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Riemannian Optimization for Convex and Non-Convex Signal Processing and Machine Learning Applications
Get PDFThe performance of most algorithms for signal processing and machine learning applications highly depends on the underlying optimization algorithms. Multiple techniques have been proposed for solving convex and non-convex problems such as interior-point methods and semidefinite programming. However, it is well known that these algorithms are not ideally suited for large-scale optimization with a high number of variables and/or constraints. This thesis exploits a novel optimization method, known as Riemannian optimization, for efficiently solving convex and non-convex problems with signal processing and machine learning applications. Unlike most optimization techniques whose complexities increase with the number of constraints, Riemannian methods smartly exploit the structure of the search space, a.k.a., the set of feasible solutions, to reduce the embedded dimension and efficiently solve optimization problems in a reasonable time. However, such efficiency comes at the expense of universality as the geometry of each manifold needs to be investigated individually. This thesis explains the steps of designing first and second-order Riemannian optimization methods for smooth matrix manifolds through the study and design of optimization algorithms for various applications. In particular, the paper is interested in contemporary applications in signal processing and machine learning, such as community detection, graph-based clustering, phase retrieval, and indoor and outdoor location determination. Simulation results are provided to attest to the efficiency of the proposed methods against popular generic and specialized solvers for each of the above applications
Superconductivity in Graphene Hetero-Structures: From Fundamental Physics to Functional Devices
Get PDFWhile graphene has been dubbed as a "wonder material" because of its amazing characteristics, such as the ability to conduct electricity better than copper and being two hundred times stronger than steel, until recently, the key quantum phenomenon of superconductivity was missing from the list of properties exhibited by graphene. In 2018, an astonishing discovery showed that by placing two sheets of graphene on top of each other in a structure known as Twisted Bilayer Graphene, it is possible to realize superconductivity when the rotation angle between the sheets is close to the "Magic Angle" value of 1.1°. More surprisingly, superconductivity in the initial reports was observed in close proximity to insulating states - resembling the phase diagram of High Tc superconductors. This sparked a fierce debate about its origin and its possible relation to High Tc superconductors. In this thesis, we show that by carefully engineering the dielectric environment of TBG, it is possible to stabilize superconductivity in non-magic angle TBG devices without the presence of any insulating states. This discovery imposes severe constraints on the origin of superconductivity in TBG. We also report, for the first time, the successful induction of spin-orbit coupling in TBG and discuss its implications.
Superconductivity can also be induced into graphene via coupling to conventional superconductors, and the strength of the induced supercurrent depends strongly on temperature. We employ this thermal dependence by integrating graphene into superconducting circuits that serves two purposes a) to investigate graphene's thermal behavior at milliKelvin temperatures and b) to utilize its extremely low heat capacity in making functional devices that have the potential to achieve ultra-high thermal sensitivity.</p
3D Microfluidics for Environmental Pathogen Detection and Single-cell Phenotype-to-Genotype Analysis
Get PDFThe emergence of microfluidic technologies has enabled the miniaturization of cell analysis processes, including nucleic acid analysis, single cell phenotypic analysis, single cell DNA and RNA sequencing, etc. Traditional chip fabrication via soft lithography cost thousands of dollars just in personnel training and capital cost. The design of these systems is also confined to two dimensions limited by their fabrication. To address the needs of smooth transition from technology to adoption by end-users, less complexity is urgently needed for microfluidics to be applied in pathogen detection under low-resource settings and more powerful integration of analyses to understand single cells. This dissertation presents my explorations in 3D microfluidics involving simulation-aided design of pretreatment devices for pathogen detection, fabrication through 3D printing, utilization of alternative commercial parts, and the combination with hydrogel material to link phenotypic analysis with in situ molecular detection for single cells. The main outputs of this dissertation are as follows:
1) COMSOL Multiphysics® was used to aid the design and understanding of microfluidic systems for environmental pathogen detection. In the development of an asymmetric membrane for concentration and digital detection of bacteria, the quantification requires Poisson distribution of cells into membrane pores; the flow field and particle trajectories were simulated to validate the cell distribution in capturing pores. In electrochemical bacterial DNA extraction, the hydroxide ion generation, species diffusion, and cation exchange were modeled to understand the pH gradient within the chamber. To address the overestimated risk by polymerase chain reactions (PCR) that detects all target nucleic acids regardless of cell viability, we developed a microfluidic device to carry out on-chip propidium monoazide (PMA) pretreatment. The design utilizes split-and-recombine (SAR) mixers for initial PMA-sample mixing and a serpentine flow channel containing herringbone structures for dark and light incubation. Ten SAR mixers were employed based on fluid flow and diffusion simulation. High-resolution 3D printing was used for prototyping. On-chip PMA pretreatment to differentiate live and dead bacterial cells in buffer and natural pond water samples was experimentally demonstrated.
