Equilibrium in dynamic economic models

The main theme running through these three chapters is that economic agents are often forced to respond to events that are not a direct result of their actions or other agents actions. The optimal response to these shocks will necessarily depend on agents' understanding of how these shocks arise. The economic environment in the first two chapters is analogous to the classic chain store game. In this setting, the addition of unintended trembles by the agents creates an environment better suited to reputation building. The third chapter considers the competitive equilibrium price dynamics in an overlapping generations environment when there are supply and demand shocks.

The first chapter is a game theoretic investigation of a reputation building game. A sequential equilibrium model, called the "error prone agents" model, is developed. In this model, agents believe that all actions are potentially subjected to an error process. Inclusion of this belief into the equilibrium calculation provides for a richer class of reputation building possibilities than when perfect implementation is assumed.

In the second chapter, maximum likelihood estimation is employed to test the consistency of this new model and other models with data from experiments run by other researchers that served as the basis for prominent papers in this field. The alternate models considered are essentially modifications to the standard sequential equilibrium. While some models perform quite well in that the nature of the modification seems to explain deviations from the sequential equilibrium quite well, the degree to which these modifications must be applied shows no consistency across different experimental designs.

The third chapter is a study of price dynamics in an overlapping generations model. It establishes the existence of a unique perfect-foresight competitive equilibrium price path in a pure exchange economy with a finite time horizon when there are arbitrarily many shocks to supply or demand. One main reason for the interest in this equilibrium is that overlapping generations environments are very fruitful for the study of price dynamics, especially in experimental settings. The perfect foresight assumption is an important place to start when examining these environments because it will produce the ex post socially efficient allocation of goods. This characteristic makes this a natural baseline to which other models of price dynamics could be compared.

Financial equilibrium, voting procedures, and coalition structures in allocational mechanisms

This thesis is comprised of three chapters, each of which is concerned with properties of allocational mechanisms which include voting procedures as part of their operation. The theme of interaction between economic and political forces recurs in the three chapters, as described below.

Chapter One demonstrates existence of a non-controlling interest shareholders' equilibrium for a stylized one-period stock market economy with fewer securities than states of the world. The economy has two decision mechanisms: Owners vote to change firms' production plans across states, fixing shareholdings; and individuals trade shares and the current production / consumption good, fixing production plans. A shareholders' equilibrium is a production plan profile, and a shares / current good allocation stable for both mechanisms. In equilibrium, no (Kramer direction-restricted) plan revision is supported by a share-weighted majority, and there exists no Pareto superior reallocation.

Chapter Two addresses efficient management of stationary-site, fixed-budget, partisan voter registration drives. Sufficient conditions obtain for unique optimal registrar deployment within contested districts. Each census tract is assigned an expected net plurality return to registration investment index, computed from estimates of registration, partisanship, and turnout. Optimum registration intensity is a logarithmic transformation of a tract's index. These conditions are tested using a merged data set including both census variables and Los Angeles County Registrar data from several 1984 Assembly registration drives. Marginal registration spending benefits, registrar compensation, and the general campaign problem are also discussed.

The last chapter considers social decision procedures at a higher level of abstraction. Chapter Three analyzes the structure of decisive coalition families, given a quasitransitive-valued social decision procedure satisfying the universal domain and ITA axioms. By identifying those alternatives X* ⊆ X on which the Pareto principle fails, imposition in the social ranking is characterized. Every coaliton is weakly decisive for X* over X~X*, and weakly antidecisive for X~X* over X*; therefore, alternatives in X~X* are never socially ranked above X*. Repeated filtering of alternatives causing Pareto failure shows states in X^n*~X^((n+1))* are never socially ranked above X^((n+1))*. Limiting results of iterated application of the *-operator are also discussed.

