### Deep Tissue Fluorescence Imaging with Time-Reversed Light

Ying Min Wang
Advances in optical techniques have enabled many breakthroughs in biology and medicine. However, light scattering by biological tissues remains a great obstacle, restricting the use of optical methods to thin ex vivo sections or superficial layers in vivo. In this thesis, we present two related methods that overcome the optical depth limit—digital time reversal of ultrasound encoded light (digital TRUE) and time reversal of variance-encoded light (TROVE). These two techniques share the same principle of...

### Dense, Efficient Chip-to-Chip Communication at the Extremes of Computing

Matthew Loh Rui Yan
The scalability of CMOS technology has driven computation into a diverse range of applications across the power consumption, performance and size spectra. Communication is a necessary adjunct to computation, and whether this is to push data from node-to-node in a high-performance computing cluster or from the receiver of wireless link to a neural stimulator in a biomedical implant, interconnect can take up a significant portion of the overall system power budget. Although a single interconnect...

### Dirac Spectra, Summation Formulae, and the Spectral Action

Kevin Kai-Wen Teh
Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and...

### Conditional Independence in Quantum Many-Body Systems

Isaac Hyun Kim
In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application,...

### Robot Navigation in Dense Crowds: Statistical Models and Experimental Studies of Human Robot Cooperation

Peter Trautman
This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused...

### Characterization of Exoplanet Atmospheres: Spectral Retrieval and Chemistry

Michael Robert Line
The study of exoplanets is rapidly evolving into an important and exciting field of its own. My investigations over the past half-decade have focused on understanding just a small sliver of what they are trying to tell us. That small sliver is their atmospheres. Atmospheres are the buffer between the bulk planet and the vacuum of space. The atmosphere is an important component of a planet as it is the most readily observable and contains...

### Topics in Gravitational-Wave Science: Macroscopic Quantum Mechanics and Black Hole Physics

Huan Yang
The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics. Gravitational waves are "ripples of space-time", long predicted by general relativity....

### Mathematical Study of Complex Networks: Brain, Internet, and Power Grid

Somayeh Sojoudi
The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored,...

### Quantum Error Correction with Biased Noise

Peter Bernard Brooks
Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security. At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise...

### Capturing Protein Dynamics with Time-Resolved Luminescence Spectroscopy

Nicole Danielle Bouley Ford
The presented doctoral research utilizes time-resolved spectroscopy to characterize protein dynamics and folding mechanisms. We resolve millisecond-timescale folding by coupling time-resolved fluorescence energy transfer (trFRET) to a continuous flow microfluidic mixer to obtain intramolecular distance distributions throughout the folding process. We have elucidated the folding mechanisms of two cytochromes---one that exhibits two-state folding (cytochrome cb562) and one that has both a kinetic refolding intermediate ensemble and a distinct equilibrium unfolding intermediate (cytochrome c552). Our data...

### Reactions of Small Molecules Facilitated by Metal-Acceptor Interactions

Daniel Leif Migdow Suess
The role of metal-acceptor interactions arising from M–BR3 and M–PR3 bonding is discussed with respect to reactions between first-row transition metals and N2, H2, and CO. Thermally robust, S = 1/2 (TPB)Co(H2) and (TPB)Co(N2) complexes (TPB = tris(2- (diisopropylphosphino)phenyl)borane) are described and the energetics of N2 and H2 binding are measured. The H2 and N2 ligands are bound more weakly in the (TPB)Co complexes than in related (SiP3)M(L) complexes (SiP3 = tris(2- (diisopropylphosphino)phenyl)silyl). Comparisons within...

### Grain Growth in Protoplanetary Disks

Laura María Pérez Muñoz
The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the...

### Distributed Optimization in Power Networks and General Multi-agent Systems

Na (Lina) Li
The dissertation studies the general area of complex networked systems that consist of interconnected and active heterogeneous components and usually operate in uncertain environments and with incomplete information. Problems associated with those systems are typically large-scale and computationally intractable, yet they are also very well-structured and have features that can be exploited by appropriate modeling and computational methods. The goal of this thesis is to develop foundational theories and tools to exploit those structures that...

