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A Biophysical Approach to Normalization and Trajectory Inference in Single-Cell RNA Sequencing Data Analysis
Single-cell genomics assays, particularly single-cell RNA sequencing that enables genome-wide profiling of gene expression, have been driven forward by a combination of technological and computational advances. While producing extraordinary large amounts of data for biological discovery, methods for mining results currently rely heavily on heuristics and lack of modeling has resulted in limited mechanistic biological insight. This thesis presents two models for normalization and trajectory inference in single-cell RNA sequencing analysis to demonstrate how biophysical modeling, when combined with principled statistical inference, can yield interpretable insights grounded in rigorous theoretical frameworks.
We begin by explaining the two cultures in single-cell RNA sequencing analysis. Next, we present the chemical master equation, which forms the theoretical foundation for biophysically informed stochastic models of gene expression, and explore an existing gap in developing uniform approximations over time under the large-volume limit. Returning to single-cell RNA sequencing data analysis, we introduce two mechanistic models for normalization and trajectory inference, which are essential components of single-cell RNA sequencing analysis.</p
Spatial Biology Tools to Accelerate and Refine Adeno-Associated Virus Engineering and Application
The transfer of exogenous genetic material into living cells is a fundamental technique for basic research and, increasingly, for the treatment of human disease. Adeno-associated viruses (AAVs) are small, unenveloped viruses that can carry a limited DNA cargo of 4.4 kb (plus 0.3 kb inverted terminal repeats). These vectors are workhorses for in vivo gene transfer into mammalian systems, both for fundamental research and for therapeutic purposes. Natural serotypes of AAVs generally show broad tropism for easy to access tissues. Engineering of AAVs, through modification to the capsid surface and/or to the DNA genome, can enable access to otherwise privileged organs (e.g., brain) and can refine tropism to specific cell types (e.g., Purkinje cells of the cerebellum). Such engineering efforts can generate hundreds to thousands of interesting variants, but there is a dearth of high-throughput methods to characterize these variants. Furthermore, despite widespread usage, including in human patients, many questions on fundamental AAV biology remain unanswered.
In this thesis, I attempt to address some of these outstanding bottlenecks and open questions. In Chapter 2, I address the lack of high-throughput methods for broadly characterizing engineered AAV vectors in vivo, by developing and applying high-throughput spatial transcriptomics for AAV transcripts. In Chapter 3, I focus on understanding the biology of AAV genome processing, illuminated by novel spatial genomics methods. Using these novel methods, I then profile and mechanistically dissect transcriptional crosstalk between codelivered AAV vectors (Chapter 4). Finally, in Chapter 5, I address the limited packaging capacity of AAV vectors by leveraging AAV transcriptional crosstalk to enable minimally invasive, all-AAV cell type-specific gene editing in wildtype animals, with enough efficiency to recapitulate known phenotypes.
The work presented in this thesis will help to accelerate and refine AAV engineering and application. Furthermore, this thesis highlights potential confounds for AAV genome engineering, but also opens new avenues for AAV-powered functional genetics in mammalian systems.</p
Electrically Reconfigurable Optical Metasurfaces for Universal Wavefront Shaping
The ability to control the properties of light in a compact, reconfigurable platform is essential for advancing nanophotonic technologies. Active metasurfaces --- flat optical components with tunable subwavelength elements --- enable real-time manipulation of wavefronts and thus offer a path toward versatile optical systems. This thesis furthers the development of electrically programmable metasurfaces as a step toward a universal platform for independent and comprehensive wavefront control. By integrating system-level optimization strategies, novel operation modes, and advanced material platforms, we establish a framework for next-generation, on-demand optical processing components.
First, we introduce an array-level inverse design approach for beam steering metasurfaces, that co-optimizes the spatial amplitude and phase responses to enhance target functionalities. Using the platform of a plasmonic, indium tin oxide (ITO)-based active metasurfaces, we demonstrate non-intuitive configurations that achieve high-directivity, continuous-angle beam steering up to 70°. Experimental validation confirms the effectiveness of this approach, which we further extend to advanced applications including flat-top beams, tunable beam widths, and multi-beam steering.
To expand the functional channel capacity of active metasurfaces, we then explore space-time modulation as a means of enabling multi-frequency operation. By modulating ITO-based metasurfaces operating at near-infrared wavelengths with tailored waveforms at frequencies up to 10 MHz, we experimentally generate desired frequency harmonics, which appear as sidebands offset from the incident laser frequency. Introducing phase offsets between the driving waveforms enables tunable diffraction of frequency-shifted light. Theoretical extensions of this work highlight the potential of space-time metasurfaces to realize active multitasking components capable of dynamically performing multiple independent functions.
