves resistive magnetohydrodynamic instabilities thatenhance stochastic transport. Furthermore, the plasmaconfinement properties are in general improved in the presenceof mode rotation. The possibility of reducing the stochastictransport and thereby further improving the confinement hasbeen demonstrated in a current profile control experiment.These results indicate that long pulse operations with aresisitive shell and current profile control are indeedfeasible. KeywordsEXTRAP T2, T2R, reversed field pinch, dynamo,energy confinement time, transport, CCD, bolometer,interferometer, neutral particle energy analyser, PPCD, MonteCarlo / QC 20100524

LCModel, which is performed on Linux, has been widely used for quantitative analysis of MRS. Its interface, LCMgui, converts MRS data of various formats to RAW file for LCModel analysis automatically. In this work, we had a web-based MRS analysis tool for GE MRS, GE MRS with Phase-Array and GE 2D-MRSI and improve the capability of web-based MRS analysis tool for GE 3D-MRSI, Siemens MRS/MRSI, and Philips MRS/MRSI. Meanwhile, T2 correction has been involved in the absolute quantification with LCModel. With the same echo-time, the different T2 value of each metabolite results in different degree of signal decay. In order to correct and make absolute concentrations more accurate, we exploit a factor to correct effect of different T2. Two groups of MRS data (TE = 35 and 272 ms) have been studied for comparison.

The present work is mainly concerned with the commercial relations between the Arab world and India in the 3rd and 4th / 9th and 10th centuries. The thesis consists of an Introduction and five chapters. The introduction contains a brief survey of the historical background to the Arab-Indian trade links In the period prior to the period of the research. lt also includes the reasons for choosing the subject, and the difficulties with which the research was faced. The introduction also contains the methods of the research and a study of the main sources. Chapter One deals with the Arab provinces, the main kingdoms of India, the political situation in the Arab world and India, and its effects on the subject. It also deals with the main economic products in the countries concerned. Moreover, the chapter focuses on the factors which encouraged the Arab-Indian trade. Chapter Two deals with the trade routes (Land and Sea routes), the caravans, ships, the sea ports and the commercial cities in the Arab world and India. Chapter Three deals with the trade procedures between the Arab world and India. It also deals with the taxes levied in ports and some land posts. The chapter ends by giving some details of the prices of of goods in both countries. Chapter Four gives a detailed account of goods exported and imported by both sides, and the real causes behind the export and import of these goods. The chapter also gives an account of how sometimes goods are imported by one side from the other in order to meet the local demands or to be exported in a process of trading nn a world wide scale. Chapter Five deals with a conclusion of what has been discussed earlier, in addition to some cultural aspects which have not been dealt with in the chapters above.

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MRI is a powerful imaging method that offers several advantages including non-ionizing radiation, significant depth of penetration, and great spatial resolution. Current demand for precision medicine and the movement toward personalized medicine have encouraged researchers in the field of medical imaging to develop MRI-based techniques. Various techniques are now available for molecular imaging by MRI. MRI started by utilizing T1 relaxation properties of molecules but soon after other relaxation mechanisms such as T2 and recently Chemical Exchange Saturation Transfer (CEST) were developed. Each of those MRI techniques offers advantages and disadvantages such as differences in experimental procedures, complexity of the method, selectivity and specificity of signals, and translation into clinical applications. We have been developing MRI techniques and responsive contrast agents for CEST MRI in the Pagel laboratory (Contrast Agent and Molecular Imaging Laboratory, also called CAMEL) for the past decade. We have mainly utilized MRI techniques and responsive contrast agents to detect and measure cancer biomarkers. Detection of the activity of enzymes and measurement of pH have been our main focus, and we have developed catalyCEST MRI probes and techniques for the detection of the activity of enzymes and acidoCEST for the measurement of pH. My research started with investigation on paramagnetic agents as potential CEST MRI probes (paraCEST) and continued with an investigation on diamagnetic agents (diaCEST). I completed several projects in which I prepared and evaluated paraCEST and diaCEST contrast agents for the detection of DT-diaphorase, and alkaline phosphatase enzymes, respectively. Although CEST MRI was my main activity in CAMEL, I started a new direction in CAMEL after encountering a series of observations that were unexplainable with CEST MRI. Through my research, I introduced a new class of responsive contrast agents based on the T2-Exchange (T2-Ex) relaxation mechanism. I employed the T2-Ex mechanism to evaluate responsive contrast agents for the detection of nitric oxide biomolecule and nitroreductase enzyme. My research activities in the CAMEL group resulted in one review paper, one book chapter, two published research articles, and two submitted research manuscripts at the time of preparing my PhD dissertation. In addition to my projects, I was involved in another project that focused on nanocapsule drug delivery, which resulted in a second author publication.

