Indiana University-Purdue University Indianapolis (IUPUI) / More than a decade ago, it was shown that non-Hermitian Hamiltonians with combined parity (P) and time-reversal (T ) symmetry exhibit real eigenvalues over a range of parameters. Since then, the field of PT symmetry has seen rapid progress on both the theoretical and experimental fronts. These effective Hamiltonians are excellent candidates for describing open quantum systems with balanced gain and loss. Nature seems to be replete with examples of PT -symmetric systems; in fact, recent experimental investigations have observed the effects of PT symmetry breaking in systems as diverse as coupled mechanical pendula, coupled optical waveguides, and coupled electrical circuits. Recently, PT -symmetric Hamiltonians for tight-binding lattice models have been extensively investigated. Lattice models, in general, have been widely used in physics due to their analytical and numerical tractability. Perhaps one of the best systems for experimentally observing the effects of PT symmetry breaking in a one-dimensional lattice with tunable hopping is an array of evanescently-coupled optical waveguides. The tunneling between adjacent waveguides is tuned by adjusting the width of the barrier between them, and the imaginary part of the local refractive index provides the loss or gain in the respective waveguide. Calculating the time evolution of a wave packet on a lattice is relatively straightforward in the tight-binding model, allowing us to make predictions about the behavior of light propagating down an array of PT -symmetric waveguides. In this thesis, I investigate the the strength of the PT -symmetric phase (the region over which the eigenvalues are purely real) in lattices with a variety of PT - symmetric potentials. In Chapter 1, I begin with a brief review of the postulates of quantum mechanics, followed by an outline of the fundamental principles of PT - symmetric systems. Chapter 2 focuses on one-dimensional uniform lattices with a pair of PT -symmetric impurities in the case of open boundary conditions. I find that the PT phase is algebraically fragile except in the case of closest impurities, where the PT phase remains nonzero. In Chapter 3, I examine the case of periodic boundary conditions in uniform lattices, finding that the PT phase is not only nonzero, but also independent of the impurity spacing on the lattice. In addition, I explore the time evolution of a single-particle wave packet initially localized at a site. I find that in the case of periodic boundary conditions, the wave packet undergoes a preferential clockwise or counterclockwise motion around the ring. This behavior is quantified by a discrete momentum operator which assumes a maximum value at the PT -symmetry- breaking threshold. In Chapter 4, I investigate nonuniform lattices where the parity-symmetric hop- ping between neighboring sites can be tuned. I find that the PT phase remains strong in the case of closest impurities and fragile elsewhere. Chapter 5 explores the effects of the competition between localized and extended PT potentials on a lattice. I show that when the short-range impurities are maximally separated on the lattice, the PT phase is strengthened by adding short-range loss in the broad-loss region. Consequently, I predict that a broken PT symmetry can be restored by increasing the strength of the short-range impurities. Lastly, Chapter 6 summarizes my salient results and discusses areas which can be further developed in future research.

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For the last ten years, DVD-R media have played an important role in the storage of large amounts of digital data throughout the world. During this time it was assumed that the DVD-R was as long-lasting and stable as its predecessor, the CD-R. Several reports have surfaced over the last few years questioning the DVD-R's ability to maintain many of its claims regarding archival quality life spans. These reports have shown a wide range of longevity between the different brands. While some DVD-Rs may last a while, others may result in an early and unexpected failure. Compounding this problem is the lack of information available for consumers to know the quality of the media they own. While the industry works on devising a standard for labeling the quality of future media, it is currently up to the consumer to pay close attention to their own DVD-R archives and work diligently to prevent data loss. This research shows that through accelerated aging and the use of logistic regression analysis on data collected through periodic monitoring of disc read-back errors it is possible to accurately predict unrecoverable failures in the test discs. This study analyzed various measurements of PIE errors, PIE8 Sum errors, POF errors and jitter data from three areas of the disc: the whole disc, the region of the disc where it first failed as well as the last half of the disc. From this data five unique predictive equations were produced, each with the ability to predict disc failure. In conclusion, the relative value of these equations for end-of-life predictions is discussed.