For improved efficiency and broadband operation, we investigate electro-optically tunable metasurfaces based on the Pockels effect in barium titanate (BTO). We develop a scalable fabrication technique to obtain high-quality, thin-film BTO via stress-induced exfoliation from single-crystal substrates, preserving its bulk electro-optic properties. The experimentally measured Pockels coefficient r₃₃ exceeds that of commercially available thin-film lithium niobate, demonstrating the potential of this material platform for integration into high-speed, low-loss optical metasurfaces. Leveraging these properties, we design transmissive BTO-based metasurfaces for high efficiency beam steering at visible wavelengths.
The results presented in this thesis lay the foundation for next-generation programmable metasurfaces by addressing key challenges in materials, design methodologies, and system-level control architectures. We conclude with a discussion of future directions, including the discovery of high-performance tunable materials, the development of advanced unit cell designs for independent control over multiple optical properties, and the miniaturization of control networks for large-scale metasurfaces. Ultimately, this work advances the development of reconfigurable and intelligent optical systems capable of adapting to diverse technological demands in a broad range of imaging, communication, and computing applications.</p
Materials and Interfaces to Enable Reversible Mg Electrochemistry for Energy Storage Applications
Climate change drives the need for a dramatically increased deployment of electric vehicles and intermittent renewable energy sources. Each of these depends intimately on batteries for range and reliability. Although Li-ion batteries are the current industry standard for electrochemical energy storage, they are based on scarce and unevenly distributed resources. It is thus crucial to develop rechargeable battery chemistries based on more energy dense and resource equitable materials. Orders of magnitude more abundant and energy dense than Li, Mg is an attractive alternative to Li for energy storage. Despite its many attractive properties, deployment of Mg-based chemistries is hindered by a lack of cathode, anode, and electrolyte materials which support Mg electrochemistry and are mutually compatible. This thesis endeavors to deploy new materials to sustain reversible Mg electrochemistry and to understand how certain material properties impact electrochemical performance. First, we investigate new cathode materials based on Earth-abundant transition metal chlorides. These cathodes cycle somewhat reversibly but are prone to rapid capacity fade due to active material dissolution and shuttle. We identify electrolyte modification as a means to combat this fade. Next, we characterize halide-free Mg electrolytes based on weakly coordinating Si-centered anions. These electrolytes display impressively high oxidative stabilities but also relatively high reductive overpotentials and a fatal vulnerability to passivation by H₂O. We then consider a class of electrolytes based on B-centered anions with aryl ligands. These systems show exceptionally low reductive overpotentials among halide-free Mg electrolytes. We increase the bulk of the anion and correspondingly observe a slight increase in the reductive overpotential and an enhancement in rate performance. Though this class of compounds shows a low oxidative stability, the structure-property relationships gleaned from it may prove useful in future electrolyte studies. Finally, we deploy Al as an Earth-abundant, high capacity alloying anode for Mg-based batteries. Though the native kinetics for Mg-Al alloying prove too sluggish for practical systems, we use Bi to enhance the alloying kinetics of Al by two orders of magnitude. Though alloying capacity is limited by a large particle size, we present a viable method for enhancing Al alloying kinetics to relevant rates, thereby unlocking a highly desirable material for future studies. Taken together, this work expands the scope of cathode, electrolyte, and anode materials which support reversible Mg electrochemistry. Though imperfect, the lessons we learn from them may inform future design decisions to enable reversible Mg-based batteries
Buoyancy-Driven Fluid Dynamics for Enhanced Ocular Drug Delivery
The CDC has identified vision loss as a growing public health concern, with eye disease prevalence on the rise. Three of the most common and vision-threatening eye diseases, wet age-related macular degeneration, proliferative diabetic retinopathy, and diabetic macular edema, are typically managed through periodic intravitreal injections. However, treatment effectiveness varies. Given that the half-life of the drug is limited, one possible cause of the ineffective treatment is inefficient delivery to the target region. This thesis investigates heat-induced convective flow in an in-vitro eye model as a method for enhancing drug delivery by accelerating fluid transport.
