VictorJuiz/thesis huggingface dataset:
Quantum groups and the Yang-Baxter equation [electronic resource]

In this thesis we will present a series of reconstruction results for Hopf algebras due to Saavedra-Rivano, Majid and Ulbrich. We will then apply them to solutions of the non-parametrized Yang-Baxter equation and recover the FRT construction, due to Faddeev, Reshetikhin and Takhtajan. The novel part is the application of the reconstruction theorem to a parametrized solution of the Yang-Baxter equation to develop a parametrized FRT construction. We apply this construction to the parametrized solution of the Yang-Baxter equation corresponding to the quantum group $U_q(\widehat{\mathfrak{sl}_2})$ and to another solution with parameter group $GL(2, \mathbb{C}) \times GL(1, \mathbb{C})$ that doesn't come from any known quantum group and build two new quantum groups. We study the representation theory of the newly built objects.

Keywords: Mathematics.
Advisor: Bump Daniel
Venkatesh Akshay
Yun Zhiwei
Quantum metrology using large ensembles of entangled atoms [electronic resource]

Atomic sensors are pushing the boundaries in precision for timekeeping, magnetometry, and gravity gradiometry. Conventional atomic sensors are ultimately limited by the quantum projection noise. In this thesis, the quantum projection noise limit on sensing precision is circumvented by exploiting entanglement—quantum correlations between the atoms. Entangled states enabling 100-fold measurement precision enhancement were generated using cavity-based measurements. Additionally, a new method was developed which allows entanglement-enhanced metrology without detection noise beyond the quantum projection noise limit.

Keywords: Physics.
Advisor: Kasevich Mark A. primary advisor. Thesis advisor
Hollberg Leo (Leo William)
Schleier-Smith Monika advisor. Thesis advisor
Quasi-Monte Carlo methods in non-cubical spaces [electronic resource]

Monte Carlo integration is a widely used technique for approximating high dimensional integrals. However, due to the inherent randomness of this method, the convergence is typically slow. Quasi-Monte Carlo (QMC) on the other hand gives a much better rate of convergence by using low-discrepancy sequences. These point sets are much more uniformly distributed than random samples. Most QMC research focuses on sampling from the unit cube. However, many problems in real-world applications are defined over much more general spaces, such as triangle, spheres, spherical triangles and discs. This dissertation deals with solving such problems of numerical integration defined over non-cubical domains. We introduce two QMC constructions in the triangle with a vanishing discrepancy. The first is a version of the van der Corput sequence customized to the unit triangle. The second construction rotates an integer lattice through an angle whose tangent is a quadratic irrational number. We then generalize the van der Corput construction to study the problem of numerical integration over the Cartesian products of s spaces of dimension d via scrambled geometric nets. We also show the asymptotic normality of the scrambled geometric net estimator. We further discuss some of the issues of why transformations of the unit cube to the domain of interest fails to give good results. Since products of simplices is throughout of special interest to us, we end the dissertation with few results of QMC tractability on that domain.

Keywords: Statistics.
Advisor: Owen Art B. primary advisor. Thesis advisor
Candès Emmanuel J. (Emmanuel Jean) advisor. Thesis advisor
Chatterjee Sourav advisor. Thesis advisor
The queen of heaven and a goddess for all the people [electronic resource] : kingship, religion, and cultural evolution between Greece and the Near East, 3000-500 BCE

This dissertation traces the evolution of the ideologies of divine kingship within the cultural groups of western Asia and the eastern Mediterranean across the Bronze and Iron Ages through textual and material sources concerning the worship of the Queen of Heaven. Using a range of case studies from the Bronze and Iron Ages to understand the shifting meanings of this deity and her relation to earthly kingship, I argue that the Iron Age Greeks, even as they experimented with novel egalitarian forms of rule, engaged with and transformed discourses of divine kingship through mythical and ritual practices that critiqued and reoriented human beings' relationships with the gods. The major aim of this study is to develop a comprehensive historical perspective on Greece and its cultural, social, and political relations with cultural groups to the east through the shared ritual language surrounding divine kingship. To this end, along with my case studies, I consider theories of cultural evolution of religion, and in particular religion's role in the cultural and cognitive shifts that heralded the axial age, to understand the trajectories and meanings of these shifting relationships, between Greece and the Near East, king and society, and humans and their gods.