2) Water-in-oil droplet-based microfluidic platforms for digital nucleic acid analysis eliminates the need for calibration that is required for qPCR-based environmental pathogen detection. However, utilizing droplet microfluidics generally requires fabrication of sub-100 µm channels and complicated operation of multiple syringe pumps, thus hindering the wide adoption of this powerful tool. We designed a disposable centrifugal droplet generation device made simply from needles and microcentrifuge tubes. The aqueous phase was added into the Luer-Lock of the commercial needle, with the oil at the bottom of the tube. The average droplet size was tunable from 96 μm to 334 μm and the coefficient of variance (CV) was minimized to 5%. For droplets of a diameter of 175 μm, each standard 20 μL reaction could produce ~10⁴ droplets. Based on this calculated compartmentalization, the dynamic range is theoretically from 0.5 to 3×10³ target copies or cells per μL, and the detection limit is 0.1 copies or cells per μL.
3) Based on the disposable droplet generation device, we further developed a novel platform that enables both high-throughput digital molecular detection and single-cell phenotypic analysis, utilizing nanoliter-sized biocompatible polyethylene glycol (PEG) hydrogel beads. The crosslinked hydrogel network in aqueous phase adds additional robustness to droplet microfluidics by allowing reagent exchange. The hydrogel beads demonstrated enhanced thermal stability, and achieved uncompromised efficiencies in digital PCR, digital loop-mediated isothermal amplification (dLAMP), and single cell phenotyping. The crosslinked hydrogel network highlights the prospective linkage of various subsequent molecular analyses to address the genotypic differences between cellular subpopulations exhibiting distinct phenotypes. This platform has the potential to advance the understanding of single cell genotype-to-phenotype correlations.
4) For effective sorting of the hydrogel beads after single cell phenotyping, a gravity-driven acoustic fluorescence-based hydrogel beads sorter was developed. The design involves a 3D-printed microfluidic tube, two sequential photodetectors, acoustic actuator, and a control system. Instead of bulky syringe pumps used in traditional cell or droplet sorting, this invention drives beads suspended in heavier fluorinated oil simply by buoyancy force to have the beads float through a vertical channel. Along the channel, sequential photodetectors quantify the bead acceleration and inform the action of downstream acoustic actuator. Hydrogel beads with different fluorescence intensity level were led into different collection chambers. The developed sorter promises cheap instrumentation, easy operation, and low contamination for beads sorting, and thus the full establishment of the single cell phenotype-genotype link.
In summary, the work in this dissertation established a) the simulation-aided design and 3D printing to reduce the complexity of microfluidics, and thus lowered its barrier for environmental applications, b) a simple and disposable device using cheap commercial components to produce monodispersed water-in-oil droplets to enable easy adoption of droplet microfluidics by non-specialized labs, c) a hydrogel bead-based analysis platform that links single-cell phenotype and genotype to open new research avenues, and d) a gravity-driven portable bead sorting system that may extend to a broader application of hydrogel microfluidics to point of care and point of sample collection. These simple-for-end-user solutions are envisioned to open new research avenues to tackle problems in antibiotic heteroresistance, environmental microbial ecology, and other related fundamental problems.</p
Role of the Ventral CA1 to Primary Auditory Cortex Projection in Associative Learning
No full textAs we understand more about individual brain regions, more studies begin to focus on how different regions communicate with each other. Having long been established as the center for learning and memory, the hippocampus has connections to most of neocortex as well as many subcortical regions. Some recent findings revealed that the hippocampus not only receive input from primary sensory cortices but also provide feedback projections to these areas. Do these projections play a role in sensory associative learning? Our project focused on the role of hippocampus to primary auditory cortex (A1) projections in auditory associative learning. Optogenetics was used to study the function of a direct projection from the ventral CA1 region of the hippocampus to primary auditory cortex (A1) in an auditory go/no-go task using head-fixed mice. Preliminary results show that activation of this projection does not affect task acquisition or generalization. Our next step is to investigate the effect of inhibiting the CA1 to A1 projections on auditory associative learning
Signatures of the r-Process in Ancient Stellar Populations Using Barium Abundances
Get PDFFor over sixty years scientists have known that a large percentage of heavy elements are created by the rapid neutron-capture process (r-process). However, a clear picture of where the r-process occurs has remained elusive. Many astrophysical origins have been proposed -- each with a range of possible chemical yields and rates. Discovering which origin (or combinations of origins) truly produce the heavy elements we see on Earth is a daunting task.
