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Three Essays on Mechanism Design
Get PDFThis thesis addresses mechanism design problems in three different contexts.
Chapter 2 compares two widely used student assignment mechanisms, the deferred-acceptance algorithm (DA) and the Boston algorithm (BA), in the context of the Chinese College Admission System. Two features of this system separate the study in this chapter from previous studies. First, the maximal number of schools that a student can apply to is fixed, and is significantly smaller than the total number of schools nationwide. Second, schools’ preferences over applicants are not publicly observed. Under further assumptions, which include that applicants have the same preferences over schools and schools rank applicants by a common standard, I find that students are more likely to compete for seats at top schools under DA than BA. Furthermore, there are cases in which students’ over-competition of top schools under DA results in a less efficient outcome compared to BA.
Chapter 3 studies the mechanism design problem in a market where buyers have type-dependent outside options. Previous literature usually assumes that buyers obtain a fixed value if they do not participate in a sale. This chapter focuses on scenarios in which the value of the option outside of a particular sale varies across different types of buyers. In such a scenario, an optimal mechanism for selling a private-valued item to unit-demand buyers is a second-price auction, with either a reserve price or a fixed show-up fee. This mechanism induces segregation of the market: buyers with a type which values the item high enough will exercise their outside option.
Chapter 4 analyzes grant-issuing processes in a mechanism design framework. Applicants submit their proposals for projects that may not be carried out without external funds. The grant issuer makes a selection from the proposals and decides the amount to award each selected project within a budget. This chapter characterizes optimal mechanisms to efficiently allocate the grant-issuer’s budget. The optimal mechanism overcomes the problem of mis-allocation of the current merit-based mechanism. However, the problem of crowding-out private funds still stands. This chapter also shows how the specific formof institutional constraints—the flexibility of the budget constraint, and whether an applicant can reject a grant after being rewarded — affects the form of the optimal grant-issuing mechanism.</p
Glacial Ocean Dynamics: Insight from Deep-Sea Coral Reconstructions and A Time-Dependent Dynamical Box Model
Get PDFGlacial-interglacial cycles, occurring at a period of approximately 100,000 years, have dominated Earth's climate over the past 800,000 years. These cycles involve major changes in land ice, global sea level, ocean circulation, and the carbon cycle. While it is generally agreed that the ultimate driver of global climate is changes in insolation, glacial cycles do not look like insolation forcing. Notably, there is a highly non-linear warming response at 100,000 years to a relatively small forcing, implicating a more complicated system of biogeochemical and physical drivers. The ocean plays a pivotal role in glacial-interglacial climate through direct equator-to-pole transport of heat and its role in the carbon cycle. The deep ocean contains 60 times more carbon than the atmosphere, and therefore even small changes in ocean circulation can have a large impact on atmospheric CO2, a crucial amplifier in the climate system. In order to better understand the role that ocean circulation plays in glacial-interglacial climate we focus on the last glacial-interglacial transition. In this thesis, we present reconstructions of changes in intermediate water circulation and explore a new time-dependent dynamical box model. We reconstruct circulation using radiocarbon and clumped isotope measurements on U/Th dated deep-sea corals from the New England and Corner Rise Seamounts in the western basin of the North Atlantic and from south of Tasmania in the Indo-Pacific sector of the Southern Ocean. Our new time-dependent model contains key aspects of ocean physics, including Southern Ocean Residual Mean theory, and allows us to explore dynamical mechanisms which drive abrupt climate transitions during the last glacial period.