Keywords: Classics.
Advisor: Morris Ian
López-Ruiz Carolina advisor. Thesis advisor
Martin Richard P. advisor. Thesis advisor
Ober Josiah advisor. Thesis advisor
Questioning terrorism [electronic resource] : Islam, religious violence, & secular law in America

Based on 18 months of fieldwork in New York City, this dissertation explores the ways in which secular law in the United States intervenes in defining, regulating, and containing Islam through terrorism cases. Through ethnographic data culled from seven domestic terrorism trials, fieldwork amongst three Muslim civil liberties organizations, and ethnographic interviews with the families and friends of terrorism defendants, this dissertation argues that what is at stake in terrorism prosecutions is not merely the elimination of violence, but also forms of Islamic thought and practice deemed to exceed the secular state's definition of legal or "permissible" religion. While social science research has primarily focused on the experience of everyday Muslims following 9/11, this dissertation focuses on what the social and legal life of terrorism cases - both inside and outside of courtrooms - reveals about the contradictions, contingencies and anxieties of the secular security state, and the place of Muslims in America today.

Keywords: Anthropology.
Advisor: Luhrmann T. M. (Tanya M.)
Hansen Thomas
Tambar Kabir advisor. Thesis advisor
Questions, answers, participants and interactions in open asynchronous online forums for learning English [electronic resource]

On community question-answering (QA) sites, anyone on the open Internet can post a question, give a response, or browse a discussion. The availability of interested individuals, including content experts, implies that personalized tutoring can be crowd-sourced at no financial cost to users. Importantly, these forums maintain banks of knowledge often ranked by Internet search engines, thereby exerting influence over a wide audience. In addition, in the context of second language learning, the asynchronous format of the forums allows learners to ask questions in a low-stress environment while they attend to both language form and meaning. The current study focused on online forums that aimed at providing answers to questions from learners of English as a second or foreign language. To examine the characteristics of the questions, the participant networks, the quality of the answers, and the characteristics of the verbal interactions in the knowledge transfer and construction processes, this project conducted case studies of two QA sites with distinct differences in history and design, especially in terms of their levels of gamification and their discussion structures, and compared a sample of similar threads on the two sites. The coding schemes for answer quality and verbal interactions were developed based on the literature on information quality, and that on online collaborative learning, respectively. The most prominent strength of the sites was found to be their timeliness in delivering responses. In most cases, original questioners received answers within 24 hours. Even though the majority of the top answers offered usable conclusions and fully accurate information, a notable minority could be misleading in the sense that they seemed to allow questioners to arrive at conclusions but provided only partially accurate information. Consequently, potential users are recommended to view the information from QA sites only as one of multiple sources of information, and to further extract value by taking note of the citations the answers include. The two sites were markedly different in terms of answerer composition, likely as a result of their distinct historical roots. The study also found differences in answer characteristics, particularly in terms of accuracy and the use of references. Some interactive moves of the participants, especially the frequencies of responses, disagreement and answer revisions, appeared to be associated with the composition of the communities, gamified incentives, discussion structures, or some combination of the above. Further research is needed to identify any causal relations involved in order to better inform the design of online communities.

Keywords: Education.
Advisor: Hakuta Kenji primary advisor. Thesis advisor
Padilla Amado M. primary advisor. Thesis advisor
Hubbard Phil advisor. Thesis advisor
Rabbinic textuality and the rise of Jewish literature in imperial Russia, 1867-1904 [electronic resource]

In "Rabbinic Textuality and the Rise of Jewish Literature in Imperial Russia, " I propose a new account of the development of Jewish literature in the Russian Empire, by analyzing the works and personal histories of seven central Jewish writers: A.U. Kovner (1842-1905), Y.E. Kovner (1840-1891), M.L. Lilienblum (1843-1910), M.Y. Berdichevsky (1865-1921), H.N. Bialik (1873-1934), S. An-sky (1863-1920) and Y.L. Peretz (1852-1915). The dissertation tells the story of Talmud-learners, trained in the rabbinic practice of textual study for its own sake (Torah lishma), who struggled to transform themselves into secular writers in a world where the production of literature was required to serve a practical purpose. Using a comparative lens, I illuminate the formation of Jewish literature alongside a parallel and equally-troubled process among the Jewish writers' contemporaries, the 19th-century Russian Orthodox seminarians who became secular writers, situating the formation of secular literatures in the Russian imperial context.

Keywords: Comparative Literature.
Advisor: Safran Gabriella
Greenleaf Monika
Shemtov Vered Karti advisor. Thesis advisor
Zipperstein Steven J.
Race, place, and political action [electronic resource] : how social norms and racial segregation shape participatory patterns in America

The question of why some but not all citizens become politically active is one of the oldest in American politics, yet remains insufficiently answered. In particular, theories to date are unable to explain differences in political participation across racial and ethnic groups, a phenomenon that is increasingly important as America continues to diversify. In response, I present the Segregated Influence Model, a novel theory of political participation that considers how race and community alter the social context of political action and in turn, the choice to engage. Through original survey experiments, observational data, and qualitative research, I demonstrate that racial segregation leads to variation in social norms regarding the value and meaning of political action in America. This variance alters the rate at which individuals choose to become active, producing differences in aggregate participatory patterns. By considering the impact of social context on political behavior, I provide in this book a nuanced account of normative influence and am able to explain the macro- level patterns of political participation central to understanding politics in the modern United States.