This thesis seeks to provide observational constraints to pinpoint the dominant origin of the r-process. The majority of this thesis uses Galactic Archaeology to look for r-process signatures in ancient stellar populations (e.g., dwarf galaxies and globular clusters). These ancient stellar populations provide the clearest "experiments" to observe how quickly and how much r-process was created. The r-process signature we observe is the amount of barium in individual red giant branch stars in these stellar populations. Chapter 2 discusses how these barium measurements are made from individual extragalactic stars and presents the largest catalog of barium abundances in dwarf galaxies to date.
Chapter 3 compares the r-process signature -- barium -- to other elements (e.g., magnesium and iron) in the same galaxy to see how the timescale of r-process enrichment compares to the other abundances (whose origins are known). This analysis found that the r-process timescale was more delayed than core-collapse supernovae. This points to neutron star mergers (NSMs) as the dominant source of r-process in the early history of dwarf galaxies.
Chapter 4 uses a galactic chemical evolution model to test what r-process timescales, yields, and rates are needed to recreate the observations presented in Chapter 2. Preliminary results indicate that NSMs must be included in order for the model to match the observations. In addition, Chapter 4 presents what yield of barium is needed from NSMs to recreate the observations.
Chapter 5 tests if the stars in the globular cluster M15 were enriched by the r-process after they were born. M15 has an unusual abundance pattern with ~ 1 dex variation in r-process abundances even though most other elements, including iron, do not show a variation. New measurements of barium abundances in main sequence and red giant branch stars of M15 show that the stars were born with their r-process enrichment. This means that an r-process event occurred quickly after the cluster was born -- while it was still forming stars -- and resulted in uneven enrichment.
Finally, Chapter 6 presents a solution to one of the technical challenges in locating the sites of r-process nucleosynthesis. Chapter 6 describes how to accurately measure the position and orientation of the CCDs in Zwicky Transient Facility's (ZTF's) camera. ZTF is a transient survey that -- among other science goals -- searches for the electromagnetic counterpart of NSM detections with LIGO. The work included in this chapter increased the survey efficiency of ZTF, which will aid ZTF in localizing transient events, including NSMs. Following up NSMs found by LIGO can provide direct measurements of the amount of r-process material created by NSMs.
Altogether, this thesis has made strides to identifying the origin of the r-process. Chapters 3 and 4 identify NSMs as the dominant source of r-process elements in dwarf galaxies. However, Chapter 5 found that globular cluster M15 needs a r-process event to occur quickly -- quicker than is typically expected from a NSM. The observational constraints that have resulted from this thesis provide important clues to where the heaviest elements are made.</p
Chemical and Physical Mechanisms of Calcite Dissolution in Seawater
Get PDFCalcium carbonates are among the most abundant and reactive minerals on Earth, and their dissolution/preservation in the ocean helps to regulate changes in atmospheric pCO2. The chemistry of the oceans has varied significantly over the past several billion years, and it is changing at an unprecedented rate today in response to anthropogenic burning of fossil fuels. The excess CO2 from human activities is acidifying the oceans and decreasing the saturation state (Ω = ([Ca2+][CO32-])/Ksp') of marine carbonates, increasing their propensity to dissolve. Despite its importance, the rate of carbonate dissolution in seawater is still described by a purely empirical expression, and the physical and chemical mechanisms setting the overall kinetics remain unknown. This stands in contrast to calcite dissolution in freshwater, where fully coupled surface-solution models have been identified. The lack of mechanistic understanding in seawater limits our ability to predict how carbonate dissolution kinetics, and therefore the buffering capacity of the ocean, are affected by changes in chemistry. This thesis advances our knowledge of the physical and chemical mechanisms responsible for carbonate dissolution by making new measurements in seawater both in the lab and in-situ.
I first probe the activation energy of the reaction in seawater by dissolving 13C-labeled CaCO3 across the full range of Ω at 5, 12, 21, and 37°C. I find that a surface-based framework is required to explain the strong non-linearity of the data near equilibrium. In this framework, dissolution proceeds by the retreat of pre-existing steps for 0.9<Ω<1, defect-assisted etch pit formation for 0.75<Ω<0.9, and homogenous etch pit formation for 0<Ω<0.75. I provide the first seawater estimates of kinetic coefficients (β), nucleation site densities (ns), and step edge free energies (α) for each mechanism, as well as the activation energy for detachment from steps (ϵstep) and the kinetic energy barrier to etch pit initiation (ϵinit).
