This honors project was born out of a desire to understand individuals who abandoned political glory in favor of serving other leaders. I wanted to study and know who can go head-to-head with \u2014 and command the respect of \u2014 the U.S. President on a daily basis. I limited my search to friends of the presidents who held powerful positions: I identified Harry Hopkins, Robert McNamara, and Condoleezza Rice. This thesis is broken into the following sections. To begin, we follow each official in their rise to prominence and discover how they captured the attention of their respective presidents. Next, we delve into their relationships with the Oval Office -- what is similar or different about each of their connections with the presidents. The bulk of the work focuses on pivotal moments in our country's history \u2014 events that shaped the United States of today. Specifically, we look at the New Deal, World War II, the Cuban Missile Crisis, the Vietnam War, the Middle East, and nuclear weapons proliferation. Then, we dissect similarities and differences between their relationships with their presidents, and wrap up with some takeaways about how one could go about becoming a presidential advisor. Their distinctive styles can be grouped into doers or planners. Hopkins and McNamara were proud and self-proclaimed doers. Rice stands alone as a fantastic planner. If one seeks to emulate any of these three, there are three things to commit to. First, skills both matter and don't matter. Second, there are two paths to getting presidential attention and becoming close enough for them to seek one out for advice. The first is to understand which wheels need greasing, and grease them. The other is to have a potential solution to an unsolved problem -- that is powerful. Be great, a maverick, and public, or look to create your own role from scratch and hope that you are an expert when a time of great need comes. Third, once you are friends with and have the political ear of the president, know that loyalty is the only thing that truly matters. This thesis is an attempt to better understand leadership through the lens of powerful followers. This project strives to inform the reader of the context within which these actors played, the actions that they took, and the consequences that were incurred, all while being personally close to the most powerful position on the planet. I have tried to give context and understanding for pivotal moments in American history while shining a spotlight on a few underappreciated historical actors.

Walking ability is a complex process that is essential to humans, critical for performing a range of everyday tasks and enables a healthy, independent lifestyle. Human gait has evolved to be robust, adapting to a wide range of external stimuli, including variable walking surface compliance. Unfortunately, many people suffer from impaired gait as a result of conditions such as stroke. For these individuals, recovering their gait is a priority and a challenge. The ASU Variable Stiffness Treadmill (VST) is a device that is able to the change its surface compliance through its unique variable stiffness mechanism. By doing this, the VST can be used to investigate gait and has potential as a rehabilitation tool. The objective of this research is to design a variable damping mechanism for the VST, which addresses the need to control effective surface damping, the only form of mechanical impedance that the VST does not currently control. Thus, this project will contribute toward the development of the Variable Impedance Treadmill (VIT), which will encompass a wider range of variable surface compliance and enable all forms of impedance to be con- trolled for the first time. To achieve this, the final design of the mechanism will employ eddy current damping using several permanent magnets mounted to the treadmill and a large copper plate stationed on the ground. Variable damping is obtained by using lead screw mechanisms to remove magnets from acting on the copper plate, which effectively eliminates their effect on damping and changes the overall treadmill surface damping. Results from experimentation validate the mechanism's ability to provide variable damping to the VST. A model for effective surface damping is generated based on open-loop characterization experiments and is generalized for future experimental setups. Overall, this project progresses to the development of the VIT and has potential applications in walking surface simulation, gait investigation, and robot-assisted rehabilitation technology.

The purpose of this thesis project is to analyze the legalization of physician-assisted suicide (PAS) as an option for the terminally ill in the United States from a rule-utilitarian perspective. The moral theory of utilitarianism is a consequentialist theory that judges the moral permissibility of an action or rule based on the best possible outcomes. Rule-utilitarianism conforms an action to an articulated moral rule that leads to the greatest good whereas act-utilitarianism only considers the best possible consequences on a case-by-case basis. Since legalization of PAS is a policy that requires passage of laws, rule-utilitarianism is more appropriate compared to act-utilitarianism. Euthanasia is a controversial topic worldwide that dates as far back as the 5th century BC with the Greeks and Romans. Comparing the euthanasia then and now, the nations are slowly but surely reconsidering the policies regarding PAS. There are both benefits and harms that the paper addresses. The possible benefits include the prevention of elongation of suffering, both physically and psychologically, respect for the patient autonomy, the right to die with dignity, and the decriminalization of the innocents. The potential harms include undermining the integrity of the medical profession and the aim of medicine, violation of the Hippocratic Oath, targeting of the vulnerable population, unmotivating the efforts to develop and improve better palliative and hospice care, and the slippery slope argument, which implies that the legalization of PAS would eventually set the precedence to legalizing voluntary active euthanasia and nonvoluntary euthanasia. Overall, the moral calculus that the paper provides comes to the conclusion that the benefits outweigh the harms.

I conduct a two-fold study on the relationship between adverse selection and nonlinear pricing in competitive insurance markets. First, I reassess empirical evidence of adverse selection in life insurance with the Health and Retirement Study (HRS) data used by Cawley and Philipson (1999). Specifically, I evaluate the shape of the premium schedule and present indications of quantity premia beyond a certain coverage level. The observed pricing schedule appears like the "backward-S-shaped" curve described by Chade and Schlee (2012); I discuss why this result cannot be entirely explained by fixed costs of underwriting. Second, I critique the arguments against adverse selection in existing literature by modifying the Rothschild and Stiglitz (1976) model of competitive insurance markets. I present several existing models and a new framework to explain how adverse selection and quantity discounts can coexist in equilibrium. These modifications deviate from the standard models of competitive insurance, but produce plausible hypotheses with conclusions contrary to conventional theoretical results.