[pt] Desvios de Paridade Coberta da Taxa de Juros (CIP) têm sido amplos e persistentes, entre economias do G10, desde a crise financeira mundial de 2008. Uma das explicações para a quebra na relação de paridade (CIP) são as novas regulações bancárias que surgiram no período pós-crise. Por outro lado, desvios de CIP na economia brasileira têm sido associados ao índice EMBI+, que é uma medida de risco país, tal como em Garcia and Didier (2003). A partir da literatura recente sobre desvios de CIP (i.e., a currency basis) entre as economias do G10, eu mostro a evolução recente da cross-currency basis para essas economias, durante a pandemia de 2020, e então eu estudo os determinantes macroeconômicos e regulatórios da basis do Real. Usando a estratégia empírica de Cerutti et al (2021), eu encontro que o bid-ask spread (medida de liquidez) do dólar futuro tem um efeito proeminente. Em uma abordagem de diferença-em-diferenças, eu encontro que a basis brasileira sobe aos finais de trimestres, coincidindo com o período em que os contratos futuros aparecem no balanço patrimonial dos bancos. Tal evidência sugere um efeito causal de regulação bancária na currency basis, em linha com Du, Tepper and Verdelhan (2018). / [en] Covered Interest Parity deviations (CIP) have been large and persistent among G10 currencies since the global financial crisis in 2008. One of the explanations for the CIP condition breakdown are the new banking regulations that arose in the post-crisis period. On the other hand, CIP deviations for the Brazilian economy have been associated with the EMBI+ index, which is a measure of country risk, as in Garcia and Didier (2003). Building on the recent literature on Covered Interest Parity deviations (i.e, the currency basis) among G10 currencies, I show the recent evolution of the cross-currency basis for the G10 economies, during the 2020 pandemic crisis, and then I study the macroeconomic and regulatory drivers of the Brazilian currency basis. Using the regression approach of Cerutti et al (2021), I find that the FX bid-ask spread has a prominent effect on the real/dollar basis. Using a difference-in-differences approach, I find that the Brazilian currency basis rises at quarter-ends, which is the period when forward contracts appear on banks balance sheets. This points to a causal effect of banking regulation on the currency basis, in line with Du, Tepper and Verdelhan (2018).

Under de senaste 14 åren har den svenska kronan genomgått en period av depreciering mot många andra valutor. Detta väcker frågan om vad som ligger till grund för växelkursens rörelser. Denna studie ämnar därför undersöka om det öppna ränteparitetsvillkoret kan förklara relationen mellan förändringar i växelkurser och räntedifferenser på kort sikt. För att undersöka frågan har två regressionsmodeller konstruerats med räntedifferenser som förklarande variabel och fluktuationer i växelkursen som beroende variabel. Studien begränsas till att undersöka förhållandet mellan Sverige som inhemskt land och Euroområdet samt USA som utländska områden/länder. Eftersom euron och den amerikanska dollarn kategoriseras som “safe haven” valutor inkluderas safe haven teorin som en sekundär aspekt i analysen. Studien använder månadsvis data över perioden 1999-2022. Regressionsmodellernas resultat visar en korrelation som är något avvikande från det öppna ränteparitetsvillkoret. Regressionsmodellerna presenterar icke-signifikanta resultat och studiens slutsats är därmed att undersökningen inte presenterar tillräckligt med bevis för att säkerställa att den sanna relationen mellan räntedifferenser och förändringar i växelkursen skiljer sig signifikant från ränteparitetsvillkoret. / Over the past fourteen years the Swedish krona has undergone a period of depreciation against many other currencies. This raises the question of what factors drive the movements of the exchange rate. This study intends to examine if the open interest parity condition can explain the relationship between fluctuations in the exchange rate and the interest rate differentials in the short term. To examine the subject two regression models have been constructed with the interest rate differentials as the explanatory variable and fluctuations in the exchange rate as the dependent variable. The research is narrowed down to examine the relationship between Sweden as the domestic country and the euro area and USA as foreign areas/countries. As the euro and the american dollar are categorized as “safe haven” currencies the safe haven theory is also included as a secondary aspect of the analysis. The study utilizes monthly data over the period 1999-2022. The results of the regression models show a correlation that deviates somewhat from the open interest parity condition. The regression models present non-significant results and the study's conclusion is thus that the study does not present enough evidence to ensure that the true relationship between interest rate differentials and changes in the exchange rate differs significantly from the interest parity condition.

