12023 research outputs found
Sort by
Efficiently Characterizing Games Consistent with Perturbed Equilibrium Observations
Get PDFIn this thesis, we study the problem of characterizing the set of games that are consistent with observed equilibrium play, a fundamental problem in econometrics. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem, for many classes of games and observation models of interest. Our approach provides a sharp, computationally efficient characterization of the extent to which a particular set of observations constrains the space of games that could have generated them. This allows us to solve a number of variants of this problem as well as to quantify the power of games from particular classes (e.g., zero-sum, potential, linearly parameterized) to explain player behavior.
We illustrate our approach with numerical simulations.</p
Development and Characterization of Catalytic Systems for Biomass-Derived Chemical Feedstocks
Get PDFHeterogeneous catalysis by Brønsted and/or Lewis acid sites isolated within microporous environments is a topic that is perpetually growing in scope and importance. While Brønsted acid sites in zeolites have been studied and applied extensively in the petrochemical industry, new opportunities for green processes based on renewable chemical feedstocks call for applications of new microporous materials that possess Lewis acid sites (e.g., zeotypes with framework Sn, Ti, Zr, or Hf). Characterization of such materials and the specific structures of the Lewis acid sites provides insights for rational catalyst design and application.
This work provides experimental evidence for the identities of the active sites in Sn-Beta zeotype for the 1,2-intramolecular hydride shift (1,2-HS) reaction that results in D-glucose isomerization to D-fructose, and for the 1,2-intramolecular carbon shift (1,2-CS) reaction that results in D-glucose isomerization to D-mannose. Specifically, by selective poisoning experiments, the partially-hydrolyzed, "open" Sn site is shown to be the active site for the 1,2-HS reaction. The participation of the proximal silanol of such an open Sn site in the 1,2-HS reaction is demonstrated thorough alkali-exchange experiments. Such experiments also reveal that the active site for the 1,2-CS reaction is an open Sn site with a cation-exchanged proximal silanol.
1,2-CS catalysts, in general, are shown to also catalyze retro-aldol reactions of hexoses at moderate temperatures (ca. 100 °C), and to be compatible with microporous 1,2-HS catalysts in tandem catalytic schemes that enable production of alkyl lactates.
Finally, the Lewis acidity of framework Zn in zincosilicate microporous materials is demonstrated through probe-molecule infrared spectroscopy. One such material is then shown to catalyze Diels-Alder cycloaddition-dehydration reactions of oxygenated furans and ethylene. To the best of our knowledge, these materials are the first heterogeneous catalysts reported to catalyze the direct formation of terephthalate esters from ethylene and dimethyl 2,5-furandicarboxylate with appreciable selectivity. </p
What Can We Infer About the Atmospheric Composition Within the South Coast Air Basin from Remote Sensing?
Get PDFTo observe a change in a gas (e.g., CO2) flux from an area, the change must exceed the error of the flux estimate. Changing bias could be misinterpreted as a change in flux, and should be avoided. Errors can arise in column CO2 (XCO2) retrievals, in mis-interpreting XCO2 variations, or in the models to estimate fluxes. My thesis work has focused on recognizing and quantifying these errors and biases.
The most widely-used ground-based observations of XCO2 are from the Total Carbon Column Observing Network (TCCON), which uses observations from similar spectrometers at high (0.02 cm-1) resolution. Within the past 5 years there has been increased use of portable, lower resolution (0.5 cm-1) spectrometers for focused, short-term campaigns. This thesis discusses sources of errors and biases in retrievals from these lower resolution spectrometers.
Previous error estimates for the TCCON were made by propagating various perturbations through the retrieval. These uncertainty estimates were about 0.2 % for CO2 and 0.4 % for CH4. A pair of portable 0.5 cm-1 resolution spectrometers were used to empirically diagnose the magnitude of bias among TCCON sites. Median estimates were about 0.1 %.
Column measurements have increased in popularity within the last 15 years because of their reduced sensitivity to the dry mole fractions (DMF) of gases near the surface. However, in the presence of a sharp gradient between the atmospheric mixed layer (ML) and free troposphere rapid changes in terrain may cause the ML height above ground level and XCO2 to vary significantly over a small area. This explains ~20-36 % of the difference in XCO2 between 2 sites (Caltech and JPL) within 10 km of each other in the South Coast Air Basin (SoCAB).
Dynamical models may have biases (e.g., in wind speed) compared to true atmospheric behavior. This may cause biases in flux estimates. An estimate of the SoCAB CO2 flux using readily available model data is higher than those reported by bottom-up methods, perhaps due to a high wind speed bias. The flux is also sensitive to sub-sampling, which highlights the need to filter out biased data and the benefits additional observations could provide.