Keywords: Political Science.
Advisor: Segura Gary M.
Grimmer Justin advisor. Thesis advisor
McAdam Doug advisor. Thesis advisor
Rags to riches? [electronic resource] : social origin-based stratification among early career college graduates

The purpose of this dissertation is to investigate the consequences of low social origins among young college-educated adults. I argue that the relevance of social origins among college graduates grew over the past thirty years and, among recent cohorts, low social origins negatively influence early career outcomes. In the first empirical chapter of my dissertation I examine what the relationship between social origins and early career economic outcomes looks like and how it has changed over time. Next I examine specific differences in early career outcomes within one cohort of college graduates and the extent to which they can be explained by demographic or other characteristics. The third empirical chapter explores differences across institutions in the relationship between origins and economic outcomes. I then suggest that these relationships cannot be explained by academic trajectories or institutional differences and suggest several paths forward for research. Collectively, these analyses illustrate that college has become less of an equalizer among adults early in their career.

Keywords: Sociology.
Advisor: Grusky David B. primary advisor. Thesis advisor
Jackson Michelle Victoria advisor. Thesis advisor
Jiménez Tomás R. (Tomás Roberto)
Randomized linear algebra for large-scale data applications [electronic resource]

As the ability to generate datasets with billions of records in relatively automated ways continues to grow, new challenges are posed to modern large-scale data analysis from several points of view such as scalability, feasibility, and interpretability. Thus, improved algorithms on large-scale data platforms are of interest. Recent years have seen great interest in Randomized Linear Algebra (RLA) algorithms. RLA is an interdisciplinary research area that exploits randomization as a computational resource for the development of improved algorithms for common matrix problems such as least-squares approximation, low-rank matrix approximation, and Laplacian-based linear equation solvers. In this thesis, our focus is on the underlying theory and practical implementation of RLA algorithms. In particular: Chapter 3 describes a novel sampling algorithm for large-scale over-determined quantile regression problems whose running time is roughly proportional to the number of non-zero elements in the matrix plus a term that depends on the low dimension only. Chapter 4 describes a hybrid algorithm named pwSGD --- precondition weighted stochastic gradient descent that combines RLA and SGD. We prove that pwSGD inherits faster convergence rates that only depend on the lower dimension of the linear system, while maintaining low computation complexity. Chapter 5 describes a class of randomized Newton-type algorithms that exploit non-uniform sub-sampling as well as inexact updates for a class of constrained optimization problems. We show that our methods are more robust to ill-conditioned problems than other similar previous approaches. Chapter 6 presents results of implementing RLA algorithms for least-squares problems, quantile regression, and CX decomposition problems in parallel and distributed environments using Apache Spark, and discuss various tradeoffs in the implementations. In particular, we demonstrate that least-squares problems with up to terabyte-sized data can be solved to low, medium, or high precision on existing distributed systems. Chapter 7 demonstrates that applying CX/CUR decomposition to large-scale Mass Spectrometry Imaging (MSI) datasets returns interpretable results as it successfully identifies important ions and locations in complex biological samples. All in all, we show that RLA is a powerful tool for deriving scalable algorithms for large-scale regression and optimization problems, and we demonstrate that RLA algorithms are amenable to distributed computing platforms and are useful in scientific applications.

Advisor: Saunders Michael
Mahoney Michael advisor. Thesis advisor
Ré Christopher advisor. Thesis advisor
Rapid adaptation in complex demographic scenarios [electronic resource]

This thesis explores the population genetics of rapid adaptation in demographically complex scenarios, extending analyses that were previously developed modeling populations of constant size. The first chapter extends the understanding of soft selective sweeps—adaptive events where more than one adaptive allele spreads through a population while selection is acting on a common trait—in the Wright-Fisher model of evolution to populations that fluctuate arbitrarily but predictably through time. The second chapter investigates soft selective sweeps in the context of evolutionary rescue, an phenomenon where a population destined for extinction is 'rescued' by the appearance and spread of an adaptive mutation. The third chapter reviews a specific case of rapid adaptation, the evolution of drug resistance, and the population genetic insights that have been gained and applied to the study of drug resistance.