In Chapter 2 we present a compilation of reconnaissance dated deep-sea corals from the Caltech collection. Reconnaissance dating facilitates sample selection for our high-precision radiocarbon and temperature time series and patterns in the depth distribution of deep-sea corals over time contain additional relevant climate information. In Chapter 3, we present a high-resolution radiocarbon record from south of Tasmania which highlights variability in Southern Ocean Intermediate Water radiocarbon during the deglaciation, particularly during the Antarctic Cold Reversal. We use our radiocarbon data, in combination with other deglacial climate records, to infer changes in overturning circulation configuration across this time interval. In Chapter 4 we present our time-dependent dynamical box model. Our model displays hysteresis in basin stratification and Southern Ocean isopycnal outcrop position as a function of North Atlantic Deep Water formation rate. In a dynamical system, hysteresis implies that there are multiple stable states, and switches between these states can lead to abrupt transitions, such as those observed during the middle of the last glacial period. In Chapter 5 we present paired radiocarbon and temperature time series from the North Atlantic and Southern Ocean spanning the late part of the last glacial. We explore the mechanisms driving trends in radiocarbon and temperature by looking at cross-plots of the data, and we make inferences about changes in circulation configuration using insight gained from our dynamical box model.</p
Elucidating the Role of O-GlcNAc Glycosylation in Neurobiology and Neurodegeneration
Get PDFO-GlcNAc glycosylation is a dynamic, inducible post-translational modification (PTM) essential for neuronal homeostasis and found on proteins associated with neurodegenerative diseases such as α-synuclein, amyloid precursor protein, and tau. Intracellularly, O-GlcNAc modification is cycled by two enzymes in mammalian cells: O-GlcNAc transferase (OGT) appends O-GlcNAc to serine or threonine residues and O-GlcNAcase (OGA) removes O-GlcNAc. OGT modifies over 1000 different proteins, but the lack of a well-defined consensus sequence or substrate structural constraints has hampered efforts to predict sites a priori. Furthermore, the identification of O-GlcNAc modification sites has been obstructed by the difficulty of enriching and detecting O-GlcNAc using traditional biochemical methods. Here, we established and employed biological and chemical tools to illuminate the role of O-GlcNAc in neuronal function.
In Chapter 2, we sought to determine the role of O-GlcNAc in learning, memory, and neurodegeneration. Deletion of the OGT gene causes early postnatal lethality in mice, complicating efforts to study O-GlcNAc glycosylation in mature neuronal function and dysfunction. We demonstrated that the loss of OGT in the forebrain of adult mice (OGT cKO) leads to progressive neurodegeneration, including neuronal death, neuroinflammation, hyperphosphorylated tau, amyloidogenic Aβ-peptides, and memory deficits. In the hippocampus, we showed that OGT ablation lead to the upregulation of neuroinflammatory genes and the downregulation of cholesterol biosynthetic genes. Additionally, a gene network analysis (WGCNA), qPCR, and immunohistochemistry (IHC) revealed that loss of O-GlcNAc perturbed cell cycle progression in the hippocampal neurons. In the hippocampus, we identified increased neuroinflammatory gene transcription in OGT cKO mice and both tau neurofibrillary tangle (NFT)-forming and amyloid-forming Alzheimer’s disease (AD) mouse models. However, only OGT cKO and NFT-forming mice displayed decreased synaptic gene expression, suggesting that NFT formation and OGT cKO compromise hippocampal synaptic transcription. These studies indicate that O-GlcNAcylation regulates pathways vital for the maintenance of neuronal health and suggest that dysfunctional O-GlcNAc signaling may be an important contributor to neurodegenerative diseases.
In order to understand the critical O-GlcNAc-mediated neuronal functions that underlie OGT cKO dysfunction, we next developed and utilized novel biological and chemical tools in order to identify key OGT interactors and substrates in the brain in Chapter 3. Due to the lack of a well-defined OGT substrate sequence and structural constraints, OGT is believed to obtain its substrate specificity through its interactome where specific interactors target OGT to specific substrates. In order to identify these interactors, we used CRISPR/Cas9 to generate a novel mouse with a minimally tagged OGT in order to identify the endogenous OGT brain interactome using tandem affinity purification and MS methods. The preliminary OGT brain interactome consisted of previously identified OGT interactors and substrates as well as novel interactors. The identified OGT interactors were enriched for ribosomal and cytoskeletal proteins in addition to axonal, dendritic, and neuronal cell body proteins, implicating OGT as a pivotal mediator of neuronal structure and function.
In addition to the OGT interactome, we sought to uncover OGT’s substrates or the O-GlcNAcome. We developed an improved approach to quantitatively label and enrich O-GlcNAcylated proteins for site identification. Chemoenzymatic labeling followed by Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) installed a new MS-compatible linker designed for facile purification and release of O-GlcNAcylated proteins for downstream MS analysis. We validated the approach by identifying several established O-GlcNAc sites on the proteins α-crystallin and OGT as well as discovering new, previously unreported sites on both proteins. Notably, these novel sites on OGT lie in key functional domains of OGT, underscoring how this site identification method can reveal important biological insights into protein activity and regulation.