Following the global financial crisis, both risk-based and heuristic portfolio construction methods have received much attention from both academics and practitioners since these methods do not rely on the estimation of expected returns and as such are assumed to be more stable than Markowitz's traditional mean-variance portfolio. In 2016, Lopéz de Prado presented the Hierarchical Risk Parity (HRP), a new approach to portfolio construction which combines hierarchical clustering of assets with a heuristic risk-based allocation strategy in order to increase stability and improve out-of-sample performance. Using Monte Carlo simulations, Lopéz de Prado was able to demonstrate promising results. This thesis attempts to evaluate HRP using walk-forward analysis and historical data from equity index and bond futures, against more realistic benchmark methods and using additional performance measures relevant to practitioners. The main conclusion is that applying hierarchical clustering to risk-based portfolio construction does indeed improve the out-of-sample return and Sharpe ratio. However, the resulting portfolio is also associated with a remarkably high turnover, which may indicate numerical instability and sensitivity to estimation errors. It is also identified that Lopéz de Prado's original HRP approach has an undesirable property and alternative approaches to HRP have consequently been developed. Compared to Lopéz de Prado's original HRP approach, these alternative approaches increase the Sharpe ratio with ~10% and reduce the turnover with 60-65%. However, it should be noted that compared to more mainstream portfolios the turnover is still rather high, indicating that these alternative approaches to HRP are still somewhat unstable and sensitive to estimation errors. / Efter den globala finanskrisen har intresset för riskbaserade och heuristiska metoder för portföljallokering ökat inom såväl akademin som finansindustrin. Det ökade intresset grundar sig i att dessa metoder inte kräver estimering av förväntad avkastning och därför kan antas vara mer stabila än portföljer med grund i Markowitz moderna portföljteori. Lopéz de Prado presenterade 2016 en ny metod för portföljallokering, Hierarchical Risk Parity (HRP), som kombinerar hierarkisk klustring med en heuristisk riskbaserad portföljkonstruktion och vars syfte är att öka stabiliteten och förbättra avkastningen. Baserat på Monte Carlo-simuleringar har Lopéz de Prado lyckats påvisa lovande resultat. Syftet med detta examensarbete är att utvärdera HRP med hjälp av walk-forward-analys och empirisk data från aktieindex- och obligationsterminer. I denna utvärdering jämförs HRP med andra vanliga portföljmetoder med avseende på prestandamått relevanta för portföljförvaltare. Den huvudsakliga slutsatsen är att tillämpning av hierarkisk klustring inom ramen för riskbaserad portföljallokering förbättrar såväl den absoluta avkastningen som Sharpekvoten. Däremot är det tydligt att vikterna i en HRP-portfölj har hög omsättning över tid, vilket kan tyda på numerisk instabilitet och hög känslighet för skattningsfel. Vidare har en oönskad egenskap i Lopéz de Prados ursprungliga HRP-metod identifierats, varför två alternativa HRP-metoder har utvecklats inom ramen för examensarbetet. Jämfört med Lopéz de Prados ursprungliga metod förbättrar de två alternativa metoderna Sharpekvoten med 10% och minskar omsättningen av portföljvikterna med 60-65%. Det bör dock understrykas att även de nya metoderna har en förhållandevis hög omsättning, vilket tyder på att numerisk instabilitet och hög känslighet för skattningsfel till viss del fortfarande kvarstår.

