Virtual knot theory is an extension of classical knot theory based on a combinatorial presentation of crossing information. The appropriate extensions of braid groups and string link monoids have also been studied. While some previously known knot invariants can be evaluated for virtual objects, entirely new techniques can also be used, for example, the concept of index of a crossing, and its resulting (Gaussian) parity theory. In general, a parity is a rule which assigns 0 or 1 to each crossing in a knot or link diagram. Recently, they have also been defined for virtual braids. Here, novel parities for knots, braids, and string links are defined, some of their applications are explored, most notably, defining a new subgroup of the virtual braid groups. / Thesis / Master of Science (MSc)

Qweak will determine the weak charge of the proton, QpW, via an asymmetry measurement of parity-violating elastic electron-proton scattering at low four momentum transfer to a precision of 4%. QpW has firm Standard Model prediction and is related to the weak mixing angle, sin20W, a well-defined Standard Model parameter. Qweak will probe a subset of new physics to the TeV mass scale and test the Standard Model. The details of how this measurement was performed and the analysis of the 25% elastic dataset will be presented in this thesis. Also, an analysis of an auxiliary measurement of the parity-violating asymmetry in the N >> Δ transition is presented. It is used as a systematic inelastic background correction in the elastic analysis and to extract information about the hadronic parity violation through the low energy constant, dΔ. The elastic asymmetry at Q2 = 0:0252 ± 0:0007 GeV2 was measured to be Aep = -265 ± 40 ± 22 ± 68 ppb (stat., sys., and blinding). Extrapolated to Q2 = 0, the value of the proton's weak charge was measured to be QpW = 0:077 ± 0:019 (stat. and sys.) ±0:026 (blinding). This is within 1 o of the Standard Model prediction of QpW = 0:0705 ± 0:0008. The N >> Δ inelastic asymmetry at Q2 = 0:02078 ± 0:0005 GeV2 and W = 1205 MeV was measured to be Ainel = -3:03 ± 0:65 ± 0:73 ± 0:07 ppm (stat., sys., and blinding). This result constrains the low energy constant to be dΔ = 5:8 ± 22gπ, and, if the result of the G0 experiment is included, dΔ = 5:8 ± 17gπ. This result rules out suggested large values of dΔ motivated by radiative hyperon decays. The elastic measurement is the first direct measurement of the weak charge of the proton while the inelastic measurement is only the second measurement of the neutral current excitation of the Δ resonance. It is currently the best constraint for the low energy constant, dΔ. / Ph. D.

