Alzheimer’s disease (AD) is the most common type of dementia affecting more than 44 million patients in worldwide. AD accounts for 60 to 80 percent of dementia cases. AD is characterized by the progressive loss of memory and cognition. The pathological hallmark of AD is the deposition of fibrillar amyloid plaques in the brains of AD patients. Amyloid beta (Aβ) proteins, the major constituents of these plaques, are derived by enzymatic cleavage from the transmembrane amyloid precursor protein (APP). Although accumulation of Aβ plaques in AD brains was believed to be directly correlated to the disease, increasing evidence indicates that small Aβ oligomers are the main toxic species. However, the exact disease mechanism has not yet been fully elucidated. A prevailing mechanism of AD pathology postulates that Aβ oligomers negatively affect neuronal function and survival by forming ion permeable pores, resulting in the destabilization of cell ionic homeostasis. This dissertation investigates the structures and ion conducting properties of Aβ oligomers in lipid membranes as well as develops new technique that can be applied to elucidate the mechanism of unknown disease pathologies. In chapter 2, I present the biophysical characterizations of two most abundant Aβ proteins (Aβ1-42 and AβpE3-42) in lipid membranes using AFM and Black Lipid Membrane (BLM) techniques to give insight toward finding the disease mechanisms. In chapter 3, I show the structures and ion conducting properties of Aβ1-42 and Aβ17-42 (or p3) in membranes comprised of natural brain total lipid extract and compare the results from other model lipid membranes. In chapter 4, I show the effect of an AD therapeutic candidate molecule on Aβ structures and ion conducting activities. In chapter 5, I show the development of new technique called Nanofiber optical force transducer. This new technique can measure sub pN force from living organisms. This multiscale study of structure-function relationship in Aβ proteins provides insight into AD mechanism and specific targets for the development of therapeutic strategies for the treatment AD.

Though there have been numerous studies of freeway weaving sections (i.e., segments in which an on-ramp is followed by an off-ramp), there remains a significant lack of empirical and theoretical understanding of the traffic behavior that causes weaving sections to become bottlenecks with varying discharge flows. The present research entails empirical analysis and theoretical modeling of what triggered the bottleneck activations and discharge flow changes in two freeway weaving sections. Both sites were recurrent bottlenecks during the rush, and investigations revealed that changes in the spatial patterns of vehicular lane-changes, especially among Freeway-to-Ramp (F-R) maneuvers, caused variations in bottleneck discharge flow. When the F-R maneuvers were concentrated near a weaving section’s on-ramp, they became more disruptive, resulting in bottleneck activations with diminished discharge flows. Findings further indicated that the spatial distributions of these lane changes, in turn, were dictated by the traffic conditions in the auxiliary lane (i.e., the lane connecting the off-ramp to the upstream on-ramp). Reductions in on-ramp flows increased the attractiveness of the auxiliary lane, thus motivating F-R drivers to perform their maneuvers nearer the onramp. Conversely, increases in on-ramp flows motivated F-R drivers to perform their maneuvers over a wider stretch of the weaving section.

This thesis studies a class of mean field games (MFG) with singular controls of bounded velocity. By relaxing absolute continuity of control processes, it generalizes the MFG framework of Lasry and Lions \cite{LL2007} and Huang, Malham e, and Caines \cite{HMC2006}. It provides a unique solution to the MFG with singular controls of bounded velocity and its explicit optimal control policy establishes an \epsilon-Nash equilibrium of the corresponding stochastic differential N player game with singular controls.

It also includes MFGs on an infinite time horizon. Our method to approach MFGs with singular controls is from bounded velocity processes, and we analyse the relationship between singular controls with finite variation processes and singular controls with bounded velocity.

Finally, it illustrates particular MFGs with explicit solutions in a systemic risk model originally formulated by Carmona, Fouque, and Sun \cite{CFS2013} in a regular control setting and an optimal partially reversible investment problem with N players originally formulated by Guo and Pham \cite{GP2005} in a single player setting.