Next, I use a custom designed in-situ reactor to measure calcite dissolution rates across a transect of the North Pacific. I find that the same surface mechanisms and "critical" Ωs identified in lab also govern the dissolution of calcite in the open ocean. In-situ dissolution rates are ~4x slower than in the lab, but I use a combination of chemical spike experiments and measurements in archived seawater to show that this discrepancy can be explained by the presence of dissolved organic carbon in-situ. I propose an empirical rate equation that describes all previous in-situ measurements of inorganic calcite dissolution rates.
Changes in the relation between dissolution rate and Ω can be explained by the activation of different surface processes, but the surface theory cannot account for much of the near-equilibrium dissolution behavior and temperature dependence. I therefore continue on in this thesis to combine the latest speciation models with dissolution measurements in artificial seawater of varying sulfate concentrations. I find that low sulfate solutions suppress dissolution rates by two orders of magnitude near equilibrium, while dissolution rates in the same solutions are enhanced far-from-equilibrium. Using these results, I fit a mechanistic model of dissolution that couples surface and solution processes. The model satisfies the principle of microscopic reversibility, provides an excellent estimate of calcite solubility product in seawater, and explains near equilibrium (Ω > 0.75) dissolution rates in 0, 14, and 28 mM [SO42-] seawater at 21°C. The model cannot explain dissolution rates for Ω < 0.75 when etch pits begin opening homogenously across the surface, so I suggest areas of improvement for future models.
Previous work has demonstrated that calcite dissolution rates are enhanced in the presence of the enzyme carbonic anhydrase (CA). In the final chapter of this thesis, I evaluate the mechanism of CA rate enhancement by comparing the catalytic effects of freely dissolved CA, CA immobilized within hydrogels, and CA chemically bound onto porous silica beads. At the same time, I design and test a fluidized bed reactor and demonstrate its efficacy as a carbon capture device by attaching it directly to the Caltech cogeneration power plant smokestack. I find that dissolution rates within the reactor are only enhanced when CA is freely dissolved, strongly suggesting that the catalytic mechanism is direct proton transfer from the enzyme to the calcite surface.</p
Wave-Scattering by Periodic Media
Get PDFThis thesis presents a full-spectrum, well-conditioned, Green-function methodology for evaluation of scattering by general periodic structures, which remains applicable on a set of challenging singular configurations, usually called Rayleigh-Wood (RW) anomalies, where most existing methods break down. After reviewing a variety of existing fast-converging numerical procedures commonly used to compute the classical quasi-periodic Green-function, the present work explores the difficulties they present around RW-anomalies and introduces the concept of hybrid "spatial/spectral" representations. Such expressions allow both the modification of existing methods to obtain convergence at RW-anomalies as well as the application of a slight generalization of the Woodbury-Sherman-Morrison formulae together with a limiting procedure to bypass the singularities. Although, for definiteness, the overall approach is applied to the scalar (acoustic) wave-scattering problem in the frequency domain, the approach can be extended in a straightforward manner to the harmonic Maxwell's and elasticity equations. Ultimately, the thorough understanding of RW-anomalies this thesis provides yields fast and highly-accurate solvers, which are demonstrated with a variety of simulations of wave-scattering phenomena by arrays of particles, crossed impenetrable and penetrable diffraction gratings, and other related structures. In particular, the methods developed in this thesis can be used to "upgrade" classical approaches, resulting in algorithms that are applicable throughout the spectrum, and it provides new methods for cases where previous approaches are either costly or fail altogether. In particular, it is suggested that the proposed shifted Green function approach may provide the only viable alternative for treatment of three-dimensional high-frequency configurations. A variety of computational examples are presented which demonstrate the flexibility of the overall approach, including, in particular, a problem of diffraction by a double-helix structure, for which numerical simulations did not previously exist, and for which the scattering pattern presented in this thesis closely resembles those obtained in crystallography experiments for DNA molecules.</p
Real-Time Biosensing and Energy Harvesting on Human Body
Get PDFThis thesis covers two technologies that can be applied to the human body for real-time applicable usages: biosensors and energy harvesters. The first part of the thesis describes optical biosensing techniques based on surface-enhanced Raman spectroscopy (SERS). Our large-scale spatially uniform Raman enhancing substrates allow low-level bio molecule detection due to their strong plasmonic enhancement of the 3D Au-NP clusters. This method also enables low-level insulin sensing as well as insulin concentration analysis in islet secretion. These results can lead to developing simple and easy biosensing methods allowing real-time biosensing applications including convenient monitoring of health, early disease detection, and diabetes-related clinical measurements.
