Regression Discontinuity Design with Covariates

This thesis studies regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We prove asymptotic normality of the covariate-adjusted estimator under sufficient regularity conditions. In the case of a high-dimensional setting with a large number of covariates depending on the number of observations, we discuss a Lasso-based selection approach as well as alternatives based on calculated correlation thresholds. We present simulation results on those alternative selection strategies.:1. Introduction 2. Preliminaries 3. Regression Discontinuity Designs 4. Setup and Notation 5. Computing the Bias 6. Asymptotic Behavior 7. Asymptotic Normality of the Estimator 8. Including Potentially Many Covariates 9. Simulations 10. Conclusio

A Generalization of the Iteration Theorem for Recognizable Formal Power Series on Trees

Berstel and Reutenauer stated the iteration theorem for recognizable formal power series on trees over fields and vector spaces. The key idea of its proof is the existence of pseudo-regular matrices in matrix-products. This theorem is generalized to integral domains and modules over integral domains in this thesis. It only requires the reader to have basic knowledge in linear algebra. Concepts from the advanced linear algebra and abstract algebra are introduced in the preliminary chapter.:1. Introduction 2. Preliminaries 3. Long products of matrices 4. Formal power series on trees 5. The generalized iteration theorem 6. Conclusio

Assessing the Benefits of Extra-pair Mating for Female Purple Martins (Progne subis)

Approximately 75% of socially monogamous passerines pursue extra-pair mating with the frequency of extra-pair paternity varying among and within taxonomic groups. Despite the ubiquity of extra-pair mating systems, substantial research into the subject has produced mixed results and the benefits to females remain elusive. Two genetic benefits hypotheses, the good genes hypothesis and heterozygosity theory, predict that extra-pair offspring (EPO) should generally be more fit than within-pair offspring (WPO). This study aims to test for genetic-based benefits to extra-pair mating in purple martins (Progne subis) by comparing EPO and WPO. Specifically, I compare the first year survival estimates of EPO and WPO and of those offspring that are recruited into the breeding population, I compare the reproductive success of EPO and WPO. I found no differences in first-year survival probability nor did I find any differences in reproductive success between EPO and WPO. I conclude that female purple martins are not benefiting from extra-pair mating through the improved survival or reproductive success of their offspring. Such benefits may be context-dependent or historical contexts in which the benefits of extra-pair mating for females may no longer exist for this semi-domesticated species

Estimating Average Treatment Effects in Regression Discontinuity Designs with Covariates under Minimal Assumptions

We study regression discontinuity designs with the use of additional covariates for estimation of the average treatment effect. We provide a detailed proof of asymptotic normality of the covariate-adjusted estimator under minimal assumptions, which may serve as an accessible text to the mathematics behind regression discontinuity with covariates. In addition, this proof carries at least three benefits. First of all, it allows to draw straightforward consequences concerning the impact of the covariates on the bias and variance of the estimator. In fact, we can provide conditions under which the influence of the covariates on the bias vanishes. Moreover, we show that the variance in the covariate-adjusted case is never worse than in the case of the baseline estimator under a very general invertibility condition. Finally, our approach does not require the existence of potential outcomes, allowing for a sensitivity analysis in case confounding cannot be ruled out, e.g., by a manipulated forcing variable.Comment: 36 page

Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D Signaling

The rate flexibility and probabilistic shaping gain of $4$-dimensional signaling is experimentally tested for short-reach, unrepeated transmission. A rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher based on a simple look-up table.Comment: Presented at OFC'18, San Diego, CA, US

Rapid Targeted Gene Disruption in Bacillus Anthracis

Anthrax is a zoonotic disease recognized to affect herbivores since Biblical times and has the widest range of susceptible host species of any known pathogen. The ease with which the bacterium can be weaponized and its recent deliberate use as an agent of terror, have highlighted the importance of gaining a deeper understanding and effective countermeasures for this important pathogen. High quality sequence data has opened the possibility of systematic dissection of how genes distributed on both the bacterial chromosome and associated plasmids have made it such a successful pathogen. However, low transformation efficiency and relatively few genetic tools for chromosomal manipulation have hampered full interrogation of its genome. Results: Group II introns have been developed into an efficient tool for site-specific gene inactivation in several organisms. We have adapted group II intron targeting technology for application in Bacillus anthracis and generated vectors that permit gene inactivation through group II intron insertion. The vectors developed permit screening for the desired insertion through PCR or direct selection of intron insertions using a selection scheme that activates a kanamycin resistance marker upon successful intron insertion. Conclusions: The design and vector construction described here provides a useful tool for high throughput experimental interrogation of the Bacillus anthracis genome and will benefit efforts to develop improved vaccines and therapeutics.Chem-Bio Diagnostics program from the Department of Defense Chemical and Biological Defense program through the Defense Threat Reduction Agency (DTRA) B102387MNIH GM037949Welch Foundation F-1607Cellular and Molecular Biolog