Carbon dioxide is not the only radiative forcer---aerosols are the largest source of uncertainty on the global radiative forcing budget, and additional measurements may better constrain their impacts. Estimate of changes in aerosol optical depth (AOD) can be made using portable spectrometers. While these estimates are not highly accurate, they are a value-added product and may increase the understanding of atmospheric behavior.</p
Non-Canonical Amino Acid Mutagenesis of Position B28 In Insulin with Proline Analogs
Get PDFInsulin is a protein hormone that is crucial for maintaining the concentration of blood glucose in vivo and is used clinically as a drug for the treatment of diabetes.
Chapter I provides for an overview and background on the state of the art in insulin treatment of diabetes and the many attempts, over 95 years, to improve the pharmaceutically relevant properties of insulin and improve our understanding of the model globular protein.
Chapter II demonstrates the incorporation of hydroxyproline analogs into insulin and shares the discovery of insulin with enhanced stability and an accelerated kinetic rate of dissociation. We also provide the highest resolution structure deposited in the PDB of insulin in the T2 state and the 3rd highest of any insulin to date.
Chapter III extends the incorporation of proline analogs in insulin to include fluorinated insulins. We also provide, for the first time, high-resolution structures of a single globular protein systematically mutated with all possible stereoisomers of fluorination at the 4-position on a single proline residue (4S, 4R, di-substituted).
Chapter IV extends the incorporation of proline analogs in insulin to include ring variant analogs. We also provide, for the first time, high-resolution structures of globular proteins containing pipecolic acid, azetidine-2-carboxylic acid and 3,4 dehydroproline in the polypeptide chain.
Chapter V discusses the significance of the findings described herein and discusses future directions to undertake in further engineering insulin for improved characteristics.
This thesis describes a systematic approach, akin to medicinal chemistry, of altering a particular protein side chain by atomistic changes. I hope that the breadth of different amino acids incorporated into a single globular protein combined with the structural, functional, thermodynamic and kinetic information contained within this set of mutants will provide future protein engineers, computational protein designers and proline enthusiasts with a wealth of new information to be used to improve our understanding of proteins and predictive power.</p
The Rhetoric of Change
No full textThe early 20th century saw a plethora of declarations, proclamations, and calls to arms for change in China. Some authors, such as Mao Zedong, represented prominent political movements, while others, like Lu Xun, expressed their ideas in passing through a preface to a collection of short stories. Among these writers, some take a practical approach, reflecting a belief that revolution begins with concrete, tangible changes that will improve the lives of the common man. Others favor ideological appeal based on the assumption that true change comes from a fundamental shift in political structure or mindset. Each writer arrives at a rhetorical strategy based on whether he prioritizes unifying the people or inspiring a strong, independent China
Mathematical Results on Quantum Many-body Physics
Get PDFThe collective behavior exhibited by a large number of microscopic quantum particles is at the heart of some of the most striking phenomena in condensed matter physics such as Bose-Einstein condensation and superconductivity. Physicists and mathematicians have made great progress in understanding when and how these collective phenomena emerge through the interplay of particle statistics, particle interaction and the value of thermodynamic parameters like the temperature or the chemical potential. Due to the extreme complexity of realistic many-body systems, it is natural to introduce appropriate simplifications to render their analysis feasible. Three examples of such simplifications which have proven themselves as viable starting points for a fruitful and mathematically rigorous analysis of many-body systems are the following: (a) the study of integrable models; (b) the derivation of effective theories, valid on a macroscopic scale, from more fundamental microscopic theories under appropriate coarse-graining; and (c) the use of quantum information theory to understand general connections between correlation, entanglement and particle statistics.
In this thesis, we present mathematically rigorous results that were obtained in these three directions. (1) We prove anomalous quantum many-body transport in XY quantum spin chains for certain choices of the external magnetic field. The anomalous transport is described via new kinds of anomalous Lieb-Robinson bounds, including one of power-law type. We note that the XY spin chain is integrable as it can be mapped to free fermions via the non-local Jordan-Wigner transformation. (2) We derive effective macroscopic theories of Ginzburg-Landau type from the microscopic BCS theory of superconductivity in certain circumstances. We study the case of a multi-component order parameter for translation-invariant systems and the condensation of fermion pairs at zero temperature in a domain with a hard boundary. (3) We use techniques from quantum information-theory to derive bounds on the entropy of fermionic reduced density matrices, a measure of the entanglement inherent to a fermionic quantum state.</p
Development of a High-Throughput Protein Interaction Assay and its Applications
Get PDFProtein-protein interactions (PPIs) form the backbone for a vast array of biological processes in an organism, ranging from signal transduction to gene regulation to intercellular signaling. Therefore, mapping out protein interactomes has been a crucial and prolific area of scientific research. In recent years, much progress has been made in generating high throughput protein interaction data in a variety of organisms, including S. cerevisiae, C. elegans, and D. melanogaster, as well as in human cell culture. The strength of protein interactions varies widely, from almost irreversible assembly of complexes to highly transient interactions. Because of their diversity and complexity, a wide variety of methods have been used to study protein interactions. This includes such commonly-used assays like yeast two-hybrid, to mass spectrometry, ELISA, affinity pulldowns, etc.
