• Preface
• Acknowledgements
• Part I. Why Sequoia? Why Sequoyah?
• Part II. The twenty-first century counterfactual arguments
• Part III. Sequoia and Sequoyah
• Appendix A. The science of Endlicher's times in the Austrian empire
• Appendix B. Tables listing genera named by Endlicher
• Appendix C. Endlicher's description of the genus Sequoia in Synopsis conferarum
• References.

Since the publication of Gary D. Lowe's "How the Sequoias Were Named" in 2013, attempts by others to falsify the theory that Endlicher named the genus Sequoia from a derivative of the Latin verb "sequor", based on his having classified the genus, along with four other genera, as following a precise recursive numerical sequence of the median number of seeds per cone scale has resulted in additional historical research that recovered hitherto unidentified information. By necessity, "Debunking the Sequoia honoring Sequoyah Myth" is a new book and not a second edition of the earlier work.

In this dissertation, I propose novel approaches to causal inference in the settings characterized by an explicit clustering structure. I study different aspects of this problem, considering settings with few large clusters as well as with many small clusters. The dissertation consists of two essays. The first essay proposes a new model for causal inference in the settings with few large clusters and cluster-level treatment assignment. The second essay studies causal inference questions in the settings with many clusters of moderate size and individual-level treatment assignment. In the first essay, I construct a nonlinear model for causal inference in the empirical settings where researchers observe individual-level data for few large clusters over at least two time periods. It allows for identification (sometimes partial) of the counterfactual distribution, in particular, identifying average treatment effects and quantile treatment effects. The model is flexible enough to handle multiple outcome variables, multidimensional heterogeneity, and multiple clusters. It applies to the settings where the new policy is introduced in some of the clusters, and a researcher additionally has information about the pretreatment periods. I argue that in such environments we need to deal with two different sources of bias: selection and technological. In my model, I employ standard methods of causal inference to address the selection problem and use pretreatment information to eliminate the technological bias. In case of one-dimensional heterogeneity, identification is achieved under natural monotonicity assumptions. The situation is considerably more complicated in case of multidimensional heterogeneity where I propose three different approaches to identification using results from transportation theory. The second essay is co-authored with Guido Imbens. We develop a new estimator for the average treatment effect in the observational studies with unobserved cluster-level heterogeneity. We show that under particular assumptions on the sampling scheme the unobserved confounders can be integrated out conditioning on the empirical distribution of covariates and policy variable within the cluster. To make this result practical we impose a particular exponential family structure that implies that a low-dimensional sufficient statistic can summarize the empirical distribution. Then we use modern causal inference methods to construct a novel doubly robust estimator. The proposed estimator uses the estimated propensity score to adjust the familiar fixed effect estimator.

This thesis consists of three essays, which examine several problems in active asset management and financial intermediation. The first essay demonstrates that skill and scale are significantly mismatched among actively managed equity mutual funds. The second essay models dealer balance sheet costs that arise from debt-overhang, and shows how these balance sheet costs affect valuation, pricing, and liquidity in dealer-intermediated market. The third essay shows that the funding costs to derivatives dealers' shareholders for carrying and hedging dealing inventory have an economically important impact on derivatives prices. An implication is that some supposed ``no-arbitrage" pricing relationships, such as put-call parity, frequently break down. Specifically, the first essay demonstrates that skill and scale are mismatched among actively managed equity mutual funds. Many mutual fund investors behave as though they rely on the Capital Asset Pricing Model. They confuse the effects of fund exposures to other common factors with managerial skill. Actively managed mutual funds with positive factor-related past returns thus accumulate assets to the point that they significantly underperform. I also show that the negative aggregate benchmark-adjusted performance of all actively managed equity mutual funds is caused mainly by the poor performance of this small subset of oversized funds. I find that less skilled active fund managers are inclined to tilt their portfolios toward common factors in order to gather more flows and collect more fees. The second essay, co-authored with Leif Andersen and Darrell Duffie, demonstrates that the funding value adjustments (FVAs) of major dealers are debt-overhang costs to their shareholders. In order to maximize shareholder value, dealer quotations therefore adjust for FVAs. Our case examples include interest-rate swap FVAs and violations of covered interest parity. Contrary to current valuation practice, FVAs are not themselves components of the market values of the positions being financed. Current dealer practice does, however, align incentives between trading desks and shareholders. We also establish a pecking order for preferred asset financing strategies and provide a new interpretation of the standard debit value adjustment (DVA). The third essay shows how debt-overhang funding costs to derivatives dealers' shareholders for carrying and hedging inventory affect mid-market derivatives prices. An implication is that some supposed ``no-arbitrage" pricing relationships, such as options put-call parity, frequently break down. I also explore the implications for measuring the term structure of S& P 500 dividend risk premia.

Centuries before the modern conception of surveillance, medieval subjects imagined an entity that monitored their every move: Christ Pantokrator (Ruler of All). My dissertation, The Medieval Art of Fear, investigates how Byzantine image-makers constructed this all-seeing figure in three-dimensions and manipulated spaces in order to create immersive encounters with the fearsome image. Following the crisis of Byzantine Iconoclasm (726-843), the making and display of Christ Pantokrator structured the visual perception of absolute power. Dramatic poetry, rituals and theologies, replete with fear of the Last Judgment, established the modes through which the faithful would perceive the image. My study taps into this textual evidence as it engages in close analysis of how specific monuments and objects were embedded in public and private rituals that invoked this all-seeing figure. Ultimately this dissertation argues for the critical significance of the image of Christ Pantokrator to the study of fear as a visual, spatial and material experience.

Tumors often result from temporal and spatial dysregulation of developmental signaling pathways. A striking example is medulloblastoma, the most common malignant pediatric brain tumor. During normal cerebellar development, granule neuron precursors (GNPs) proliferate extensively in response to hedgehog (Hh) signaling before differentiating into granule neurons. Sustained Hh signaling in GNPs, due either to reduced function of pathway components that negatively regulate Hh signal transduction or to heightened function of activating Hh signal transducers, results in continued maintenance and division of precursor cells beyond the normal proliferative stage of development, and eventually to formation of a medulloblastoma. To better understand the molecular mechanisms driving proliferation in GNPs and medulloblastoma, I characterized changes in transcript, protein and protein phosphorylation at the beginning of the proliferative stage of GNP development (P1), at peak proliferation (P7) and in the first moments of differentiation (P14). The proliferative period of GNP development had few changes in transcript (<5% of all transcripts changed greater than 2-fold, of which 92% decreased), or protein abundance (<4% of all quantified proteins changed greater than 2-fold, 50% decreased). In contrast, GNP differentiation was accompanied by a moderate increase in transcription (<5% changed 2-fold, 86% of which increased) and widespread protein turn-over (31% of the entire proteome changed 2-fold or more, equally up and down). Notably, phosphorylation was highest at P7 (4.9% of the phosphorylation sites increased >2-fold between P1 and P7) but differentiation was accompanied by widespread dephosphorylation (21.4% of the phosphoproteome decreased > 2-fold). The medulloblastoma-like, peak proliferative stage of GNP development was characterized by high levels of phosphorylation of a specific set of proteins which become dephosphorylated upon differentiation. This suggests that increased activity of a particular kinase might played a role in proliferation of GNPs, and by inference, medulloblastoma. Protein kinase CK2 emerged as a driver of hundreds of phosphorylation events during the proliferative, medulloblastoma-like stage of GNP growth, including three of the eight genes commonly amplified in medulloblastoma. I found that CK2 is required for normal GNP proliferation due to its action on two late steps in Hh signal transduction: stabilizing the transcription factor Gli2 and promoting Gli2-regulated transcription. Treatment of highly aggressive human SHH MB cell lines with CK2 inhibitors resulted in a dose-dependent increase in cell death. Furthermore, treatment of medulloblastoma-bearing mice with CK2 inhibitors blocked growth of mouse medulloblastomas resistant to previous hedgehog inhibitors and resulted in longterm tumor regression. This work has now directly led to a phase 1/2 clinical trial investigating the use of the CK2 inhibitor CX-4945 for treatment of SHH medulloblastoma.

This dissertation examines the nature, frequency, and intensity of violent political conflict (stasis) in the c. 1,100 city-states (poleis) inhabited by the ancient Greeks between 500 and 301 BCE. Against existing scholarship, which conflates stasis with modern analogs like civil war, revolution, and internal war, I highlight the many ways in which stasis was a historically distinctive concept. I show that most poleis experienced stasis at an average rate of more than once per decade and that most staseis produced fewer than a dozen casualties. I also introduce new methods and new tools to overcome three of the most significant obstacles that face attempts to study Greek history on a panhellenic scale: the scarcity, ambiguity, and deep biases of the evidentiary record.

This thesis considers several learning problems where interaction between the end-user and the algorithm play an important role. The thesis is organized as follows. The first chapter provides background material on mechanism design and reinforcement learning, and discusses related work. This sets us up for the next three chapters, which cover our contributions. In the second chapter, we consider recommendation systems. Many recommendation algorithms rely on user data to generate recommendations. However, these recommendations also affect the data obtained from future users. We aim to understand the effects of this dynamic interaction. We propose a simple model where users with heterogeneous preferences arrive over time. Based on this model, we prove that naive estimators, i.e. those which ignore this feedback loop, are not consistent. We show that consistent estimators are efficient in the presence of myopic agents. Our results are validated using simulations. In the third chapter, we consider a platform that wants to learn a personalized policy for each user, but the platform faces the risk of a user abandoning the platform if they are dissatisfied with the actions of the platform. For example, a platform is interested in personalizing the number of newsletters it sends, but faces the risk that the user unsubscribes forever. We propose a general thresholded learning model for scenarios like this, and discuss the structure of optimal policies. We describe salient features of optimal personalization algorithms and how feedback the platform receives impacts the results. Furthermore, we investigate how the platform can efficiently learn the heterogeneity across users by interacting with a population and provide performance guarantees. In the fourth chapter, we propose a new experimentation framework for the setting where there are many hypotheses and observations are costly. In such scenario, it is important to internalize the opportunity cost of assigning a sample to an experiment. We fully characterize the optimal policy and give an algorithm to compute it. Furthermore, we provide a simple heuristic that helps understand the optimal policy. Simulations based on baseball batting average data demonstrate superior performance compared to alternative algorithms. We also discuss more general insights gained from this testing paradigm, such as the paradox of power; high-powered tests can lead to inefficient sampling.

We study problems of classification of Lagrangian embeddings of a torus in a symplectic 4-manifold. First we complete the proof of a claim that all Lagrangian tori in R^4 are isotopic. Next we present a construction of Lagrangian tori and Klein bottles in monotone S^2xS^2. Finally we show that all monotone tori may be produced from such a construction, and outline a new approach to the problem of finding the Hamiltonian isotopy classes of monotone tori in S^2xS^2.

This dissertation addresses the question of spatial organization in living systems, a fundamental problem in understanding the physics of living systems. The structure and layout of the cell plays a key role in biophysical processes such as force transduction, diffusion, transport, and signaling. Using bacteria as a model system, I will present two examples of how cells generate, exploit, and interact with the spatial organization of their intracellular and extracellular environments. First, at the single-cell scale, I will discuss how L-forms (spheroplast-like, cell-wall deficient bacteria) of Escherichia coli can recover their normal rod-like shape without a pre-existing template. I will give a detailed, quantitative characterization of the recovery process at the morphological, biochemical, and molecular level. I will also discuss how our study of L-forms led us to investigate the mechanical properties of the bacterial outer membrane. Finally, I will propose that cell-wall synthesis is regulated by the local shape of the cell, giving rise to a biophysical model for rod morphogenesis. Second, at the community scale, I will discuss the vast, diverse, and poorly understood microbial ecosystem that resides in our digestive systems. I will present a quantitative image analysis platform for measuring host-microbe and microbe-microbe association in fixed sections of the intestinal tract, and show how diet shifts drive changes in the organization of the gut microbiome in gnotobiotic mice. In particular, I will demonstrate that polysaccharide starvation thins the host mucus layer, drives bacteria closer to host tissue, and alters clustering of several bacterial taxa.

The ability to form a visual interpretation of the world from natural language is pivotal to human communication. Similarly, from a computational perspective, mapping descriptions of scenes to 3D geometric representations is useful in many areas such as robotics, interior design and even education. Text to 3D scene generation is a task which addresses this problem space. A user provides natural language as input and the output is a plausible 3D scene interpretation. This is a challenging domain connecting NLP and computer graphics. The few existing systems for generating 3D scenes from text are severely restricted in scope and robustness. The key challenge, and focus of this dissertation, is in incorporating prior knowledge which is essential for successfully generating 3D scenes from highly under-specified natural scene descriptions. Prior systems do not leverage such priors, requiring explicit and verbose language. This dissertation formalizes and decomposes the problem of text to 3D scene generation, and describes the implementation of a new text to scene framework that enables incorporation of priors learned from data. I propose viewing the problem as extracting a set of explicit constraints from input descriptions, combining them with learned common-sense priors for inferring implicit constraints, and then selecting objects and positioning them to satisfy the constraints and generate plausible scenes. To capture the basic semantics of a scene, I define the scene template representation which consists of the objects, their attributes, and relations between them. A given scene template, can be used to generate many matching scenes whose plausibility can be scored. I then define two subtasks: scene template parsing where templates are parsed from natural language, and scene inference where templates are expanded with additional objects and spatial constraints. From the expanded scene templates, my system grounds object references by selecting appropriate 3D models, and then computationally arranges the selected objects to satisfy spatial constraints and maximize plausibility. I then demonstrate how to extend the text to scene system to allow iterative refinement of the generated scenes using natural language commands to add, remove, replace, and manipulate objects. In building the text to scene framework presented here, I learn a set of common-sense priors using datasets of 3D models and scenes and evaluate their impact on the quality of generated 3D scenes. From the scene data, I collect several sets of priors: (1) object occurrence priors to determine what other objects should be present, (2) support and relative position priors to determine where objects are placed, and (3) attachment priors to determine how objects are attached. In addition, I collect a new dataset of 3D scenes corresponded with textual descriptions and use it to learn how to ground spatial relation language and object descriptions. I provide this dataset to the community and perform an empirical evaluation of the output of the system against manually designed scenes and simpler rule-based baselines. Using a perceptual evaluation study, I show that the system can generate high quality 3D scenes given natural language input. This initial step in connecting language with 3D geometry opens up many areas of research for bridging the gap between language, semantics and geometry.

• V. 1. Chapters 1-8
• v. 2A.
• Chapter 9
• v. 2B. Chapters 9-13.

A new Magnetic Resonance Imaging (MRI) technique was developed to measure the three-dimensional, time-averaged scalar concentration distributions in turbulent mixing applications. The diagnostic was initially developed and tested in a turbulent free shear layer experiment where it was validated using planar laser induced fluorescence (PLIF) experiments. The remainder of the study examined a three-dimensional mixing flow motivated by trailing edge film cooling of an aircraft gas turbine blade. A modern slotted trailing edge cutback geometry was added in which coolant was discharged from rectangular slots separated by tapered lands. Water, and water with copper sulfate were the working fluids, and the MR-based experiments were conducted at Reynolds numbers based on airfoil chord and bulk velocity from 100,000-250,000. The magnetic resonance concentration (MRC) technique was further refined in the film cooling apparatus to reduce the uncertainty to under 6.0% in concentration and to provide robust measurement of the surface concentration. Combined magnetic resonance velocimetry (MRV) and MRC measurements were acquired for a generic trailing edge cutback geometry. The effect of variations in the blowing ratio and Reynolds number were examined. Reynolds number was found to have no significant effect while the variations in blowing ratio produced relatively small changes. Combined MRV and MRC data sets were analyzed in detail for insight into the mean flow structures primarily responsible for rapid mixing of the mainstream and coolant flows. Longitudinal vortices formed inside the slot feed channels and at the edges of the lands played a critical role as did the separation bubble behind the slot lip. Three modifications to the breakout geometry were designed with the goal of minimizing the adverse effects of these flow structures. Performance improvements with the redesigned trailing edge geometries indicate as much as a 40% improvement in the averaged surface effectiveness using a non-dimensional performance parameter.

This thesis considers the numerical simulation of rigid and deformable bodies, as well as compressible fluids. We consider each of these types of simulations independently, and in particular we focus on what it takes to make these simulations both efficient and scalable. First, we develop a robust parallelized method for simulating cloth and we demonstrate simulations consisting of up to 2 million triangles. This added level of detail allows us to achieve high detailed folds and wrinkles. We propose a robust history-based repulsion/collision framework where repulsions are treated accurately and efficiently on a per time step basis. Distributed memory parallelism is used for both time evolution and collisions and we specifically address Gauss-Seidel ordering of repulsion/collision response. Next, we propose a method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. Our method is based on the pressure evolution equation, so it works for arbitrary equations of state, chemical species, etc. The relaxed CFL condition allows us to simulate shocks, contacts and rarefactions accurately while taking much larger time steps than before. Then, we turn to the simulation of rigid bodies, where we present an algorithm for conserving energy and momentum when advancing rigid body orientations. Furthermore, we develop a technique for clamping energy gain during contact and collisions. Together, these methods allow us to prevent energy increase during rigid body simulations, regardless of the time step size. This allows us to reduce the computation needed while still producing stable and physically plausible simulations. We also introduce a technique for fast and realistic fracture of rigid bodies using a novel collision-centered prescoring algorithm. Finally, we extend the use of energy preservation techniques to the simulation of deformable bodies, again with the goal of reducing the cost of these simulations. We propose a new spring that, in one spatial dimension, gives the exact solution regardless of the size of the time step chosen. In multiple spatial dimensions, the problem becomes nonlinear because the direction of the spring changes over time, and thus we propose an iterative approach. Then, we consider the simulation of more complicated elements such as triangles, tetrahedra, and finally full meshes and propose a novel technique that allows us to cut the iterative approach short and instead apply a final correction globally to the mesh.

Mixing processes in the ocean play a key role in controlling the large-scale circulation and energy distribution of the ocean. Internal tide-driven mixing is most important among the processes to mix the ocean interior. In the past decade, significant efforts have been made to understand tidal mixing processes. However, more details and better understanding are still required for some fundamental problems, such as the mechanisms that govern internal tide generation, radiation, and dissipation processes and the associated energy partitioning. This research aims to understand the energetics and dynamics of tidal mixing processes through both theoretical analysis and numerical simulations. The complete form of barotropic and baroclinic energy equations are derived and employed as the theoretical framework for analyzing the tidal energy budget. These equations provide a more accurate and detailed energy analysis because they include the full nonlinear and nonhydrostatic energy flux contributions as well as an improved evaluation of the available potential energy. This approach has been implemented in the hydrodynamic SUNTANS model, which is being employed to study the energetics of barotropic-to-baroclinic tidal conversion over complex bathymetry in the real ocean. Three-dimensional, high-resolution simulations of the barotropic and baroclinic tides in the Monterey Bay area are conducted using the SUNTANS model. A detailed analysis of the energy budget is performed to address the question of how the barotropic tidal energy is partitioned between local barotropic dissipation and local generation of baroclinic energy. After that, we then assess how much of this generated baroclinic energy is lost locally versus how much is radiated away and made available for open-ocean mixing. The mechanism of internal tide generation is investigated by examining the dependence of barotropic-to-baroclinic energy conversion on three nondimensional parameters, namely the steepness parameter, the tidal excursion parameter, and the Froude number. Finally, a simple parametric model is presented to estimate the barotropic-to-baroclinic energy conversion.

The number of reports per year on single-molecule imaging experiments has grown roughly exponentially since the first successful efforts to optically detect a single molecule were completed over two decades ago. Single-molecule spectroscopy has developed into a field that includes a wealth of experiments at room temperature and inside living cells. The fast growth of single-molecule biophysics has resulted from its benefits in probing heterogeneous populations, one molecule at a time, as well as from advances in microscopes and detectors. There is a need for new fluorophores that can be used for single-molecule imaging in biological media, because imaging in cells and in organisms require emitters that are bright and photostable, red-shifted to avoid pumping cellular autofluorescence, and chemically and photophysically tunable. To this end, we have designed and characterized fluorescent probes based on a class of nonlinear-optical chromophores termed DCDHFs. This dissertation describes various physical and optical studies on these emitters, from sensing local environment to photoactivation. Chapter 1 is a general introduction to fluorescence and single-molecule spectroscopy and imaging. Single-molecule experiments in living cells are discussed and probes used for such experiments are summarized and compared. Chapter 2 explores the basic photophysics of the DCDHF fluorophores and some general methods of measuring relevant spectroscopic parameters, including photostability. Chapter 3 discusses the various approaches we have taken to modify particular properties by changing the fluorophore's structure. We have redesigned the DCDHF fluorophore into a photoactivatable fluorogen--a chromophore that is nonfluorescent until converted to a fluorescent form using light--described in Chapter 4. Finally, a different, chemical route to fluorescence activation is presented in Chapter 5. The remainder of the Dissertation is the Appendix and a full Bibliography. The Appendix includes a table of photophysical parameter for DCDHF fluorophore, various protocols used in the experiments discussed, MatLab codes, and NMR spectra.