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Low-Density Parity-Check (LDPC) codes are linear error-correcting codes used to establish reliable communication between units on a noisy transmission channel in mobile telecommunications. LDPC algorithms detect and recover altered or corrupted message bits using sparse parity-check matrices in order to decipher messages correctly. LDPC codes have been shown to be fitting coding schemes for the fifth generation (5G) New Radio (NR), according to the third generation partnership project (3GPP).  TietoEvry, a consultant in telecom, has discovered that optimizations of LDPC decoding algorithms can be achieved/obtained with the use of a parallel computing platform called Compute Unified Device Architecture (CUDA), developed by NVIDIA. This platform utilizes the capabilities of a graphics processing unit (GPU) rather than a central processing unit (CPU), which in turn provides parallel computing. An optimized version of an LDPC decoding algorithm, the Min-Sum Algorithm (MSA), is implemented in CUDA and in C++ for comparison in terms of CPU execution time, to explore the capabilities that CUDA offers. The testing is done with a set of 12 sparse parity-check matrices and input-channel messages with different sizes. As a result, the CUDA implementation executes approximately 55% faster than a standard, unoptimized C++ implementation.

[pt] A presente tese de pesquisa doutoral estará alicerçada no conceito tridimensional de justiça desenvolvido pela filósofa contemporânea da teoria crítica - Nancy Fraser. O objetivo é investigar os impactos que o Programa Bolsa Família - PBF - gerou na diminuição das desigualdades sociais na vida das famílias beneficiárias quanto aos aspectos da redistribuição, do reconhecimento e da participação paritária. Realizamos análise bibliográfica das pesquisas feitas sobre o Programa Bolsa Família do ano de 2003 a 2014. O percurso teórico desta tese buscou o aprofundamento dos conceitos de pobreza e de exclusão social, a análise do processo de desenvolvimento brasileiro e das políticas públicas para o enfrentamento das desigualdades sociais nas décadas de 60 a 90, focalizando também a experiência da transição democrática pós-Constituição Federal de 1988. Levamos em consideração os princípios constitucionais de 1988 e os tratados internacionais que respaldam a responsabilidade do Estado e da sociedade brasileira para a implantação de políticas sociais como o Programa Bolsa Família. Concluímos que o PBF produziu resultados importantes na vida dos beneficiários, garantindo a justiça redistributiva e de reconhecimento e potencializando essas pessoas para a paridade participativa como sujeitos integrais na sociedade. Reconhecemos o avanço do desenho institucional da política social brasileira, proporcionado pelo PBF, inaugurando assim um novo modelo de proteção social, capaz de identificar a vulnerabilidade social das famílias brasileiras em situação de pobreza e de articular a redistribuição de renda e o reconhecimento, por meio do Sistema Único da Assistência Social - Suas. / [en] This doctoral research thesis is founded on the three-dimensional concept of justice developed by contemporary philosopher of critical theory Nancy Fraser. The objective is to investigate the impact that the Bolsa Família Program (PBF) generated in the reduction of social inequalities in the lives of beneficiary families considering aspects of redistribution, recognition and equal participation. An literature review of research was conducted on the Bolsa Família Program from 2003 to 2014. The theoretical path of this thesis aimed the investigation of the concepts of poverty and social exclusion, the analysis of the Brazilian development process and the public policies for dealing with social inequalities from the 60 s to the 90 s also focusing on the democratic transition experience post-constitution of 1988. We took into account the constitutional principles of 1988 and international treaties that support the responsibility of the Brazilian State and society to the implementation of social policies such as the Bolsa Família Program. We concluded that the PBF produced important results in the lives of the beneficiaries, ensuring redistributive and recognition justice, empowering those people to participatory parity as integral individuals in society. We recognize the progress of the institutional design of the Brazilian social policy, provided by the PBF, starting a new model of social protection, able to identify the social vulnerability of the Brazilian families in state of poverty and to articulate the redistribution of income and the recognition by the Single Social Assistance System - Suas.