Despite the plethora of assays and data sets generated for PPIs, interactions involving cell surface and secreted proteins (CSSPs) remains underrepresented in the results. This is due to the fact that CSSP interactions tend to have lower KDs (around the μM range), and are generally highly transient and difficult to perform using standard assays such as yeast two-hybrid. To circumvent these problems, we designed a high-throughput PPI assay with high sensitivity. To validate the effectiveness of the assay, we utilized it to probe for interactions among two families of Drosophila CSS proteins, the Beats and the Sides, to see if we could recapitulate known interactions and uncover new ones. We were able to recapitulate almost all of the known interactions, as well as discover three novel ones. Additionally, we also studied the expression patterns of members of the Beat and Side families in Drosophila embryos and larvae, as well as analyzed the effects of mutations of Side-VI and Beat-Vs in embryos.</p
Compressing Positive Semidefinite Operators with Sparse/Localized Bases
Get PDFGiven a positive semidefinite (PSD) operator, such as a PSD matrix, an elliptic operator with rough coefficients, a covariance operator of a random field, or the Hamiltonian of a quantum system, we would like to find its best finite rank approximation with a given rank. One way to achieve this objective is to project the operator to its eigenspace that corresponds to the smallest or largest eigenvalues, depending on the setting. The eigenfunctions are typically global, i.e. nonzero almost everywhere, but our interest is to find the sparsest or most localized bases for these subspaces. The sparse/localized basis functions lead to better physical interpretation and preserve some sparsity structure in the original operator. Moreover, sparse/localized basis functions also enable us to develop more efficient numerical algorithms to solve these problems.
In this thesis, we present two methods for this purpose, namely the sparse operator compression (Sparse OC) and the intrinsic sparse mode decomposition (ISMD). The Sparse OC is a general strategy to construct finite rank approximations to PSD operators, for which the range space of the finite rank approximation is spanned by a set of sparse/localized basis functions. The basis functions are energy minimizing functions on local patches. When applied to approximate the solution operator of elliptic operators with rough coefficients and various homogeneous boundary conditions, the Sparse OC achieves the optimal convergence rate with nearly optimally localized basis functions. Our localized basis functions can be used as multiscale basis functions to solve elliptic equations with multiscale coefficients and provide the optimal convergence rate O(hk) for 2k'th order elliptic problems in the energy norm. From the perspective of operator compression, these localized basis functions provide an efficient and optimal way to approximate the principal eigen-space of the elliptic operators. From the perspective of the Sparse PCA, we can approximate a large set of covariance functions by a rank-n operator with a localized basis and with the optimal accuracy. While the Sparse OC works well on the solution operator of elliptic operators, we also propose the ISMD that works well on low rank or nearly low rank PSD operators. Given a rank-n PSD operator, say a N-by-N PSD matrix A (n ≤ N), the ISMD decomposes it into n rank-one matrices Σni=1gigTi where the mode {gi}ni=1 are required to be as sparse as possible. Under the regular-sparse assumption (see Definition 1.3.2), we have proved that the ISMD gives the optimal patchwise sparse decomposition, and is stable to small perturbations in the matrix to be decomposed. We provide several applications in both the physical and data sciences to demonstrate the effectiveness of the proposed strategies.</p
Aspects of Definability for Equivalence Relations
Get PDFThis thesis will show that in the constructible universe L and set forcing extensions of L, there are no almost Borel reductions of the well-ordering equivalence relation into the admissibility equivalence relation and no Borel reductions of the isomorphism relation of any counterexample to Vaught's conjecture into the admissibility equivalence relation.
Let E be an analytic equivalence relation on a Polish space X with all classes Borel. Let I be a sigma-ideal on X such that its associated forcing of I-positive Borel subsets is a proper forcing. Assuming sharps of appropriate sets exist, it will be shown that there is an I-positive Borel subset of X on which the restriction of E is a Borel equivalence relation.
Assuming there are infinitely many Woodin cardinals below a measurable cardinal, then for any equivalence relation E in L(R) with all Borel classes and sigma-ideal I whose associated forcing is proper, there is an I-positive Borel set on which the restriction of E is Borel.</p