First, an optical distortion study was conducted to identify a vitreous model that matches both the viscosity of the human vitreous and the refractive index of the eye model. Next planar two-component and volumetric three-component flow visualization and measurement experiments capture the impact of thermal pad size on the resulting flow fields, with consideration given to particle trajectories for targeted delivery. Finally, a physics-informed neural network, trained on planar velocity data and tested against additional planes from volumetric measurements, demonstrates the potential for data-driven modeling to simplify future flow visualization experiments. The outcomes of this work further our fundamental understanding of fluid dynamics in the eye and encourage continued investigation into interdisciplinary approaches for improving drug delivery, and ultimately, patient outcomes.</p
Advancing Applications of Quantum Computers in Quantum Simulation, Optimization, Learning, and Topological Data Analysis
This thesis investigates novel directions for harnessing the potential of quantum computers in future applications. It is structured into three sections.
Quantum Simulation.
We address two key questions: what systems exhibit quantum advantage in predicting ground state properties, and how can we reduce the cost of quantum simulations? For the former, we find that strongly interacting fermionic systems have promising characteristics for quantum advantage. For the latter, we develop an improved method for compiling block encodings using sum-of-squares optimization.
Learning with Entangled Measurements.
We explore the benefits of leveraging entangled measurements on quantum states stored in quantum memory. These learning algorithms can be applied to the readout stage of quantum simulations, or to learn from quantum data from nature.
Topological Data Analysis.
Using complexity-theoretic insights, we demonstrate that certain problems in topological data analysis possess a quantum mechanical structure, suggesting opportunities for quantum algorithms in this area.</p
An "InCLOSE" View of the Circumgalactic Medium of z~2 Star-Forming Galaxies
This thesis focuses on using diffuse gas to investigate the galactic chemical evolution and circumgalactic medium of galaxies near the peak of cosmic star-formation rate density z ~ 2. There are many fundamental questions that remain unanswered about these processes due to the lack of large observational samples including what the typical yields of massive stars are, the interplay between diffuse circumgalactic and dense interstellar gas in terms of kinematic complexity, metal content, stellar mass, and star formation rate, and the evolution of circumgalactic gas over cosmic time. The common thread between each investigation is the use of QSO absorption line objects (QSO absorbers) to probe diffuse gas that otherwise would be unseen due to its diffusivity.
The chemical evolution of galaxies requires accounting for all sources of nucleosynthesis. During the earliest stages of galactic chemical evolution, the metal yields from core-collapse supernovae (CCSNe) are very important but acquiring empirical constraints is difficult because they cannot be easily disentangled from objects that currently exist because they have been enriched by some fraction of CCSNe and late time nucleosynthetic processes e.g., Type Ia SN. To address this, I used the metal abundances of very-metal poor (VMP; [Fe/H] <-2) Damped Lyman Alpha Absorbers (DLAs; QSO absorbers with high H I column density comparable to the interstellar medium, log(NHI/cm⁻² > 20.3) to place empirical constraints on the yields of low-metallicity CCSNe. I found that this approach is comparable to, and sometimes superior to, using abundances from the atmospheres of metal poor stars because of the model-independent nature of measuring abundances from dense, cold gas provided by the DLA.
It has been known in the literature that DLAs and other QSO absorbers have a variety of origins so I began an observational campaign to find galaxies associated with QSO absorbers that would allow detailed analysis of the circumgalactic medium (CGM) of z ~ 2 galaxies. This has historically been challenging at all z, but especially at z ~ 2 where, before this thesis, there were only nine galaxies with their inner CGM analyzed (within a projected distance of 100 kpc) and with characterized nebular emission and stellar population properties.
To this end, I am leading a survey that builds on the Keck Baryonic Structure Survey (KBSS) that aims to find close-in galaxy-QSO pairs to directly connect the Inner CGM of QSO Line Of Sight Emitting (InCLOSE) galaxies with their ISM. KBSS-InCLOSE relies on new observations that I have conducted using the twin Keck telescopes on Mauna Kea in Hawaii. I use the new optical integral field unit (rest-FUV at z ~ 2.3) called KCWI to discover new "InCLOSE" galaxies; obtain follow Keck/MOSFIRE near infrared (NIR) spectroscopy to confirm their redshifts and infer nebular properties including star-formation rate; use ground- and space-based optical and NIR images to infer stellar mass and age; and finally use high-resolution optical spectra of the KBSS QSOs to perform detailed analysis of CGM gas seen as absorption in the QSO spectra. The novelty of KBSS-InCLOSE goes beyond its large size (55 galaxies currently); the NIR spectra and images allow for the direct determination of galaxy properties, including stellar mass, which are rarely included in similar high-z surveys.