This dissertation describes the application and development of electron crystallography in the realm of small molecules and, in particular, natural products (NPs). Natural products serve as a major inspiration for drug discovery, but the rate of discovering novel NPs is hindered by limitations in existing characterization techniques. This dissertation highlights microcrystal electron diffraction (MicroED) as a powerful approach to overcome these limitations and structurally characterize NPs and other small molecules. Overall, this work demonstrates the general applicability of MicroED in natural product and small molecule characterization. Moreover, using MicroED as a platform, an efficient workflow for NP identification is developed, with the goal of accelerating the rate of novel natural product discovery as well as drug discovery. Chapter One is a brief overview of the current state of research on using electron diffraction to elucidate structures of natural products. This chapter serves as both a prelude to and a summary of the remaining chapters, and will be referenced throughout this dissertation. Brief history of electron diffraction and background of MicroED is provided, focusing on the scope of MicroED in small molecule regime. Furthermore, the application of MicroED in natural products and currently remaining challenges are highlighted, drawing on our experiences as well as others’. Chapters Two through Five describe the applications of MicroED in NP characterization. Chapter Two highlights the structural elucidation of a glucosyluric metabolite in C. elegans, whose MicroED structure was used to complement the NMR data that was ambiguous due to poor line shapes. Chapter Three showcases the structure determination of a biosynthetic intermediate to a fungal metabolite (–)-sambutoxin, whose relative stereochemistry was validated using MicroED. Chapter Four discusses the synergy between MicroED and genome mining by rediscovering the biosynthetic pathway to fischerin and revising its relative stereochemistry that was incorrectly assigned using computational studies. In this chapter, a novel compound is isolated and characterized using MicroED, demonstrating the first example of a novel, non-peptidyl NP structurally elucidated via MicroED. Additionally, this study highlights MicroED’s impressive sensitivity by detecting structural information from only 3 ng of material. Chapter Five reports the structural revision of the lomaiviticins enabled by MicroED analysis. The lomaiviticins are highly cytotoxic bacterial metabolites that have been extensively studied for decades, with multiple total synthesis efforts that failed. This structural revision, supported by high-field NMR as well as DFT calculations, enables scientists to embark on future synthetic efforts and studies on mechanisms of action with more confidence. Chapter Six highlights the development of a MicroED platform to enable highthroughput screening for crystalline NPs. Initial studies demonstrate MicroED’s ability to obtain crystal structures in complex mixtures of natural products. These preliminary experiments are used to envision a workflow coupling liquid chromatography and MicroED, which is further developed into a high-throughput strategy. Using this platform, NPs produced in insufficient amounts for other analytical techniques can be detected and characterized, accelerating the rate of NP discovery. Chapter Seven describes the expansion of the scope of MicroED further in the small molecule regime by solving structures of reactive organometallic species and synthetic reaction products. These examples showcase the ability of MicroED in obtaining crystal structures that were previously unattainable, and demonstrate the structural integrity of MicroED structures when compared with structures obtained by X-ray crystallography. Notably, we discuss the utility of room temperature MicroED experiments, which provide a facile and quick method of screening for diffraction and become an integral part of the workflow in structural elucidation of small molecules.

The key focus of this dissertation is on how to understand and measure treatment effect heterogeneity in experimental or quasi-experimental evaluations of educational policy interventions. When testing the impact of an intervention, it can be important to know not just the overall or average effect of the intervention on key outcomes but also how the effect varies across subgroups of study participants, as defined by several dimensions including their pre-treatment characteristics, site-level contexts, and the distribution of an outcome measure. Heterogeneity or variation in effects has critical implications for understanding how interventions work and which aspects of an intervention's implementation are most closely associated with its effectiveness. This dissertation examines both methodological and substantive questions that pertain to such heterogeneity.