The Q_weak Experiment ran for two and a half years at the Thomas Jefferson National Accelerator Facility in pursuit of Q_w^p, the neutral weak analog to the electric charge of the proton. Qweak measured the parity-violating asymmetry in elastic electron-proton scattering at an extreme forward angle (Q² = 0.0249 (GeV/c)² ). From the data gathered via the 1.16 GeV 180 μA longitudinally polarized electron beam scattering off the unpolarized photons in the liquid hydrogen target, a value of Q_w^p (PVES) = 0.0719 ± 0.0045 was determined. The Standard Model has a definite prediction of Q_w^p (SM) = 0.0708 ± 0.0003, consistent with the value determined by Q_weak which sets a limit on possible new physics up to 7.5 TeV. The theory behind the main measurement of the Q_weak Experiment is described in this document, along with the apparatus that made the measurement possible. Understanding the kinematics of the apparatus was a vital component to Qweak 's final measurement. An in-depth explanation of the tracking system responsible for benchmarking the momentum transfer and scattering angle simulations is included. The unblinded analysis of Q_weak's final result is outlined, as are additional physics results related to the N→ ∆ transition. During April 2012, an opportunity was seized to take ancillary data on the inelastic N→ ∆ transition at a different beam energy(877 MeV) than the nominal Q_weak data. This data, combined with the inelastic data taken at nominal beam energy and a previous measurement, determined a constraint on d_∆ , a low energy constant related to hadronic parity violation, of (3.8 ± 14.7)g_π . It also resulted in a measurement of the beam-normal single-spin asymmetry of the N→ ∆ transition of 149 ± 3 (stat) ± 72 (syst) ppm. This document includes both the longitudinal and transverse analysis of the 877 MeV data. / Doctor of Philosophy / The Q_weak Experiment, run at the Thomas Jefferson National Accelerator Facility, measured the weak charge, the weak force analog of the electric charge of the electromagnetic force, of the proton. Unlike the well-know Large Hadron Collider, which operates on the energy-frontier and directly searches for new particles, Q_weak operates by precisely measuring the results of scattering electrons off of protons. This approach is referred to as the precision frontier and is used to test the Standard Model, which has a well-defined prediction for the weak charge of the proton. Deviations from the Standard Model would suggest that there was new physics beyond the Standard Model affecting the results. However, the Q_weak measured weak charge of the proton, Q_w^p (PVES) = 0.0719 ± 0.0045, is in good agreement with the Standard Model predicted value. This provides a new limit, 7.5 TeV, on possible new physics beyond the Standard Model. The theoretical background and apparatus of the Qweak experiment will be explained in this document. A vital component of the final result was understanding the path and energy of the electron as it passed through the apparatus. This was done via simulation but benchmarked by the tracking system. The tracking system will be explained in detail. The final analysis of the Q_weak measurement of the weak charge will also be explained. A secondary result discussed here focuses on data taken using the Q_weak apparatus but at a different beam energy than the nominal Q_weak data. For this data, the electron scatter inelastically off the proton. The lost kinetic energy of the electron causes the proton to be excited into the first resonance state, the ∆, which quickly decays away. This transition grants access to a low energy constant, d_∆, and a measurement linked to the spins of the electrons being polarized perpendicular to the direction of the beam, B_n. The extraction of these values is covered in detail.

Cancer research is evolving. Historically concerned with the mechanisms by which malignant cells circumvent cell death signaling and maintain unchecked proliferation, focus has shifted to the complex interactions between the tumor cell and the surrounding microenvironment. Ovarian cancer has one of the highest incidence-to-death ratios of all cancers, and is typically asymptomatic until the later stages, often resulting in metastasis prior to discovery. Naturally occurring phenotypes like lactation and child-bearing (parity) reduce ovarian cancer incidence, but the mechanisms are not understood. As the primary site for ovarian cancer metastasis, and a secondary lymphoid organ capable of mounting potent innate and adaptive immune responses, we believe the omental fat band (OFB) provides a unique opportunity to study complex interactions within the tumor microenvironment. Additionally, we hypothesize that once understood, leukocyte populations within the OFB could be modulated to disrupt the pro-tumorigenic cascade. Using fluorescence-activated cell sorting (FACS) and quantitative realtime PCR (qRT-PCR), we comparatively evaluated the changes in the compositional immune profile of the OFB as a result of parity and cancer. Parous mice were associated with a reduction in macrophages and neutrophils in the OFB, resulting in an inherent "protective state" that was refractory to metastatic cancer cell growth after intraperitoneal implantation. This indicates that the leukocyte populations within the   OFB play an important role in tumor development. Therefore we utilized the potent TH1-type immunomodulatory cytokine IL-12 in a membrane-bound form to circumvent reported side effects, such as hepatic and renal damage, cardiotoxicity and death. Targeted IL-12 delivery to the OFB resulted in delayed disease development, although not protection from subsequent challenge. This was also associated with a reduction tumor-associated macrophages (TAMs) and neutrophils (TANs) within the OFB. Kinetic studies demonstrated that these changes were induced by a significant reduction in neutrophil and macrophage chemoattractants early on in the pro-tumorigenic cascade (7 days post-implantation). This work demonstrates that the OFB is a functionally plastic tissue that can be harnessed and re-mobilized to display an anti-tumorigenic microenvironment. / Ph. D.