Complex behavior and perception in Drosophila emerges from iterative feedback-regulated reflexes

For a hungry fruit fly, locating and landing on a fermenting fruit where it can feed, find mates, and lay eggs, is an essential and difficult task requiring the integration of both olfactory and visual cues. Understanding how flies accomplish this will help provide a comprehensive ethological context for the expanding knowledge of their neural circuits involved in processing olfaction and vision, as well as inspire novel engineering solutions for control and estimation in computationally limited robotic applications. In this thesis, I use novel high throughput methods to develop a detailed overview of how flies track odor plumes, land, and regulate flight speed. Finally, I provide an example of how these insights can be applied to robotic applications to simplify complicated estimation problems. To localize an odor source, flies exhibit three iterative, reflex-driven behaviors. Upon encountering an attractive plume, flies increase their flight speed and turn upwind using visual cues. After losing the plume, flies begin zigzagging crosswind, again using visual cues to control their heading. After sensing an attractive odor, flies become more attracted to small visual features, which increases their chances of finding the plume source. Their changes in heading are largely controlled by open-loop maneuvers called saccades, which they direct towards and away from visual features. If a fly decides to land on an object, it begins to decelerate so as to maintain a stereotypical ratio of expansion to retinal size. Once they reach a stereotypical distance from the target, flies extend their legs in preparation for touchdown. Although it is unclear what cues they use to trigger this behavior, previous studies have indicated that it is likely under visual control. In Chapter 3, I use a nonlinear control theoretic analysis and robotic testbed to propose a novel and putative mechanism for how a fly might visually estimate distance by actively decelerating according to a visual control law. Throughout these behaviors, a common theme is the visual control of flight speed. Using genetic tools I show that the neuromodulator octopamine plays an important role in regulating flight speed, and propose a neural circuit for how this controller might be implemented in the flies brain. Two general biological and engineering principles are evident across my experiments: (1) complex behaviors, such as foraging, can emerge from the interactions of simple independent sensory-motor modules; (2) flies control their behavior in such a way that simplifies complex estimation problems.

Negative regulation of transcription factors by Srb10 cyclin-dependent kinase

The ubiquitin-dependent proteolytic pathway plays an important role in a broad array of cellular processes, inducting cell cycle control and transcription. Biochemical analysis of the ubiquitination of Sic1, the B-type cyclin-dependent kinase (CDK) inhibitor in budding yeast helped to define a ubiquitin ligase complex named SCF^cdc4 (for Skp1, Cdc53/cullin, F-box protein). We found that besides Sic1, the CDK inhibitor Far1 and the replication initiation protein Cdc6 are also substrates of SCF^cdc4 in vitro. A common feature in the ubiquitination of the cell cycle SCF^cdc4 substrates is that they must be phosphorylated by the major cell cycle CDK, Cdc28. Gcn4, a transcription activator involved in the general control of amino acid biosynthesis, is rapidly degraded in an SCF^cdc4-dependent manner in vivo. We have focused on this substrate to investigate the generality of the SCF^cdc4 pathway. Through biochemical fractionations, we found that the Srb10 CDK phosphorylates Gcn4 and thereby marks it for recognition by SCF^cdc4 ubiquitin ligase. Srb10 is a physiological regulator of Gcn4 stability because both phosphorylation and turnover of Gcn4 are diminished in srb10 mutants. Furthermore, we found that at least two different CDKs, Pho85 and Srb10, conspire to promote the rapid degradation of Gcn4 in vivo. The multistress response transcriptional regulator Msn2 is also a substrate for Srb10 and is hyperphosphorylated in an Srb10-dependent manner upon heat stress-induced translocation into the nucleus. Whereas Msn2 is cytoplasmic in resting wild type cells, its nuclear exclusion is partially compromised in srb10 mutant cells. Srb10 has been shown to repress a subset of genes in vivo, and has been proposed to inhibit transcription via phosphorylation of the C-terminal domain of RNA polymerase II. Our results suggest a general theme that Srb10 represses the transcription of specific genes by directly antagonizing the transcriptional activators.

Iridium and rhodium analogues of the Shilov cycle catalyst; and the investigation and applications of the Reduction-Coupled Oxo Activation (ROA) mechanistic motif towards alkane upgrading

This dissertation will cover several disparate topics, with the overarching theme centering on the investigation of organometallic C-H activation and hydrocarbon transformation and upgrading. Chapters 2 and 3 discuss iridium and rhodium analogues of the Shilov cycle catalyst for methane to methanol oxidation, and Chapter 4 on the recently discovered ROA mechanistic motif in catalysts for various alkane partial oxidation reactions. In addition, Chapter 5 discusses the mechanism of nickel pyridine bisoxazoline Negishi catalysts for asymmetric and stereoconvergent C-C coupling, and the appendices discuss smaller projects on rhodium H/D exchange catalysts and DFT method benchmarking.