This dissertation deals with quantitative perfusion analysis of MRI contrast-enhanced image time sequences. It focuses on two so far separately used methods -- Dynamic contrast-enhanced MRI (DCE-MRI) and Dynamic susceptibility contrast MRI (DSC-MRI). The common problem of such perfusion analyses is the unreliability of perfusion parameters estimation. This penalizes usage of these unique techniques on a regular basis. The presented methods are intended to improve these drawbacks, especially the problems with quantification in DSC in case of contrast agent extravasation and instability of the deconvolution process in DCE using advanced pharmacokinetic models. There are a few approaches in literature combining DCE and DSC to estimate new parameters of the examined tissue, namely the relaxivity of the vascular and of the interstitial space. Originally, in this scheme, the 2CXM DCE model was used. Here various models for DCE analysis are tested keeping in mind the DCE-DSC combination. The ATH model was found to perform better in this setting compared to 2CXM. Finally, the ATH model was used in alternating DCE-DSC optimization algorithm and then in a truly fully simultaneous DCE-DSC. The processing was tested using simulated and in-vivo data. According to the results, the proposed simultaneous algorithm performs better in comparison with sequential DCE-DSC, unleashing full potential of perfusion analysis using MRI.

Time-domain NMR, in one and higher dimensionalities, makes routine use of inversion algorithms to generate results called \T2-distributions' or joint distributions in two (or higher) dimensions of other NMR parameters, T1, diffusivity D, pore size a, etc. These are frequently referred to as \Inverse Laplace Transforms' although the standard inversion of the Laplace Transform long-established in many textbooks of mathematical physics does not perform (and cannot perform) the calculation of such distributions. The operations performed in the estimation of a \T2-distribution' are the estimation of solutions to a Fredholm Integral Equation (of the First Kind), a different and more general object whose discretization results in a standard problem in linear algebra, albeit suffering from well-known problems of ill-conditioning and computational limits for large problem sizes. The Fredholm Integral Equation is not restricted to exponential kernels; the same solution algorithms can be used with kernels of completely different form. On the other hand, (true) Inverse Laplace Transforms, treated analytically, can be of real utility in solving the diffusion problems highly relevant in the subject of NMR in porous media.

abstract: This dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information about the reciprocal of the spin-spin relaxation time function (R2*) and frequency offset function (w) in addition to the typical steady-state transverse magnetization (M) from single-shot magnetic resonance imaging (MRI) scans. Sparse regularization on an approximation to the edge map is used to solve the associated inverse problem. Several studies are carried out for both one- and two-dimensional test problems, including comparisons to the first order approximation method, as well as the first order approximation method with joint sparsity across multiple time windows enforced. The second order accurate model provides increased accuracy while reducing the amount of data required to reconstruct an image when compared to piecewise constant in time models. A key component of the proposed technique is the use of fast transforms for the forward evaluation. It is determined that the second order model is capable of providing accurate single-shot MRI reconstructions, but requires an adequate coverage of k-space to do so. Alternative data sampling schemes are investigated in an attempt to improve reconstruction with single-shot data, as current trajectories do not provide ideal k-space coverage for the proposed method. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019