The first results from KBSS-InCLOSE showcased the tools and techniques required to remove the bright QSOs from the datacubes, images, and spectra to reveal new faint, close-in galaxy-QSO pairs. Particular focus was payed on the processing of the IFU data because it serves as the main driving instrument for the survey since it provides both images and spectra of each galaxy in the field. By analyzing their CGM absorption, I showed that a M=M*=10¹⁰ M☉ z=2.43 galaxy exhibited strong, multiphase, kinematically complex, and gravitationally unbound metals in its CGM. This has been seen before in previous studies and may suggest that a consensus picture of the CGM of z ~ 2.3, M* galaxies is emerging.
In KBSS-InCLOSE II, I focused on the first low-mass galaxies examined in the sample. I showed that the galaxies were star-forming, at the same redshift, and had sizes and masses consistent with dwarf galaxies, and found preliminary insights into the low-mass CGM that would make it distinct from both the massive CGM and low-mass local CGM suggesting that there may be strong evolution of the CGM across both stellar mass and redshift.
In Chapter \ref{chapter5_InCLOSEIII} I preview work that is yet to be completed, KBSS-InCLOSE III, where I examined the entire sample showing that the z ~ 2 CGM often shows strong of metal absorption, is likely clumpy, and multiphase, and that future IFU follow-up is necessary to find more galaxies, and NIR spectroscopic follow-up is necessary to secure redshifts to mitigate mismatches between galaxy's and absorbers.
Altogether, this thesis has laid fundamental groundwork towards expanding our understanding of the galaxy-scale baryon cycle of z ~ 2 star-forming galaxies by building the largest z ~ 2 close-in galaxy-QSO pair observational dataset thus far. It provides the data required to perform the most detailed examination of the connection between galaxies and their CGM during the peak epoch for galaxy formation.</p
Exploring Cell Diversity in Complex Tissues through Spatial Genomics and Spatial Transcriptomics
The study of cellular diversity is a fundamental requirement for understanding how multicellular organisms function. During the development of multicellular organisms, cells differentiate into various cell types with different molecular compositions, exhibit different phenotypes, and show distinct morphologies. Each single cell occupies a specific spatial location within different tissues and organs and performs a unique function. A holistic understanding of cells requires the integration of multiple “omics” modalities, including genomics, epigenomics, transcriptomics, and proteomics. Current well-established single-cell sequencing methods have been used to build enormous single-cell transcriptomic atlases. While single-cell sequencing methods are now capable of multi-omic profiling, they all require cell dissociation, during which important spatial context information is lost. To study cellular diversity within its native spatial context, our lab has developed innovative spatial genomics and transcriptomics tools that enable multi-omics profiling at single-cell resolution while preserving intact tissue organization. This thesis presents two projects that leverage these tools to investigate cellular diversity in complex tissues across different biological scales, from subnuclear to tissue-level organization. In Chapter 2, we applied spatial multi-omics to the mouse cerebellum, achieving single-cell resolution profiling of 100,049 genomic loci, 17,856 nascent transcripts, 60 mature mRNAs, and 28 immunofluorescently labeled subnuclear structures. To achieve this, we developed innovative two-layer barcodes for DNA sequential fluorescence in situ hybridization (seqFISH). Combining cell-type information from nascent and mature transcriptomes, we captured the three-dimensional genomic architecture and its interactions with subnuclear compartments in a cell-type-specific manner. Our findings show that repressive chromatin compartments have greater cell-type specificity than active chromatin compartments in the mouse cerebellum. In Chapter 3, we integrated single-cell multiome sequencing, which profiles single-nucleus RNA and chromatin accessibility (ATAC) from the same cells, with seqFISH spatial transcriptomics. This approach was applied to the 17- to 18-week-old human fetal kidney, targeting 224 marker genes. By combining sequencing and spatial profiling data, we constructed a comprehensive developmental atlas of human kidney organogenesis, providing new insights into the tissue organization and gene expression patterns during kidney development
Flocculation and Transport of Mud in Rivers and Deltas