The current intellectual climate regarding economics seems to be at an agreement regarding the theory of uncovered interest parity and its unreliability within real life application. The purpose of this thesis is to test how the theory holds over periods with varying economic stability, both using a short- and long-horizon test in order to establish the usefulness of uncovered interest parity as a predictor for exchange rate movements. The short-horizon test will utilize the interbank offering rate, and the long-horizon test the yield to maturity of government 10-year benchmark bonds as the interest rate. The sample period is 2000 to 2018, covering the financial crisis of 2007. We will focus on three different time periods: pre-crisis, crisis and post-crisis. We will use ordinary least squares (OLS) regression and an extreme sampling. From the regressions we conclude that most of the time periods move against the uncovered interest parity, where only the crisis period is in line with the theory. The extreme sampling supports this result, as larger interest differentials provide the rational expectations with more predictive power of the future spot exchange rate.

Due to globalization investors have increasing opportunities to invest on international markets for diversification purposes. This thesis illustrates the added risks of investing internationally due to volatile exchange rates. The purpose is to analyze how a volatile exchange rate affect the risk and return of a portfolio invested in Sweden, when the investor is located in Japan, United Kingdom or the USA. To analyze the effect of exchange rate volatility the focus is on a portfolio consisting of Swedish stocks from the Stockholm Stock Exchange (SSE) O-list. First the risk and return to a hypothetical Swedish investor not exposed to exchange rate volatility is calculated. Then the effects the exchange rates had on the risk and return if a US investor, UK investor and a Japanese investor invested in the same portfolio is analyzed. For the historical period 2005 the portfolio generated a return of 34.36% and a risk of 7.7%. The empirical work showed that for the international investors the risk was increased with between 1.95% – 410.52% and that the actual return decreased due to weakening currencies against the Krona. In an attempt to predict future exchange rate movements the thesis analyses two financial relationships, PPP and IRP, to calculate equilibrium movements. Both PPP and IRP predicted a depreciation of the Dollar and Pound Sterling against the Krona over the next period, but an appreciation of the Yen against the Krona over the same period. The analytical discussion covers the importance of a well functioning financial system, the institutional effects on exchange rates and the confidence in government policies and their ability to succeed in doing what has been promised.

After two world wars, the West European Economy goes through serious recession. Through the cold war, the representatives of west European countries, German and France, feel that they must cooperate. Hence, by the bases of economic co-operations, the West Europe starts to integrate their resources and political alliances. From the ¡§Economic Community (EC)¡¨ to ¡§Economic and Monetary Union (EMU)¡¨, most West European countries go through several obstacles, like the Collapse of Bretton Woods System in 1971 and the European Crisis in 1992,¡K¡K, etc. Finally, in 1th, Jan., 1999, 11 countries of European Union establish EMU and expect to take Euro as their single currency formally in 2002. They also establish European Central Bank (ECB) to execute the Euro zone¡¦s single monetary policy. The status of Euro after 1th Jan., 1999 is the purpose of this study. This article tries to use the Exchange Rate decision theories, Purchasing Power Parity (PPP) and Interest Rate parity (IRP), to investigate the relationship between Euro and USD. From several statistical empirical tests, it reveals that the trends of Euro couldn¡¦t correspond with the theoretical wants, ie PPP and IRP can¡¦t catch the trends of Euro. By the outcome of ¡§Sign Test¡¨ and ¡§Wilcoxon Sign-Rank Test¡¨, it can be found obviously that the Euro indeed is undervalued from the establishment to Apr., 2000 if we don¡¦t take the transaction costs into account. As a result of the outcome of empirical finds, the article starts to investigate the reasons why the theoretical values from exchange rate decision theories are not equal with real ones. One is that if the empirical models ignore some important factors which lead to the biases of models¡Fthe other is if Euro is undervalued during this observation periods. From the economic macro-environmental analyses, the article can infer that because of the Kosov Wars, Russian economic reform problems, the increase of short interest rate gap between USD and Euro, the different economic reform paces among member countries of EMU,¡K¡K, etc. result in the main factors of the weak currency - Euro.