Finally, in Chapters 4 and 5, we focus on the post-translational modification (PTM) code on a specific transcription factor (TF), CREB (cAMP response element binding protein). CREB regulates memory formation through its transcriptional control of neuronal metabolism, activity, differentiation, development, and survival. CREB phosphorylation at serine 133 has been previously shown to enhance CREB-mediated transcription while CREB glycosylation at serine 40 has been shown to decrease CREB-mediated transcription. However, the exact gene networks modulated by and potential interplay between CREB glycosylation and phosphorylation have not been explored. Through differential expression analysis with glycosylation-deficient (S40A) and phosphorylation-deficient (S133A) CREB mutants, we showed that CREB O-GlcNAcylation is important for neuronal activity and excitability while phosphorylation at serine 133 regulated the expression of genes involved in neuronal differentiation. Using WGCNA, we demonstrated that CREB O-GlcNAcylation at serine 40 and phosphorylation at serine 133 mediate mutually exclusive gene networks. The glycosylation-deficient mutant enhanced neuronal activity- and excitotoxicity-related gene networks while the phosphorylation-deficient mutant perturbed neuronal differentiation and amino and fatty acid metabolism-related gene networks. Our work sheds light on the regulation of CREB through PTMs to modulate neuronal function and delineate the roles of O-GlcNAcylation and phosphorylation in modulating neuronal excitability and neuronal development and metabolism respectively. Altogether, these studies demonstrate that O-GlcNAc modification is a critical mediator of neuronal homeostasis and neurodegeneration.</p
The Biosynthesis of Ascarosides in Caenorhabditis elegans
Get PDFAscarosides comprise a family of small signaling molecules that have been shown to regulate important events and behaviors in the life history of the nematode Caenorhabditis elegans. Although the different roles of individual ascarosides appear to be determined by the variances in chemical structure, the mechanisms by which ascarosides are synthesized as well as the locations in which ascarosides are produced within the worm are largely unknown. In this thesis, we examined ascaroside production in the intestine, hypodermis, and body wall muscle of the worm by driving the expression of the protein DAF-22 under different tissue-specific gene promoters. While the body wall muscle and hypodermis are capable of synthesizing ascarosides, the intestine appears to be the major site of pheromone production. Additionally, we found through transgenic rescue and HPLC-MS analysis, that the acyl-CoA synthetase ACS-7 plays a significant role in the addition of moieties derived from primary metabolic pathways to the 4’-position of the ascarylose sugar core of ascr#9.</p
Visualizing mRNA Translation in situ in Single Cells
Get PDFTranslation of mRNA is tightly regulated in cells to ensure that proteins are synthesized at the right time, in the right location, and at appropriate levels. Single-molecule fluorescence in situ hybridization (smFISH) is a simple and widely used method to measure mRNA transcription through determining the abundance and localization of mRNAs in single cells. A comparable single-molecule in situ method to measure mRNA translation would enable a more complete understanding of gene regulation. In this thesis, we describe the development and characterization of a fluorescence assay to detect ribosome interactions with mRNA (FLARIM). The method adapts smFISH to visualize and characterize translation of single molecules of mRNA in fixed cells. To visualize ribosome-mRNA interactions, we use pairs of oligonucleotide probes that bind separately to ribosomes (via ribosomal RNA) and to the mRNA of interest, and that produce strong fluorescence signals via the hybridization chain reaction (HCR) when the probes are in close proximity. FLARIM does not require genetic manipulation, is applicable to practically any endogenous mRNA transcript, and provides both spatial and temporal information.