Violence in the Medieval Church before the First Crusade

The attitude of the medieval church towards violence before the First Crusade in 1095 underwent a significant institutional evolution, from the peaceful tradition of the New Testament and the Roman persecution, through the prelate-led military campaigns of the Carolingian period and the Peace of God era. It would be superficially easy to characterize this transformation as the pragmatic and entirely secular response of a growing power to the changing world. However, such a simplification does not fully do justice to the underlying theology. While church leaders from the 5th Century to the 11th had vastly different motivations and circumstances under which to develop their responses to a variety of violent activities, the teachings of Augustine of Hippo provided a unifying theme. Augustine’s just war theology, in establishing which conflicts are acceptable in the eyes of God, focused on determining whether a proper causa belli or basis for war exists, and then whether a legitimate authority declares and leads the war. Augustine masterfully integrated aspects of the Old and New Testaments to create a lasting and compelling case for his definition of justified violence. Although at different times and places his theology has been used to support a variety of different attitudes, the profound influence of his work on the medieval church’s evolving position on violence is clear.

Synthesis, Oxidation and Photophysics of Perfluoroborated Tetrakis(pyrophosphito)diplatinate (II) and Density Functional Theory (DFT) Study of Electrochemical CO2 Reduction by Mn Catalysts

In the first part of this thesis (Chapters I and II), the synthesis, characterization, reactivity and photophysics of per(difluoroborated) tetrakis(pyrophosphito)diplatinate(II) (Pt(POPBF₂)) are discussed. Pt(POP-BF₂) was obtained by reaction of [Pt₂(POP)₄]^4- with neat boron trifluoride diethyl etherate (BF₃·Et₂O). While Pt(POP-BF₂) and [Pt₂(POP)₄]^4- have similar structures and absorption spectra, they differ in significant ways. Firstly, as discussed in Chapter I, the former is less susceptible to oxidation, as evidenced by the reversibility of its oxidation by I2. Secondly, while the first excited triplet states (T₁) of both Pt(POP-BF₂) and [Pt₂(POP)₄]^4- exhibit long lifetimes (ca. 0.01 ms at room temperature) and substantial zero-field splitting (40 cm^-1), Pt(POP-BF₂) also has a remarkably long-lived (1.6 ns at room temperature) singlet excited state (S₁), indicating slow intersystem crossing (ISC). Fluorescence lifetime and quantum yield (QY) of Pt(POP-BF₂) were measured over a range of temperatures, providing insight into the slow ISC process. The remarkable spectroscopic and photophysical properties of Pt(POP-BF₂), both in solution and as a microcrystalline powder, form the theme of Chapter II.

In the second part of the thesis (Chapters III and IV), the electrochemical reduction of CO₂ to CO by [(L)Mn(CO)₃]^- catalysts is investigated using density functional theory (DFT). As discussed in Chapter III, the turnover frequency (TOF)-limiting step is the dehydroxylation of [(bpy)Mn(CO)₃(CO₂H)]^0/- (bpy = bipyridine) by trifluoroethanol (TFEH) to form [(bpy)Mn(CO)₄]^+/0. Because the dehydroxylation of [(bpy)Mn(CO)₃(CO₂H)]^- is faster, maximum TOF (TOF_max) is achieved at potentials sufficient to completely reduce [(bpy)Mn(CO)₃(CO₂H)]⁰ to [(bpy)Mn(CO)₃(CO₂H)]^-. Substitution of bipyridine with bipyrimidine reduces the overpotential needed, but at the expense of TOF_max. In Chapter IV, the decoration of the bipyrimidine ligand with a pendant alcohol is discussed as a strategy to increase CO₂ reduction activity. Our calculations predict that the pendant alcohol acts in concert with an external TFEH molecule, the latter acidifying the former, resulting in a ~ 80,000-fold improvement in the rate of TOF-limiting dehydroxylation of [(L)Mn(CO)₃(CO₂H)]^-.

An interesting strategy for the co-upgrading of light olefins and alkanes into heavier alkanes is the subject of Appendix B. The proposed scheme involves dimerization of the light olefin, operating in tandem with transfer hydrogenation between the olefin dimer and the light alkane. The work presented therein involved a Ta olefin dimerization catalyst and a silica-supported Ir transfer hydrogenation catalyst. Olefin dimer was formed under reaction conditions; however, this did not undergo transfer hydrogenation with the light alkane. A significant challenge is that the Ta catalyst selectively produces highly branched dimers, which are unable to undergo transfer hydrogenation.

