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Some Results on Two-Dimensional Lattice Random Field Models
No full textThis dissertation deals with two different stochastic processes defined on the two-dimensional integer lattice. These are the random field Ising model with Gaussian disorder and the Gaussian free field. In each case the questions we study are different but throughout the goal is to understand the large-scale (macroscopic) behavior of the process. Likewise, the techniques used to analyze each model will be different, but throughout there will be an emphasis on geometric thinking and the properties of Gaussian processes. The results can be roughly summarized as follows The correlation length of the random field Ising model scales as eε-4/3 as the disorder strength ε goes to 0. For a metric Gaussian free field defined on a square of size N and a macroscopic annulus inside that box, the length of the shortest crossing of the annulus by a path where the field is positive is at most N (log N1/4. When defined on a rectangle, the metric graph and discrete Gaussian free fields exhibit different crossing probabilities. That is, the probability that there exists a path connecting the left and right sides of the box on which the field is positive differs between the two models
Birational Geometry of Genus One Fibrations and Stability of Pencils of Plane Curves
No full textIn the first part of this thesis we give a complete classification of relative log canonical models for genus one fibrations in dimensions two and three. More concretely, we generalize the work in [2] by considering both (i) the case where it is not assumed the existence of a section, but of a multisection instead; and (ii) the case of threefolds in one dimension higher. In the second part, we investigate the stability of pencils of plane curves in the sense of geometric invariant theory. One of our main results relates the stability of a pencil of plane curves P to the log canonical threshold of pairs (P^2,C_d), where C_d is a curve in P, thus extending an idea of Hacking [23] and Kim-Lee [27]. Part of our approach consists in observing that we can sometimes determine whether a pencil P is (semi)stable or not by looking at the stability of the curves lying on it. As a beautiful application, we completely describe the stability of Halphen pencils of index two -- classical geometric objects first introduced by Halphen in 1882 [24]. Inspired by the work of Miranda in [40], we provide explicit stability criteria in terms of the geometry of their associated rational elliptic surfaces
Essays on the Economics of Health and Optimal Taxation
No full textThis dissertation consists of two chapters. Chapter 1 compares the optimal and current taxation of alcohol and cigarette with the optimal subsidization of sports goods in terms of welfare gains and distributional effects using a life cycle framework. Sports goods subsidization could optimally generate a welfare gain of $171.59 per household every year, about 16 times higher than that from the optimal taxation of the unhealthy goods. The former decreases the aggregate medical expenditure by 5.3%, while the latter only by 0.2%. Positive sports goods subsidization could benefit both high and low education groups through the effects of lower premiums and tax burdens, despite the negative distribution and health effects against the low education group. Chapter 2 investigates how firms\u27 global connectedness and market power affect their performance and resilience during crises. While global production and export networks expose firms to foreign shocks, they potentially reduce firms\u27 susceptibility to domestic shocks through international diversification. Additionally, increases in market power could provide buffers by allowing margins for adjustment. Using weekly global stock market data combined with firm-level supply chain, export, and balance sheet information, this chapter shows that firms with higher global connectedness and market power are more resilient to domestic pandemic shocks. Global connectedness (but not market power) alleviates domestic pandemic shocks only if foreign economies experience smaller shocks. Finally, pandemic-driven cross-firm reallocations were concentrated between March and May when cross-country COVID-19 dispersion dramatically increased
Hearing Power, Sounding Freedom: Black Practices of Listening, Ear-Training, and Music-Making in the British Colonial Caribbean
No full textThis dissertation explores how African and African-descended people in the British colonial Caribbean, enslaved and free, engaged with music that had its origins in Europe through listening, performance, theorizing, and composition between the banning of the transatlantic slave trade in 1807 and the granting of unrestricted freedom in 1838. By shifting perspective to how black people heard European music, rather than how white people heard colonized and enslaved black people, this project complicates traditional narratives about race and music in the colonial Caribbean, arguing that black musicians used music and listening as a tool to assert their intellectual and aesthetic capabilities, while simultaneously learning, theorizing, and sometimes subverting the music of their colonizers. I position these modes of performance and listening within a context of increased white anxiety about race in the decades before and after emancipation. Drawing on methodologies from black feminist history, this project focuses on the music lives of the enslaved from scant traces in the archive. Through chapters about enslaved fiddlers, military musicians, Christian converts, and free people of color, this dissertation acknowledges that the multiplicity of ways that enslaved and subjugated Africans and their descendants performed and interacted with European music demonstrate that European music in the colonial Caribbean was not strictly racialized as white
Synthetic Studies toward Citrofulvicin: Synthesis of the Core Ring System