Osteoarthritis is the most common type of arthritis, and is characterized by the loss of articular cartilage in a joint. This eventually leads to painful bone on bone interactions. Since the loss of cartilage is permanent, the main treatment for this disease is pain management until a full joint replacement is needed. To test new potential treatments a consistent way to measure cartilage thickness is needed. The current standard used in the knee to represent cartilage uses joint space width measured from x-rays. This measurement is highly variable, and does not directly show cartilage. Unlike x-rays, magnetic resonance imaging (MRI) can provide direct visualization of soft tissues in the body, like cartilage. One specific MRI method called balanced steady-state free precession (bSSFP) provides useful contrast between cartilage and its surrounding tissues. This allows easy delineation of the cartilage for volume and thickness measurements. Using bSSFP has unique challenges, but can provide quantitative MR tissue parameter information in addition to volume and thickness measurements.Although bSSFP provides useful contrast, it is highly sensitive to variations in the main magnetic field. This results in dark bands of signal null across an image referred to as banding artifacts. There are a few new methods for mitigating this artifact. An analysis of banding artifact reduction methods is presented in this dissertation. The new methods are shown to be better than traditional methods at reducing banding artifact. However, they do not provide as of high signal to noise ratio as traditional methods in most cases. This analysis is helpful in obtaining artifact free images for volume and thickness measurements.Image distortion can be created when there is a magnetic susceptibility mismatch between bordering substances being imaged, like in the sinuses where air and body tissues meet. A map of the main magnetic field variation can be used to fix this distortion in post processing. A novel method for obtaining a map of the main magnetic field variation is developed using bSSFP in this dissertation. In cases where bSSFP contrast is desirable this map can be obtained with no additional scan time.A new way to sift out MR tissue parameters: T2, T1, and M0 is presented in this dissertation using bSSFP. This method obtains biomarkers that can potentially show the presence of Osteoarthritis before cartilage degeneration begins at the same time as anatomical images. Adjunct scans do not need to be run to get these extra parameters saving scan time. Unlike many adjunct scans, it is also resolution matched to the anatomical images.

Profile monitoring is a well-known approach used in statistical process control where the quality of the product or process is characterized by a profile or a relationship between a response variable and one or more explanatory variables. Profile monitoring is conducted over two phases, labeled as Phase I and Phase II. In Phase I profile monitoring, regression methods are used to model each profile and to detect the possible presence of out-of-control profiles in the historical data set (HDS). The out-of-control profiles can be detected by using the statis-tic. However, previous methods of calculating the statistic are based on using all the data in the HDS including the data from the out-of-control process. Consequently, the ability of using this method can be distorted if the HDS contains data from the out-of-control process. This work provides a new profile monitoring methodology for Phase I analysis. The proposed method, referred to as the cluster-based profile monitoring method, incorporates a cluster analysis phase before calculating the statistic. Before introducing our proposed cluster-based method in profile monitoring, this cluster-based method is demonstrated to work efficiently in robust regression, referred to as cluster-based bounded influence regression or CBI. It will be demonstrated that the CBI method provides a robust, efficient and high breakdown regression parameter estimator. The CBI method first represents the data space via a special set of points, referred to as anchor points. Then a collection of single-point-added ordinary least squares regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster containing at least half the observations, with the remaining observations comprising one or more minor clusters. An initial regression estimator arises from the main cluster, with a group-additive DFFITS argument used to carefully activate the minor clusters through a bounded influence regression frame work. CBI achieves a 50% breakdown point, is regression equivariant, scale and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo results demonstrate the performance advantage of CBI over other popular robust regression procedures regarding coefficient stabil-ity, scale estimation and standard errors. The cluster-based method in Phase I profile monitoring first replaces the data from each sampled unit with an estimated profile, using some appropriate regression method. The estimated parameters for the parametric profiles are obtained from parametric models while the estimated parameters for the nonparametric profiles are obtained from the p-spline model. The cluster phase clusters the profiles based on their estimated parameters and this yields an initial main cluster which contains at least half the profiles. The initial estimated parameters for the population average (PA) profile are obtained by fitting a mixed model (parametric or nonparametric) to those profiles in the main cluster. Profiles that are not contained in the initial main cluster are iteratively added to the main cluster provided their statistics are "small" and the mixed model (parametric or nonparametric) is used to update the estimated parameters for the PA profile. Those profiles contained in the final main cluster are considered as resulting from the in-control process while those not included are considered as resulting from an out-of-control process. This cluster-based method has been applied to monitor both parametric and nonparametric profiles. A simulated example, a Monte Carlo study and an application to a real data set demonstrates the detail of the algorithm and the performance advantage of this proposed method over a non-cluster-based method is demonstrated with respect to more accurate estimates of the PA parameters and improved classification performance criteria. When the profiles can be represented by vectors, the profile monitoring process is equivalent to the detection of multivariate outliers. For this reason, we also compared our proposed method to a popular method used to identify outliers when dealing with a multivariate response. Our study demonstrated that when the out-of-control process corresponds to a sustained shift, the cluster-based method using the successive difference estimator is clearly the superior method, among those methods we considered, based on all performance criteria. In addition, the influence of accurate Phase I estimates on the performance of Phase II control charts is presented to show the further advantage of the proposed method. A simple example and Monte Carlo results show that more accurate estimates from Phase I would provide more efficient Phase II control charts. / Ph. D.