We first characterize FLARIM in mouse fibroblast cells. We show that FLARIM is sensitive to changes in ribosome association with mRNA upon inhibition of global translation with puromycin. We also show that FLARIM detects changes in ribosome association with an mRNA whose translation is upregulated in response to increased concentrations of iron. Finally, we demonstrate FLARIM in mouse hippocampal neurons, in which local translation of mRNA in the neuronal processes is essential to cell growth and development. We first demonstrate FLARIM in neurons using probes for β-actin mRNA. We then show that FLARIM detects increased transcription and translation of activity regulated cytoskeletal protein (Arc) mRNA in response to neuronal activation with brain-derived neurotrophic factor (BDNF). We also compare the cellular distribution between the major microtubule-associated protein 2 (MAP2) mRNA isoforms, whose translation will be characterized in future FLARIM experiments. Overall, this work expands the capability of smFISH to study mRNA translation in addition to transcription, and it shows the utility of in situ translation analysis in characterizing single-cell gene expression.</p
Exploring Exoplanets' Spectroscopic Secrets: Clues on the Migration and Formation of Hot Jupiters
Get PDFBefore the mid-90's, scientists' theories for planet formation were finely-tuned to explain the existence of our own Solar System. These theories were thrown into disarray when astronomers began to discover exoplanets, or planets in other solar systems. Forced to reconcile theory with observation, astronomers and planetary scientists have worked together for the past twenty years to solve the puzzles created by these thousands of exoplanets. One particularly intriguing group of newly-discovered planets were the hot Jupiters, planets the size of our Jupiter orbiting their host star every few days. This thesis details two observational campaigns that attempt to illuminate the origin and composition of hot Jupiters. Each project is powered by the NIRSPEC (Near-Infrared SPECtrometer) instrument located at Mauna Kea in Hawaii. The first project aims to determine the stellar multiplicity rate of hot Jupiter host stars. Such a metric can inform the migration histories of these planets. The second project treats a hot Jupiter and its host star as a spectroscopic binary. This treatment reveals the orbital elements and atmospheric composition of the hot Jupiter. The spectroscopic methods described in this thesis are small steps in the study of hot Jupiters and ultimately potentially habitable exoplanets
Tensor Network Representation of Many-Body Quantum States and Unitary Operators
Get PDFUnderstanding many-body quantum systems is one of the most challenging problems in contemporary condensed-matter physics. Tensor network representation of quantum states and operators are taking central stage in this pursuit and beyond. They prove to be a powerful numerical and conceptual tool, and indeed a new language altogether. This thesis investigates various aspects of these representations by focusing on two specific problems: the first half of the thesis is devoted to examining how 'stable' a tensor network representation is for two-dimensional quantum states with topological order, and the second half explores the representability of various unitary loop operators with tensor networks.
In the numerical usage of the tensor networks, the tensor is varied as to find the representation of the ground states of the given Hamiltonian. In chapter two and three of this thesis we show that such a numerical program for topological phases can be 'ill-posed'. We show that tensor network can be an unstable representation for a topological phase: even an infinitesimal variation in the representation results in the loss of topological order, completely or partially. We diagnose this problem by identifying the exact causes of this instability, and find that it is only tensor variations in certain directions that result in instability, because they result in the condensation of bosonic quasi-particles of the phase. Such unstable variations are characterized by two properties: (1) they can replace a tensor in the tensor network without making the network collapse, and (2) their presence in the network represents the presence of a non-trivial topological charge. We prove that the general tensor representation of all string-net models suffer with such instabilities. We propose an exact mathematical operator to project out all such unstable variations and show its efficacy for a few models by direct calculations. Such an operator can be useful in numerical programs involving such tensor representations. We also point out that such variations play a crucial role in simulating topological phase transitions and their presence can be vital in an accurate simulation.
In chapter four and five of this thesis we focus on the representability of unitary loop operators by tensor networks. Such operators not only provide an important tool in the study of dynamical process in one-dimensional systems, but also in understanding and classification of symmetry protected topological phases in two dimensions. To characterize all such operators, we find a necessary and sufficient condition for any loop tensor network operator of a given length to represent a unitary operator. In particular, it is shown that all unitary operators that map local operators to local operators (locality-preserving) can always be represented by a tensor network. Locality-preserving unitary loop operators are classified by a rational index called the GNVW index defined in Ref. [1] which measures how much information 'flows' along the loop. We define Rank-Ratio index for tensor network operators and show that it is completely equivalent to the GNVW index. Therefore, GNVW index of a unitary operator can be easily extracted from its tensor network representation. We find that, other than representing locality-preserving unitary maps, tensor networks can also represent unitary operators that map local operators to global (non-local) operators. These tensor network operators are found to have a long-ranged order similar to tensors that represent topological tensor network states in two dimensions.</p
Probing Microplastic Deformation in Metallic Materials