Real-World Social Cognition: Context Effects in Face and Threat Processing

As borne out by everyday social experience, social cognition is highly dependent on context, modulated by a host of factors that arise from the social environment in which we live. While streamlined laboratory research provides excellent experimental control, it can be limited to telling us about the capabilities of the brain under artificial conditions, rather than elucidating the processes that come into play in the real world. Consideration of the impact of ecologically valid contextual cues on social cognition will improve the generalizability of social neuroscience findings also to pathology, e.g., to psychiatric illnesses. To help bridge between laboratory research and social cognition as we experience it in the real world, this thesis investigates three themes: (1) increasing the naturalness of stimuli with richer contextual cues, (2) the potentially special contextual case of social cognition when two people interact directly, and (3) a third theme of experimental believability, which runs in parallel to the first two themes. Focusing on the first two themes, in work with two patient populations, we explore neural contributions to two topics in social cognition. First, we document a basic approach bias in rare patients with bilateral lesions of the amygdala. This finding is then related to the contextual factor of ambiguity, and further investigated together with other contextual cues in a sample of healthy individuals tested over the internet, finally yielding a hierarchical decision tree for social threat evaluation. Second, we demonstrate that neural processing of eye gaze in brain structures related to face, gaze, and social processing is differently modulated by the direct presence of another live person. This question is investigated using fMRI in people with autism and controls. Across a range of topics, we demonstrate that two themes of ecological validity — integration of naturalistic contextual cues, and social interaction — influence social cognition, that particular brain structures mediate this processing, and that it will be crucial to study interaction in order to understand disorders of social interaction such as autism.

Imidazolium-Based Organic Structure Directing Agents for the Synthesis of Microporous Materials

The central theme of this thesis is the use of imidazolium-based organic structure directing agents (OSDAs) in microporous materials synthesis. Imidazoliums are advantageous OSDAs as they are relatively inexpensive and simple to prepare, show robust stability under microporous material synthesis conditions, have led to a wide range of products, and have many permutations in structure that can be explored. The work I present involves the use of mono-, di-, and triquaternary imidazolium-based OSDAs in a wide variety of microporous material syntheses. Much of this work was motivated by successful computational predictions (Chapter 2) that led me to continue to explore these types of OSDAs. Some of the important discoveries with these OSDAs include the following: 1) Experimental evaluation and confirmation of a computational method that predicted a new OSDA for pure-silica STW, a desired framework containing helical pores that was previously very difficult to synthesize. 2) Discovery of a number of new imidazolium OSDAs to synthesize zeolite RTH, a zeolite desired for both the methanol-to-olefins reaction as well as NOX reduction in exhaust gases. This discovery enables the use of RTH for many additional investigations as the previous OSDA used to make this framework was difficult to synthesize, such that no large scale preparations would be practical. 3) The synthesis of pure-silica RTH by topotactic condensation from a layered precursor (denoted CIT-10), that can also be pillared to make a new framework material with an expanded pore system, denoted CIT-11, that can be calcined to form a new microporous material, denoted CIT-12. CIT-10 is also interesting since it is the first layered material to contain 8 membered rings through the layers, making it potentially useful in separations if delamination methods can be developed. 4) The synthesis of a new microporous material, denoted CIT-7 (framework code CSV) that contains a 2-dimensional system of 8 and 10 membered rings with a large cage at channel intersections. This material is especially important since it can be synthesized as a pure-silica framework under low-water, fluoride-mediated synthesis conditions, and as an aluminosilicate material under hydroxide mediated conditions. 5) The synthesis of high-silica heulandite (HEU) by topotactic condensation as well as direct synthesis, demonstrating new, more hydrothermally stable compositions of a previously known framework. 6) The synthesis of germanosilicate and aluminophosphate LTA using a triquaternary OSDA. All of these materials show the diverse range of products that can be formed from OSDAs that can be prepared by straightforward syntheses and have made many of these materials accessible for the first time under facile zeolite synthesis conditions.

Formal methods in the foundations of science

The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism.

A general definition of a formal language is presented, and this definition is used to characterize an individual’s view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence.

To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed.

An a priori probability defined on sets of observations is postulated as a reflection of an individual’s ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing an individual’s conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible – particularly in the case of scientific experimentation.

The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented, and the problems of reductionism are examined in this context.

A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language.

The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual’s selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined.