Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Warped extra dimensions: flavor, precision tests and Higgs physics

In this thesis, the phenomenology of the Randall-Sundrum setup is investigated. In this context models with and without an enlarged SU(2)_L x SU(2)_R x U(1)_X x P_{LR} gauge symmetry, which removes corrections to the T parameter and to the Z b_L \bar b_L coupling, are compared with each other. The Kaluza-Klein decomposition is formulated within the mass basis, which allows for a clear understanding of various model-specific features. A complete discussion of tree-level flavor-changing effects is presented. Exact expressions for five dimensional propagators are derived, including Yukawa interactions that mediate flavor-off-diagonal transitions. The symmetry that reduces the corrections to the left-handed Z b \bar b coupling is analyzed in detail. In the literature, Randall-Sundrum models have been used to address the measured anomaly in the t \bar t forward-backward asymmetry. However, it will be shown that this is not possible within a natural approach to flavor. The rare decays t \to cZ and t \to ch are investigated, where in particular the latter could be observed at the LHC. A calculation of \Gamma_{12}^{B_s} in the presence of new physics is presented. It is shown that the Randall-Sundrum setup allows for an improved agreement with measurements of A_{SL}^s, S_{\psi\phi}, and \Delta\Gamma_s. For the first time, a complete one-loop calculation of all relevant Higgs-boson production and decay channels in the custodial Randall-Sundrum setup is performed, revealing a sensitivity to large new-physics scales at the LHC.

Use of modern and traditional products to self-treat symptoms of sexually transmitted infections in South African women

The objective of the study is to investigate products used by women self-treating symptoms of reproductive tract infections (RTIs), including sexually transmitted infections (STIs), and their methods of administration. A household survey using a multi-stage cluster sample design was undertaken in KwaZulu-Natal, South Africa. Women aged 18-60 years were interviewed (n = 867) and information was collected on demographics, reproductive health and sexual behaviours. A fifth of women reported having RTI/STI symptoms (20.5%), of whom 41.9% were treating these symptoms (mostly discharge [79.1%], ulcers [6.8%] and itching [7.7%]). Only three women were using medication prescribed by a health provider, while the remainder were self-treating using traditional medicines and modern products, including antiseptics, soaps, petroleum jelly, menthol creams and alum. Products were administered in various ways. Although RTI/STI treatment is widely available and free in public health facilities, many women are still self-treating. Potential harm of products for self-treatment requires further investigation and efforts should be made to improve STI service uptake.

Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

Transnationalism and Identity: the Concept of Community in Ghanaian Literature and Contemporary Ghanaian Culture

In my thesis, I use anthropology, literature, and adinkra, an indigenous art, to study Ghanaian concepts of community from an interactive standpoint. While each of these disciplines has individually been used to study the concept of community, the three have not previously been discussed in relation to one another. I explore the major findings of each field—mainly that in anthropology, transnational informants find communities upheld; in literature, transnational characters find the opposite; and in adinkra, there are elements of both continuity and dissolution—to discuss Ghanaian constructs of community in the transnational world. Throughout time, there have always been transnational individuals and concepts, but as globalization continues, transnationalism has become an ever-more vital topic, and combined with the common anthropological discussion of tradition and modernity, its influence on developing countries, like Ghana, is significant. Therefore, in my thesis, I explore how differing conceptions of community present themselves in each discipline, and how those divergences create a new understanding of place and identity.

Over two decades of blended and online physics courses at Michigan State University

In Fall 1992, our first physics course offered online homework. Over two decades later, we have seven physics courses online, spanning the whole range of introductory course offerings, with a total of over 1600 students in 2014. We found that several of the the purely online courses had better learning success than traditional lecture courses, as measured by exam scores. Particularly successful were online materials with embedded assessment. This result can be interpreted in different ways, but may serve as an indicator that during in-class lectures, we are oftentimes not taking advantage of the fact that we have the students on-site.

Comparison of iron isotope variations in modern and Ordovician siliceous Fe oxyhydroxide deposits

Formation pathways of ancient siliceous iron formations and related Fe isotopic fractionation are still not completely understood. Investigating these processes, however, is difficult as good modern analogues to ancient iron formations are scarce. Modern siliceous Fe oxyhydroxide deposits are found at marine hydrothermal vent sites, where they precipitate from diffuse, low temperature fluids along faults and fissures on the seafloor. These deposits exhibit textural and chemical features that are similar to some Phanerozoic iron formations, raising the question as to whether the latter could have precipitated from diffuse hydrothermal fluids rather than from hydrothermal plumes. In this study, we present the first data on modern Fe oxyhydroxide deposits from the Jan Mayen hydrothermal vent fields, Norwegian-Greenland Sea. The samples we investigated exhibited very low δ56Fe values between -2.09‰ and -0.66‰. Due to various degrees of partial oxidation, the Fe oxyhydroxides are with one exception either indistinguishable from low-temperature hydrothermal fluids from which they precipitated (-1.84‰ and -1.53‰ in δ56Fe) or are enriched in the heavy Fe isotopes. In addition, we investigated Fe isotope variations in Ordovician jasper beds from the Løkken ophiolite complex, Norway, which have been interpreted to represent diagenetic products of siliceous ferrihydrite precursors that precipitated in a hydrothermal plume, in order to compare different formation pathways of Fe oxyhydroxide deposits. Iron isotopes in the jasper samples have higher δ56Fe values (-0.38‰ to +0.89‰) relative to modern, high-temperature hydrothermal vent fluids (ca. -0.40‰ on average), supporting the fallout model. However, formation of the Ordovician jaspers by diffuse venting cannot be excluded, due to lithological differences of the subsurface of the two investigated vent systems. Our study shows that reliable interpretation of Fe isotope variations in modern and ancient marine Fe oxyhydroxide deposits depends on comprehensive knowledge of the geological context. Furthermore, we demonstrate that very negative δ56Fe values in such samples might not be the result of microbial dissimilatory iron reduction, but could be caused instead by inorganic reactions.

Stable Isotope and Trace Element Studies on Gladiators and Contemporary Romans from Ephesus (Turkey, 2nd and 3rd Ct. AD) - Implications for Differences in Diet

The gladiator cemetery discovered in Ephesus (Turkey) in 1993 dates to the 2nd and 3rd century AD. The aim of this study is to reconstruct diverse diet, social stratification, and migration of the inhabitants of Roman Ephesus and the distinct group of gladiators. Stable carbon, nitrogen, and sulphur isotope analysis were applied, and inorganic bone elements (strontium, calcium) were determined. In total, 53 individuals, including 22 gladiators, were analysed. All individuals consumed C3 plants like wheat and barley as staple food. A few individuals show indication of consumption of C4 plants. The δ13C values of one female from the gladiator cemetery and one gladiator differ from all other individuals. Their δ34S values indicate that they probably migrated from another geographical region or consumed different foods. The δ15N values are relatively low in comparison to other sites from Roman times. A probable cause for the depletion of 15N in Ephesus could be the frequent consumption of legumes. The Sr/Ca-ratios of the gladiators were significantly higher than the values of the contemporary Roman inhabitants. Since the Sr/Ca-ratio reflects the main Ca-supplier in the diet, the elevated values of the gladiators might suggest a frequent use of a plant ash beverage, as mentioned in ancient texts.

IMRT credentialing for prospective trials using institutional virtual phantoms: results of a joint European Organization for the Research and Treatment of Cancer and Radiological Physics Center project.

BACKGROUND AND PURPOSE Intensity-modulated radiotherapy (IMRT) credentialing for a EORTC study was performed using an anthropomorphic head phantom from the Radiological Physics Center (RPC; RPC(PH)). Institutions were retrospectively requested to irradiate their institutional phantom (INST(PH)) using the same treatment plan in the framework of a Virtual Phantom Project (VPP) for IMRT credentialing. MATERIALS AND METHODS CT data set of the institutional phantom and measured 2D dose matrices were requested from centers and sent to a dedicated secure EORTC uploader. Data from the RPC(PH) and INST(PH) were thereafter centrally analyzed and inter-compared by the QA team using commercially available software (RIT; ver.5.2; Colorado Springs, USA). RESULTS Eighteen institutions participated to the VPP. The measurements of 6 (33%) institutions could not be analyzed centrally. All other centers passed both the VPP and the RPC ±7%/4 mm credentialing criteria. At the 5%/5 mm gamma criteria (90% of pixels passing), 11(92%) as compared to 12 (100%) centers pass the credentialing process with RPC(PH) and INST(PH) (p = 0.29), respectively. The corresponding pass rate for the 3%/3 mm gamma criteria (90% of pixels passing) was 2 (17%) and 9 (75%; p = 0.01), respectively. CONCLUSIONS IMRT dosimetry gamma evaluations in a single plane for a H&N prospective trial using the INST(PH) measurements showed agreement at the gamma index criteria of ±5%/5 mm (90% of pixels passing) for a small number of VPP measurements. Using more stringent, criteria, the RPC(PH) and INST(PH) comparison showed disagreement. More data is warranted and urgently required within the framework of prospective studies.