Get PDFMetallic materials deform through discrete displacement bursts that are commonly associated with abrupt dislocation activities, i.e. avalanches, during plastic flow. Dislocations might be active prior to the textbook yielding, but it is unclear whether these activities can be discerned as smaller strain events, i.e. microplasticity. Novel experimental approaches involving nanomechanical experiments are developed to detect and to quantify microplastic deformation that occurs during compression of micron- and sub-micron sized single crystalline copper nano-pillars. The experiment, focusing on metals’ pre-yield regime, reveals an evolving dissipation component in the storage and loss moduli that likely corresponds to a smooth transition from perfect elasticity to avalanche-dominated plastic deformation. This experimental investigation is corroborated by mesoscopic plasticity simulations, which apply to a minimal model that combines fast avalanche dynamics and slow relaxation processes of dislocations. The model's predictions are consistent with the microscopic experiments and provide constitutive relationship predicting microplastic crackling noise being upconverted by small stress perturbations. Another experimental investigation on unload-reload cyclic behavior of copper nano-pillars post yielding shows a decaying microplastic hysteresis with emergent power laws and scaling features, which signifies an ever-explored reversible-to- irreversible transitions in metal deformation, as seen in other nonequilibrium systems. To study microplasticity in macroscopic metallic samples, an instrument is custom-built based on Michelson interferometer and achieves unprecedented high displacement noise resolution of 10−14m/√Hz in the frequency range of 10 – 1000 Hz. The macroscopic experiment has resolved a driving-modulated microplastic noise in bulk cantilever steel samples under nominal elastic loading. The characteristics of the noise resemble those of the microplastic noise predicted from the micromechanical simulations developed from microscopic experiments
Integrated Ultra-High-Q Nonlinear Photonic Platform for On-Chip Optoelectronic Systems
Get PDFSilicon technology provided a concrete basis of the integrated microelectronics revolution, and it might usher disruptive advances in photonics again. An integrated photonic system can potentially revolutionize instrumentation, time standards, spectroscopy, and navigation. Driven by these applications, various high-Q platforms have emerged over the last decade. However, applications require to satisfy challenging combinations of ultra-high-Q (UHQ) cavity performance, monolithic integration, and nonlinear cavity designs: the monolithic integration of UHQ devices still remains elusive. In this thesis, an integrated UHQ microcavity is demonstrated for the first time. A silicon nitride waveguide is monolithically integrated with a silicon oxide cavity, and the integrated waveguide can provide nearly universal interface to other photonic devices. Significantly, this thesis discusses far beyond setting a new record for integrated Q factor: the integrated UHQ cavity provides functionality as soliton source with electronic-repetition-rates. Demonstration of low-pump-power soliton generation at 15 GHz was previously possible in only discrete devices but essentially required for integrated self-referenced comb, which can unlock new level of performance and scale in an optoelectronic system. In addition, nonlinear cavity design is another outstanding challenge towards a further development on the optoelectronic system, and will be discussed in this thesis. The dispersion-engineered platform can potentially tailor the spectral bandwidth of frequency comb, and extend the frequency comb to visible and ultraviolet band. Importantly, the design methods are directly transferable to the integrated platform
Numerical Methods for Fluid-Structure Interaction, and their Application to Flag Flapping
Get PDFThis thesis is divided into two parts. Part I is devoted to the development of numerical techniques for simulating fluid-structure interaction (FSI) systems and for educing important physical mechanisms that drive these systems’ behavior; part II discusses the application of many of these techniques to investigate a specific FSI system.
Within part I, we first describe a procedure for accurately computing the stresses on an immersed surface using the immersed-boundary method. This is a key step to simulating FSI problems, as the surface stresses simultaneously dictate the motion of the structure and enforce the no-slip boundary condition on the fluid. At the same time, accurate stress computations are also important for applications involving rigid bodies that are either stationary or moving with prescribed kinematics (e.g., characterizing the performance of wings and aerodynamic bodies in unsteady flows or understanding and controlling flow separation around bluff bodies). Thus, the method is first formulated for the rigid-body prescribed-kinematics case. The procedure described therein is subsequently incorporated into an immersed boundary method for efficiently simulating FSI problems involving arbitrarily large structural motions and rotations.
While these techniques can be used to perform high-fidelity simulations of FSI systems, the resulting data often involves a range of spatial and temporal scales in both the structure and the fluid and are thus typically difficult to interpret directly. The remainder of part I is therefore devoted to extending tools regularly used for understanding complex flows to FSI systems. We focus in particular on the application of global linear stability analysis and snapshot-based data analysis (such as dynamic mode decomposition and proper orthogonal decomposition) to FSI problems. To our knowledge, these techniques had not been applied to deforming-body problems in a manner that that accounts for both the fluid and structure leading up to this work.
Throughout part I, our methods are derived in the context of fairly general FSI systems and are validated using results from the literature for flapping flags in both the conventional configuration (in which the flag is pinned or clamped at its leading edge with respect to the oncoming flow) and the inverted configuration (in which the flag is clamped at its trailing edge). In part II, we apply many of the techniques developed in part I to uncover new physical mechanisms about inverted-flag flapping. We identify the instability-driving mechanism responsible for the initiation of flapping and further characterize the large-amplitude and chaotic flapping regimes that the system undergoes for a range of physical parameters.</p