No full textThe polyketide natural product citrofulvicin, which was isolated in 2018, presents an intriguing synthetic target due to both the structural complexity of the octacyclic ring system, which contains a 1-hydroxy-2,4,6-trioxaadamantane ring, and the reported antiosteoporotic activity of citrofulvicin. Synthetic access to this natural product would allow for further biological evaluation. This dissertation describes the synthetic efforts toward citrofulvicin. An initial approach using an isoxazole ring as a protecting group for a β-diketone on a model system targeting the core ring system of citrofulvicin led to the formation of unexpected polycyclic pyridine-containing structures. An alternative approach using a dioxolane protecting group on the model system led to the development of a concise synthesis of the key intermediate for the proposed final intramolecular cyclization cascade. Due to the observed unexpected intramolecular reactivity of this intermediate, a thioketal blocking group was introduced, which allowed for the successful cyclization cascade to occur. Removal of the thioketal blocking group led to the core ring system of citrofulvicin, which only lacked the aromatic ring substituents. Thus, the core ring system was synthesized in nine steps from readily available materials and the developed synthetic route should translate to the synthesis of citrofulvicin with a suitably substituted aromatic starting material
Team Formation and Incentives
No full textThis dissertation analyzes the incentives of workers in organizations that utilize teams. In Chapter 1, I study a moral hazard in teams model in which a principal knows that the agents she compensates are identical and independent, but does not know all of the actions they can take. In the face of this uncertainty, the principal chooses a symmetric contract that yields her the highest worst-case expected profit. I show that, counterintuitively, any such contract exhibits joint performance evaluation — each agent\u27s pay is increasing in the performance of the other — and is nonlinear in team output. In Chapter 2, Carlos Segura-Rodriguez and I study profit-maximizing matching in the presence of adverse selection and moral hazard. We show that when productive complementarities between workers are weak and effort costs are high, expected wage payments increase in the assortativity of the matching the manager implements. Hence, either random or negative assortative matching can be profit-maximizing, even when positive assortative matching is efficient. Finally, in Chapter 3, Carlos Segura-Rodriguez, Peng Shao, and I study the efficiency of decentralized team formation inside research organizations through the lens of a one-sided matching model with non-cooperative after-match information production. Our equilibrium analysis identifies two inefficiencies observed inside of non-hierarchical organizations. First, productive teams composed of workers producing complementary information may form at the expense of excluded workers who must form relatively unproductive teams consisting of workers producing substitutable information. Second, even when productive teams are efficient, they need not form; a worker in such a team may prefer to join a less productive team if she can exert less effort in this deviating team
Essays on Automation, Inequality, and Macroeconomic Performance
No full textIn the first chapter, I provide a theory that links automation to the top income inequality. I construct a model in which managing labor is harder than managing capital. Hence, an improvement in automation enables entrepreneurs to scale up their production. This leads highly productive entrepreneurs to capture a larger fraction of the market and hence this increases top income inequality. I show that the shape parameter of the Pareto distribution that characterizes the right tail of income distribution is inversely related to the automation parameter. Using cross-industry and cross-country data, I provide empirical support for the model\u27s prediction. In the second chapter, I quantitatively analyze the impact of improvements in automation technology on top wealth shares. I incorporate the production function that I consider in the first chapter into an Aiyagari model with entrepreneurs and a financial friction. An improvement in automation technology impacts wealth concentration through two channels: first, it increases the return to entrepreneurial skill; second, it increases dispersion to return to capital. I calibrate the model to the 1968 US economy and increased the automation parameter to the 2016 value. Comparing the two steady-states, the model generates one-fourth of the observed increase in wealth share of the top 1% and explains 10% of the observed increase in the top 0.1%. In consumption equivalence terms, workers\u27 welfare increases by 5%, and entrepreneurs\u27 welfare increases by 8%. The third chapter examines the strong positive correlation between job-to-job transition rates and nominal wage growth in the U.S. First, using time series regressions, structural monetary policy shocks, and survey data on search effort we provide evidence that inflationary shocks cause higher job-to-job transitions in the subsequent years. Second, we build a model with aggregate shocks and competitive on-the-job search in which wages react sluggishly to inflation. Third, we calibrate the model to the U.S. economy and find that the output response to inflation shock is non-monotonic. The monetary authority can stimulate productivity with an inflationary shock through job-to-job transitions
The Role of Active DNA Demethylation in Mammalian Epigenetic Reprogramming