The second part of the thesis suggests an energy harvesting method using vocal vibrations. The vocal folds produce mechanical vibrations that can serve as an energy source with consistent amplitude and frequency. The vibration hotspots exist at various locations on the human upper body. The energy harvesting system consisting of piezoelectric devices and energy harvesting circuits generates 3.99 mW of electrical power. The amount of energy generated from vocal vibrations is sufficient to charge a Li-Po battery which can drive an LCD display or charge Bluetooth headphones. This method demonstrating a relatively high power generation and convenience of practical use can provide a real-time complementary charging technique for wearable electronics like wireless headphones and smart glasses as well as medical implantable devices such as deep brain stimulators, cochlear implants and pacemakers.</p
Essays on Market Design and Industrial Organization
Get PDFThis dissertation contains three essays. They offer contributions to the study of matching in foster care (Chapters 1 and 2), and to the study of the effect of product market competition on managerial incentives (Chapter 3).
Chapter 1 presents an empirical framework to study the assignment of children into foster homes and its implications on placement outcomes. The empirical application uses a novel dataset of confidential foster care records from Los Angeles County, California. The estimates of the empirical model are used to examine policy interventions aimed at improving placement outcomes by increasing market thickness. If placements were assigned across all the administrative regions of the county, the model predicts that (i) the average number of foster homes children go through before exiting foster care would decrease by 8% and (ii) the distance between foster homes and children’s schools would be reduced by 54%.
Chapter 2 proposes and studies a dynamic model of centralized matching in foster care. The optimal matching policy is characterized by minimizing the number of children who remain unmatched in every period. The main finding is that the optimal matching policy gives priority to younger children. The model captures several dynamic trade-offs, most notably between children’s ages and the heterogeneity in the expected duration of placements. I also analyze federal data from the Adoption and Foster Care Analysis and Reporting System (AFCARS). I find that, in Los Angeles County, placements and their durations are strongly correlated with the race of children and their foster parents.
Chapter 3, co-authored with Kaniṣka Dam, develops an incentive contracting model under oligopolistic competition to study how incumbent firms adjust managerial incentives following deregulation policies that enhance competition. We show that firms elicit higher managerial effort by offering stronger incentives as an optimal response to entry, as long as incumbent firms act as production leaders. Our model draws a link between an industry-specific feature, the time needed to build production capacity, and the effect that product market competition has on executive compensation. We offer new testable implications regarding how this industry-specific feature shapes the incentive structure of executive pay.</p
Towards Atom Assembly on Nanophotonic Structures with Optical Tweezers
Get PDFThe integration of atomic physics and nanophotonics combines the best of two worlds. With atoms as the naturally existing qubits and nanophotonic devices as the engineered interaction medium, new frontiers can be explored for building novel quantum optical circuits for non-conventional quantum optics and exotic quantum many-body physics, as well as potentially serving as a fundamental building block for quantum computation and communication with neutral atoms. While important experimental milestones towards this goal have been reached, a grand challenge for experiments in this new field is the loading and trapping of atomic arrays with high fractional filling near complex nanophotonic structures. In this thesis, we have proposed a novel protocol for atom assembly on nanophotonic structures by integrating optical tweezer arrays and photonic crystal waveguides. This research is inspired by recent exciting progress in free-space atom assembly. However, different from the free-space counterpart, our new proposal should enable subwavelength atom arrays with complex patterns defined by precision nanofabrication. To demonstrate the basic principles behind this new proposal, we have designed and built an advanced apparatus with compact footprint that overcomes several significant experimental barriers in previous experiments. To achieve efficient atom delivery and assembly of arrays for more complex nanostructures, we have proposed a novel direct delivery scheme with optical tweezers by exploiting the rapid spatial variation of the Gouy phase of radial Laguerre-Gauss beams. With reduced dimension in the axial direction, the optical tweezer formed by supposed Laguerre-Gauss beams may find important applications in the communities of general atomic physics and super-resolution imaging. Finally, we have investigated the optomechanical properties of our nanophotonic devices for trapping atoms and evaluated potential heating mechanisms for trapped atoms. The studies presented in this thesis should provide important guidance to future atom-nanophotonic experiments.</p