Mud (grains < 62.5 μm) dominates the sediment load of rivers from continents to the ocean and contributes to building coastal land and sequestering organic carbon. However, predicting mud transport is challenging because flocculation causes mud grains to aggregate into larger, faster settling particles called flocs, which dynamically respond to local flow, water, and sediment properties. In this thesis, I examined the factors controlling mud flocculation in rivers and deltas and the effects of enhanced floc settling velocity on mud accretion in a river delta using fieldwork and data compilations from the river sediment literature. Flocs have the potential to dictate mud deposition rates and transport patterns by effectively enhancing mud settling velocity. First, I developed a semi-empirical model to predict floc diameter and settling velocity in rivers using a global river data compilation (Chapter 2). Results show that turbulence, sediment concentration and mineralogy, organic matter concentration, and water chemistry are the key flocculation factors in rivers. I conducted fieldwork in the Wax Lake Delta, Louisiana, a river delta in the Mississippi River Delta complex. Based on floc measurements at the Wax Lake Delta, I validated the semi-empirical model and showed that a complementary physics-based floc settling velocity model relies on the permeability and fractal structure of flocs (Chapter 3). To better link floc settling velocity and mud transport, I used the Wax Lake Delta field data to demonstrate that flocculated mud might behave as bed-material load rather than washload (Chapter 4). This result implies that mud concentration and flux might be readily predictable from bed-material entrainment theory using local bed and flow measurements. Connecting mud transport to delta island sedimentation and delta resilience, I analyzed discharge and sediment flux in the Wax Lake Delta to understand how sediment is delivered to and transported in islands (Chapter 5). Field data and backwater modeling results show that tall levees can block flow, but intricate feedbacks between flow depth, velocity, and water surface slope set discharge and sediment flux into the island once primary channels overflow into islands. Suspended mud settles fast enough relative to island flow depth and velocity to settle out within the island rather than bypass. As such, mud can accrete and build up the island over time as evidenced by mud-rich island deposits in Wax Lake Delta. Finally, combining Wax Lake Delta data and a river data compilation on suspended sediment grain size and mineralogy, I showed that most suspended sediment in rivers is flocculated silt (Chapter 6). This silt likely flocculates due to physical trapping mechanisms rather than typically considered interactions between clay minerals and salinity because clay minerals compose a minority of the silt. Overall, this thesis informs how flocculation affects mud transport in rivers and deltas, encompassing the mechanisms of mud flocculation, predictions of floc settling velocity and mud concentration, and the significance of mud flocculation in shaping depositional landscapes.</p
Machine Learning-Augmented Algorithms: Theory and Applications in Energy and Sustainability
Uncertainty poses a significant challenge for decision-makers in energy and sustainability domains. The ongoing energy transition—characterized by increasing penetrations of variable renewable generation, deployment of novel grid assets like battery energy storage systems, and growing risks from climate-driven natural disasters—introduces new, multifaceted uncertainties that traditional operational methods struggle to accommodate. While artificial intelligence (AI) and machine learning (ML) hold significant promise for navigating this transition and improving the efficiency of energy system operation, their direct deployment to high-stakes energy and sustainability problems presents substantial risks. In particular, current AI/ML tools typically lack guarantees on reliability, robustness, and safety, and thus pose a risk of poor performance or catastrophic failure if deployed in the real world. To make progress on decarbonization while maintaining reliability, new approaches are needed to enable the design of AI- and ML-augmented algorithms that achieve near-optimal performance while providing rigorous guarantees on robustness and reliability when deployed in real-world energy and sustainability problems.
This thesis addresses this challenge from two complementary perspectives, seeking to bridge the gap between theoretical algorithmic insights and practical impact. In the first part, we develop learning-augmented algorithms that integrate black-box AI/ML "advice" into online optimization problems while ensuring provable, worst-case performance guarantees. We propose algorithms for several classes of problems—including cases with convex costs, nonconvex costs, and long-term deadline constraints—that obtain the provably optimal tradeoff between exploiting good AI performance and worst-case robustness. We demonstrate these algorithms' ability to improve operational efficiency in energy and sustainability domains through case studies on cogeneration power plant operation under high renewables penetration and carbon-aware workload shifting for geographically-distributed datacenters.
In the second part of this thesis, we move beyond the "black box" model of AI/ML to explore how risk-awareness and reliability can be integrated as primary design criteria in AI/ML model training and algorithm development more generally. We consider this objective along several avenues, introducing new theoretical and methodological approaches for risk-aware optimization and uncertainty quantification, designing new mechanisms for pricing general forms of uncertainty in electricity markets, and developing new frameworks for training machine learning models with provable reliability guarantees. Throughout, we emphasize connections with and applications to energy and sustainability problems ranging from grid-scale battery storage operation to power grid contingency analysis. Together, these approaches highlight the challenges facing and benefits to risk- and reliability-aware learning and decision-making.</p