The purpose of this thesis is to investigate the history of the Bitcoin arbitrage premium to see if the possibility of 'risk-free' gains existed previously and whether or not the opportunity is still present today. It investigates market structure and price discrepancies in $147B of trading volume across 53 different exchanges between July 2010 and February 2017. This paper aggregates exchange trading into five minute buckets of transaction volume in order to see what exchange volume could have been successfully arbitraged within the context of two cases. The first requires trades to close within the same 5-minute interval and the second requires a 10-minute delay before the position is closed. It finds that the monthly average spreads of these cases have fallen below 3% in 2017 from nearly 10% in 2010. Once exchange fees are included, these spreads fall below 2% on average.

The problems addressed by the philosophy of mind arise anew when we consider the possibility of consciousness in artificial and non-biological systems. In this thesis I adapt traditional theories of mind and theories meaning in natural language to the new problems posed by these non-human systems, attempting answers to the questions: Can a given system think? Can a given system have subjective experiences? Can a given system have intentionality? Together these capture most of the typical features of consciousness discussed in the literature. Hence, answers to these questions have the potential to form a basis for a robust and practical future theory of consciousness in non-human systems, and I argue that the broad classes of functionalist and emergentist theories of mind are those worth considering more in the literature. The answers given in this thesis through the lenses of these two classes of theories are not exclusive, and may interact with or be supportive of one another. The functionalist account tells us that a system can be thinking, sentient, and intentional just in case it exhibits the correct structure, and the emergentist account tells us how this structure might arise from previous systems of the right complexity. What these necessary structures or complexities are depends on which functionalist and emergentist accounts we accept, and so this thesis also addresses some of the possibilities allowed for by certain variants of these theories. What we shall obtain, in the end, are some prima facie reasons for believing that certain systems can be conscious in the ways described above.

Temporal discounting refers to our tendency to discount the value of future rewards. At the extreme, temporal discounting can give rise to detrimental myopic decision-making. Most studies examining the neural basis of temporal discounting in people have been performed using functional Magnetic Resonance Imaging (fMRI). However, fMRI has relatively poor temporal resolution compared with the speed at which people make choices, so understanding choice dynamics using fMRI is difficult. We address the issue utilizing electroencephalography (EEG) to study cortical processes related to temporal discounting. The fMRI literature has found that a network of fronto-parietal brain regions plays an important role during the decision-making process. We aim to explore activity in these regions during the decision process and determine how cortical activity relates to choice parameters. Based on prior fMRI studies, we hypothesized that dorsomedial prefrontal cortex (dmPFC) may act as a regulator of dorsal lateral prefrontal cortex (dlPFC) and there will be an increase in dlPFC activity for more difficult decisions. We also hypothesized that neural activity may be directly related to the temporal discount rate we estimate behaviorally. We utilized regression analysis to determine the relationship. The results found supported our hypotheses. This study may open the door to a better understanding of the dynamic of brain regions while performing a temporal discounting task.

Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does not speak to how animals make<br/>decisions that tend to be adaptive. Using simulation studies, prior work has shown empirically<br/>that a simple decision-making heuristic tends to produce prey-choice behaviors that, on <br/>average, match the predicted behaviors of optimal foraging theory. That heuristic chooses<br/>to spend time processing an encountered prey item if that prey item's marginal rate of<br/>caloric gain (in calories per unit of processing time) is greater than the forager's<br/>current long-term rate of accumulated caloric gain (in calories per unit of total searching<br/>and processing time). Although this heuristic may seem intuitive, a rigorous mathematical<br/>argument for why it tends to produce the theorized optimal foraging theory behavior has<br/>not been developed. In this thesis, an analytical argument is given for why this<br/>simple decision-making heuristic is expected to realize the optimal performance<br/>predicted by optimal foraging theory. This theoretical guarantee not only provides support<br/>for why such a heuristic might be favored by natural selection, but it also provides<br/>support for why such a heuristic might a reliable tool for decision-making in autonomous<br/>engineered agents moving through theatres of uncertain rewards. Ultimately, this simple<br/>decision-making heuristic may provide a recipe for reinforcement learning in small robots<br/>with little computational capabilities.

The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the behavior of electrons whose combined internal angular momentum is zero. This paper will go over Dr. Bell's famous inequality, which shows why the process of entanglement cannot be explained by traditional means of local processes. Entanglement will be viewed initially through the Copenhagen Interpretation, but this paper will also look at two particular models of quantum mechanics, de-Broglie Bohm theory and Everett's Many-Worlds Interpretation, and observe how they explain the behavior of spin and entangled particles compared to the Copenhagen Interpretation.

Many current cryptographic algorithms will eventually become easily broken by Shor's Algorithm once quantum computers become more powerful. A number of new algorithms have been proposed which are not compromised by quantum computers, one of which is the Supersingular Isogeny Diffie-Hellman Key Exchange Protocol (SIDH). SIDH works by having both parties perform random walks between supersingular elliptic curves on isogeny graphs of prime degree and eventually end at the same location, a shared secret.<br/><br/>This thesis seeks to explore some of the theory and concepts underlying the security of SIDH, especially as it relates to finding supersingular elliptic curves, generating isogeny graphs, and implementing SIDH. As elliptic curves and SIDH may be an unfamiliar topic to many readers, the paper begins by providing a brief introduction to elliptic curves, isogenies, and the SIDH Protocol. Next, the paper investigates more efficient methods of generating supersingular elliptic curves, which are important for visualizing the isogeny graphs in the algorithm and the setup of the protocol. Afterwards, the paper focuses on isogeny maps of various degrees, attempting to visualize isogeny maps similar to those used in SIDH. Finally, the paper looks at an implementation of SIDH in PARI/GP and work is done to see the effects of using isogenies of degree greater than 2 and 3 on the security, runtime, and practicality of the algorithm.