No full textDNA methylation in the form of 5-methylcytosine (5mC) is an essential epigenetic regulator of gene expression and cellular identity in mammals. As a dynamic epigenetic feature, DNA methylation can be reversed through several distinct pathways. Whereas global DNA demethylation is achieved through the suppression of DNA methyltransferase (DNMT) enzymes, targeted demethylation at individual CpG sites is regulated through the activity of Ten-eleven Translocation (TET) family enzymes. TET enzymes mediate the sequential oxidation of 5mC to 5-hydroxymethylcytosine (5hmC), 5-formylcytosine (5fC), or 5-carboxycytosine (5caC). These oxidized residues are poorly recognized by maintenance methyltransferase DNMT1, allowing their steady dilution over several rounds of cellular division. Alternatively, 5fC and 5caC may be targeted for excision by thymine DNA glycosylase (TDG), restoring the unmodified cytosine through the base excision repair pathway. While these two mechanisms are collectively referred to as “active DNA demethylation”, little is known about their relative contributions to DNA demethylation in vivo. Here, using newly discovered “5hmC-stalling” TET mutants with impaired 5fC and 5caC oxidation, we tested the requirement of the fC/caC branch of active DNA demethylation for epigenetic reprogramming in two model systems. First, using an induced pluripotent stem cell (iPSC) model, we demonstrate that the fC/caC activity of TET2 is essential for DNA demethylation at reprogramming enhancers during iPSC induction, and that loss of this activity reduces the reprogramming potential of mouse embryonic fibroblasts. Next, we used CRISPR/Cas9 engineering to generate two new mouse models of TET1 activity: a 5hmC-stalling Tet1T1642V mutant, and a catalytically inactive Tet1HxD mutant. Our preliminary results indicate that the fC/caC activity of TET1 is critical for epigenetic reprogramming in the developing mouse germline, and that loss of TET1 catalytic activity in the adult mouse cortex leads to hypermethylation in promoters of genes involved in neurodevelopment and maintenance. In total, our studies represent the first in vivo characterization of the multiple activities of TET enzymes and the roles they play in regulating genomic 5mC levels and shaping cellular identity
Mentoring for Ethical Leadership in the Navy: How Mentors Support Leadership Development, and Foster Ethical Decision-Making in Commanders
No full textThe US Navy requires leaders of competence and character in combat. The elements of competence are developed in numerous schoolhouses, but the path for developing leaders of character is less well-defined, influenced by individuals and organizational culture. If the Navy fails to develop ethical decision-makers, it could cost the trust of the American people or combat effectiveness in wartime. For centuries, mentors have demonstrated influence on their protégés. One possible vehicle for ethical decision-making is the more intentional use of mentors to serve as role models for ethical leadership. We know little about the development of ethical decision-making in Navy leaders and the influence that mentors have on their preparation for command. This study investigated the impact of mentors in developing ethical leaders. I surveyed 42 Navy officers who served in command about their mentoring experiences. In addition to survey results, I interviewed 16 former Commanding Officers and thematically analyzed their leader development, preparation for command and how they evolved their ability to make ethical decisions. I found that mentors were often in the chain of command and provided support as young officers navigated the challenges of the workplace. Mentors were role models throughout their protégés’ careers and helped them establish a mental model of what good leadership looked like as their protégés prepared for command. Lastly, mentors influenced their protégés’ ethical leadership and helped them make ethical decisions in command. I will use the results of this study to recommend that the Navy include a more intentional approach to mentoring future commanding officers (COs) and to prepare COs by mentoring them for ethical decision-making. I also recommend that further study should be conducted on the impact of mentoring on ethical leadership
Investigation of RNA-Protein Interactions in PRC2 Function
No full textChromatin regulation contributes to control of gene expression and what identity a cell will adopt. In the last decade the role that RNA plays in chromatin regulation has become increasingly clear. RNA mediates protein recruitment and eviction from chromatin, forms nuclear condensates with proteins and DNA, and contributes to proper chromatin organization. Yet our knowledge of the mechanisms that govern RNA activity on chromatin lags significantly and limits our ability to understand nuclear function. To effectively answer some of the questions of RNA function in the nucleus we need a comprehensive atlas of RNA-protein interactions, which would enable generation of protein mutants defective in RNA-binding. The goal of my thesis was to develop an unbiased method to profile RNA-binding proteins in the nucleus and apply it to Polycomb repressive complex 2 (PRC2). PRC2 is an epigenetic regulatory complex that deposits mono, di- and tri- methyl lysine onto histone H3 (H3K27me3) and maintains gene silencing during development. PRC2 shows extensive contacts with RNA but their function remains unclear. In the first chapter, we present a novel method, dubbed RBR-ID, for the identification of RNA-protein interactions, which uses UV-crosslinking of photosensitive nucleotide analogs to proteins followed by high resolution mass spectrometry (LC-MS/MS). We identified over 800 RNA-binding proteins, of which 427 were novel and enriched for chromatin-related functions. In the second chapter we adapted RBR-ID to study PRC2, identifying RNA-binding-regions (RBRs) on every subunit of the complex. An RBR identified on EED fell near the regulatory center of PRC2, and we showed that RNA-mediated inhibition of PRC2 can be reversed by stimulatory peptides that bind in the regulatory center, reflecting the antagonistic relationship between RNA and PRC2. In the final chapter we present a testing method we developed for the SARS-CoV-2 virus. Our method, COV-ID, uses reverse transcription and loop-mediated isothermal amplification (RT-LAMP) from patient saliva paired with high-throughput sequencing. Using this method we can detect as little as 5-10 SARS-CoV-2 virions/μL, and we successfully replicate classification of saliva samples (10/10) from clinical COVID-19 patients. We show that COV-ID can be multiplexed to detect influenza as well as SARS-CoV-2. Finally we demonstrate that COV-ID can process saliva samples collected on filter paper with sensitivity as low as 50 virions/μL