In Chapter 1, I examine Bayesian hierarchical models for multi-site trials that allow estimation of site-specific treatment effects and their distribution. Modeling site-specific effects using observed data is a critical component in understanding the results of multisite trials. A standard approach leveraging Bayesian methods is to rely on Gaussian distributional assumptions and to use the posterior means (PM) of the random effects. The standard approach can be misleading, however, in the estimation of individual site-specific effects and their empirical distribution and ranks. In this chapter, I review the following two strategies developed to improve inferences regarding site-specific effects: (a) relaxing the normality assumption by flexible modeling of the random-effects distribution using Dirichlet process mixture (DPM) models, and (b) replacing the choice of PM as the summary of the posterior by alternative estimators, such as the constrained Bayes (CB) or the triple-goal (GR) estimators. I then examine when and to what extent the two strategies and combinations thereof work or fail under varying conditions.

In Chapter 2, I study methodological issues arise in the practice where Bayesian quantile regression (BQR) models are applied. The BQR models allow us to study treatment effect heterogeneity across the distribution of an outcome measure such as a student achievement test score. In BQR, the most commonly applied likelihood is the asymmetric Laplace (AL) likelihood because it is computationally convenient for Markov chain Monte Carlo algorithms. For easier computation, the scale parameter of the AL distribution is often fixed at a pre-estimated value or an arbitrary constant. This paper demonstrates that posterior inference in BQR with an AL likelihood is highly sensitive to the choice of the fixed scale parameter. Based on sensitivity analyses using Monte Carlo simulations and a real data example, I make two claims. First, not only the variance directly obtained from the posterior distribution, but also the adjusted posterior variance proposed by Yang et al. (2015), is highly sensitive to the value of the scale parameter. Second, in finite samples, both conventional and Bayesian point estimators can be biased at extreme quantiles. Researchers need to be aware of the possibility of low coverage probabilities at extreme quantiles mainly caused by biased point estimates.

In Chapter 3, I examine the use of the grouped/multilevel instrumental variable (IV) quantile regression approach, a quantile extension of Hausman and Taylor (1981). The common approach of estimating the shift of group-level (level-2) averages of individual-level (level-1) outcomes may mask important but more subtle effects on the outcome distribution. For example, a school-level intervention may have little effect on school-level average test score but may cause a substantial shift in the lower quantiles of the within-school test score distributions if the intervention is particularly beneficial for low-performing students. As one real-world empirical example, I used the grouped/multilevel IV quantile approach to estimate the effects of district-level increases in per-pupil spending on quantiles of the within-district distribution of school quality measures. I show how new dollars flowing to districts did affect varying mixes of teachers and organizational practices inside schools, but in ways that mitigated against narrowing disparities. Better funded high schools reduced access to college-prep courses relative to electives, and novice teachers were often assigned to courses serving English learners, inequities that widened in high-poverty schools.

Speeding is known to be related to a significant portion of highway collisions. As part of the efforts to seek safety improvements of the California highway network, the California Department of Transportation (Caltrans) is exploring the implementation issues of automated speed enforcement (ASE). This report provides an overview of Task Order 6212 undertaken by California PATH to assess various issues associated with ASE systems.

An ASE system designed for use in work zones was acquired and tested in several field experimental sites, along with several other commercially-off-the-shelf traffic monitoring devices. The objective of the study is to examine the field performance of the equipment in a real-world setting, when evaluated against other comparable traffic devices. The results from the field experiments revealed that traffic speed measurements are likely to yield discrepancies. For considerations of future deployment of ASE, the technologies can be expected to be advanced further. Since all types of sensing devices are susceptible to certain levels of interference and noises in the field, a consistent and robust method of verification and calibration for sensors used for ASE will be essential. From the design point of view, extra measures or techniques can be taken to ensure the robustness and accuracy of ASE systems.

The assessment of technical performance of ASE as carried out in this project can provide insights in the process of validating functional characteristics and seeking performance enhancements. The outcome of this study, in conjunction with the experience and knowledge gained by other agencies in their development and implementation of work-zone and general ASE systems will offer valuable support for future ASE implementation.

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