<p>Due to globalization investors have increasing opportunities to invest on international markets for diversification purposes. This thesis illustrates the added risks of investing internationally due to volatile exchange rates. The purpose is to analyze how a volatile</p><p>exchange rate affect the risk and return of a portfolio invested in Sweden, when the investor is located in Japan, United Kingdom or the USA.</p><p>To analyze the effect of exchange rate volatility the focus is on a portfolio consisting of Swedish stocks from the Stockholm Stock Exchange (SSE) O-list. First the risk and return to a hypothetical Swedish investor not exposed to exchange rate volatility is calculated.</p><p>Then the effects the exchange rates had on the risk and return if a US investor, UK investor and a Japanese investor invested in the same portfolio is analyzed. For the historical period 2005 the portfolio generated a return of 34.36% and a risk of 7.7%. The empirical work showed that for the international investors the risk was increased</p><p>with between 1.95% – 410.52% and that the actual return decreased due to weakening currencies against the Krona.</p><p>In an attempt to predict future exchange rate movements the thesis analyses two financial relationships, PPP and IRP, to calculate equilibrium movements. Both PPP and IRP predicted a depreciation of the Dollar and Pound Sterling against the Krona over the next</p><p>period, but an appreciation of the Yen against the Krona over the same period.</p><p>The analytical discussion covers the importance of a well functioning financial system, the institutional effects on exchange rates and the confidence in government policies and their ability to succeed in doing what has been promised.</p>

This study analyzes validity of the relative purchasing power parity (PPP) and the uncovered interest rate parity (IRP) theories for the dollar/euro exchange rate. The period of analysis is from 1990 to 2003. The dollar/euro exchange rate represents the currencies of a country, the USA, and a region, the Euro Area. The basic data needed for this study are the dollar/euro exchange rate, and the inflation and the interest rates for the USA and the Euro Area. Since the Euro Area was officially formed on January 1st, 1999, we had difficulty in finding the data for the Euro Area. For the lacking Euro Area data, synthetic values are created by using the individual data of Euro Area countries. These synthetic values are treated as the equivalents of the actual values and are used in the parity implied dollar/euro exchange rate calculations. The parity implied dollar/euro exchange rates are compared with the actual dollar/euro exchange rates. Our results indicate that the parity implied dollar/euro exchange rates are statistically significantly different from the actual dollar/euro exchange rates. In other words, both the PPP and the IRP theories do not hold for the dollar/euro exchange rate.

The enactment of the Mental Health Parity and Addiction Equity Act (MHPAEA) in 2008 sought to eliminate longstanding discriminatory insurance practices against behavioral health disorders by requiring health insurers of large group plans to apply no more restrictive financial requirements and treatment limitations to mental health and substance use disorder benefits relative to those applied to medical/surgical benefits. Since the parity act went into effect in 2010, the prevalence of mental health conditions has continued to rise while the proportion of those seeking mental health services has remained stagnant. As a result, an increasing trend in the percentage of Americans with a perceived unmet need for behavioral health services has been observed over the past decade. Many of those with an unmet need for services cite an inability to afford the cost of care, no insurance/underinsurance, and/or lack of available behavioral health clinicians as some of the primary reasons for not obtaining wanted care. This suggests a disconnect exists between the policy and practice of parity that warrants further investigation. Understanding the history of behavioral health coverage and parity in the United States and the current structure of America’s health insurance system provides context for why healthcare reform legislations, like the MHPAEA, are necessary. Furthermore, dissecting the provisions and limitations of the MHPAEA and the Affordable Care Act’s impact on behavioral health parity exposes barriers that perpetuate the disconnect between policy and practice. The various barriers that continue to limit access to behavioral health care despite the MHPAEA will be evaluated to better understand why they exist and how they facilitate a persistent unmet need. Mental health in America is a critical medical and public health concern as the prevalence of poor mental health has continued to grow, especially amidst the COVID-19 pandemic. The shortcomings of current legislation and the mental health care delivery system need to be addressed to develop future legislation that can be better equipped to deliver true parity in practice.