Keywords: Biology.
Advisor: Petrov Dmitri Alex
Feldman Marcus W. advisor. Thesis advisor
Fisher Daniel
Rapid melt growth technique for III-V integration on Si substrates [electronic resource]

The aggressive scaling of transistors driven by Moore's law is expected to continue in the future. Technological innovations at the system and process levels may facilitate the scaling to some extent. However, the physical limitation of Si materials is likely to put an end to Moore's law scaling. Novel materials with superior carrier transport properties are actively being studied to extend Moore's law. Among all the novel materials, III-V materials are one of the most promising candidates to replace Si due to their outstanding carrier transport properties. The heterogeneous integration of III-V materials on Si substrates not only enables the future scaling of electronic devices, but also offers a few other advantages, for instance, vertical integration of different functionalities on the same silicon-based CMOS platform, freedom of materials selection and possibilities of bandgap engineering. However, there are technological challenges to grow compound materials on silicon substrates due to the large lattice mismatch. In this thesis, a promising technique called Rapid Melt Growth is studied for III-V integration on Si substrates. A background of III-V integration on Si substrates is introduced first. Then a detailed study of the growth mechanism during RMG is performed. Three major nucleation scenarios are discussed: 3D homogeneous nucleation, 3D heterogeneous nucleation and 2D heterogeneous nucleation. The study is used to explain under what conditions the crystal growth originates from the seed region. Third, A thermal simulation is conducted to understand the thermal distribution inside the stripe during crystallization. The simulation results are then used to explain twinning crystals growth. Fourth, an analytical model is derived to predict the elemental segregation during the RMG process. This model fits the short stripe where complete mixing conditions apply. Fifth, two diffusion processes in RMG are investigated: solid state diffusion and liquid state diffusion. The effect of both diffusion processes on the crystal quality is discussed. Finally, a solution is proposed to prevent the liquid state diffusion of the Si seed region into the III-V stripe. The process optimization of this solution is described in detail. The best EBSD results of InAs RMG on Si substrates using this solution are presented. Both electrical and optical measurements are done on the as-grown InAs RMG materials to test the crystal quality.

Keywords: Materials Science and Engineering.
Advisor: McIntyre Paul Cameron primary advisor. Thesis advisor
Plummer James L.
Brongersma Mark L. advisor. Thesis advisor
Rates of convergence of Markov chains to stationarity [electronic resource] : strong stationary times, coupling, Gelfand pairs and comparison theory

The main purpose of this thesis is to find the mixing time for various random walks that the math community has been interested in. The methods used in this thesis are strong stationary times, introduced by Aldous and Diaconis, a coupling argument that was inspired by work of Aldous, bounding the eigenvalues of a walk via comparison theory and path arguments introduced by Diaconis and Saloff-Coste and via Gelfand pair theory developped by Diaconis and Shahshahani, but also finding the eigenvalues of random walks using Fourier Transform arguments as introduced by Diaconis and Shahshahani. There are many norms that can use to study the mixing time of a random walk on a finite group. Coupling is used to bound the ^1$ norm, strong stationary times are used to bound the separation distance, while the eigenvalues of a reversible Markov chain are used to bound the ^2$ norm. This thesis focuses on specific examples of Markov chains on finite spaces, some of which have been studied before but through a different norm.

Keywords: Mathematics.
Advisor: Diaconis Persi primary advisor. Thesis advisor
Soundararajan Kannan
Vondrak Ján (Mathematician) advisor Thesis advisor
Rationalizing Torture: How Giving the Public Information about Torture's Effectiveness and Necessity Influences Public Support for Torture

Recent debates on the Senate Report on Torture and statements made by Donald Drumpf that he would bring back “a hell of a lot worse than waterboarding” emphasize that the case on torture has not been closed. Given the important role that public opinion plays in modern policy choices, this research aims to address the following question: in the context of a highly threatening scenario, how does giving the public information about torture’s effectiveness and torture’s necessity influence support for torture? Findings from this research indicate that a considerable proportion of the public would disregard established legal and moral norms against torture—particularly when told that torture produced useful information, was necessary, or has a high probability of causing a terrorist suspect to produce critical intelligence.

However, findings also confirm that the public heavily rationalizes their views on torture: torture supporters define waterboarding as torture significantly less often than torture opponents (eg. 64% v. 98%) and hold less favorable feelings toward Muslims. Some evidence is suggestive of retributive motivations at play. Meanwhile, when presented with information about effectiveness and necessity, both Republicans and Democrats respond in utilitarian manner to some degree, but still express significant polarization on torture. Furthermore, they explicitly rationalize their positions differently: Democrats opposed to torture appeal primarily to deontological moral opposition while Republicans in favor of torture largely defend their support by appealing to necessity. Ultimately, this study concludes that information matters to Americans, but how they receive it may depend on their preferred side of the aisle.

Keywords: Center for International Security and Cooperation
torture
public opinion
effectiveness
necessity
waterboarding
Thesis
Advisor: Scott Sagan