### Relative Mirror Symmetry and Ramifications of a Formula for Gromov-Witten Invariants

Michel van Garrel
For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of...

### Studying Conscious and Unconscious Vision with Functional Magnetic Resonance Imaging : the BOLD Promise

Julien Christian Roger Dubois
Waking up from a dreamless sleep, I open my eyes, recognize my wife’s face and am filled with joy. In this thesis, I used functional Magnetic Resonance Imaging (fMRI) to gain insights into the mechanisms involved in this seemingly simple daily occurrence, which poses at least three great challenges to neuroscience: how does conscious experience arise from the activity of the brain? How does the brain process visual input to the point of recognizing individual...

### On-Chip Integrated Label-Free Optical Biosensing

Jacob Benjamin Sendowski
This thesis investigates the design and implementation of a label-free optical biosensing system utilizing a robust on-chip integrated platform. The goal has been to transition optical micro-resonator based label-free biosensing from a laborious and delicate laboratory demonstration to a tool for the analytical life scientist. This has been pursued along four avenues: (1) the design and fabrication of high-$Q$ integrated planar microdisk optical resonators in silicon nitride on silica, (2) the demonstration of a high...

### Completions of ε-Dense Partial Latin Squares

A classical question in combinatorics is the following: given a partial Latin square $P$, when can we complete $P$ to a Latin square $L$? In this paper, we investigate the class of textbf{$epsilon$-dense partial Latin squares}: partial Latin squares in which each symbol, row, and column contains no more than $epsilon n$-many nonblank cells. Based on a conjecture of Nash-Williams, Daykin and H"aggkvist conjectured that all $frac{1}{4}$-dense partial Latin squares are completable. In this paper,...

### The Optoelectronic Swept-Frequency Laser and Its Applications in Ranging, Three-Dimensional Imaging, and Coherent Beam Combining of Chirped-Seed Amplifiers

Arseny Vasilyev
This thesis explores the design, construction, and applications of the optoelectronic swept-frequency laser (SFL). The optoelectronic SFL is a feedback loop designed around a swept-frequency (chirped) semiconductor laser (SCL) to control its instantaneous optical frequency, such that the chirp characteristics are determined solely by a reference electronic oscillator. The resultant system generates precisely controlled optical frequency sweeps. In particular, we focus on linear chirps because of their numerous applications. We demonstrate optoelectronic SFLs based on...

### Oxygen Isotopes and Volatiles in Martian Meteorite

Melanie Beth Channon
Oxygen isotopes were measured in mineral separates from martian meteorites using laser fluorination and were found to be remarkably uniform in both δ18O and Δ17O, suggesting that martian magmas did not assimilate aqueously altered crust regardless of any other geochemical variations. Measurements of Cl, F, H, and S in apatite from martian meteorites were made using the SIMS and NanoSIMS. Martian apatites are typically higher in Cl than terrestrial apatites from mafic and ultramafic rocks,...

### CMB as a Probe of New Physics and Old Times

Vera Gluščević
Cosmic birefringence (CB)---a rotation of photon-polarization plane in vacuum---is a generic signature of new scalar fields that could provide dark energy. Previously, WMAP observations excluded a uniform CB-rotation angle larger than a degree. In this thesis, we develop a minimum-variance--estimator formalism for reconstructing direction-dependent rotation from full-sky CMB maps, and forecast more than an order-of-magnitude improvement in sensitivity with incoming Planck data and future satellite missions. Next, we perform the first analysis of WMAP-7 data...

### Interacting Single Atoms with Nanophotonics for Chip-Integrated Quantum Network

Daniel James Alton
Underlying matter and light are their building blocks of tiny atoms and photons. The ability to control and utilize matter-light interactions down to the elementary single atom and photon level at the nano-scale opens up exciting studies at the frontiers of science with applications in medicine, energy, and information technology. Of these, an intriguing front is the development of quantum networks where N >> 1 single-atom nodes are coherently linked by single photons, forming a...

### Earth-Abundant Materials for Solar Hydrogen Generation

James Robert McKone
A critical challenge for the 21st century is shifting from the predominant use of fossil fuels to renewables for energy. Among many options, sunlight is the only single renewable resource with sufficient abundance to replace most or all of our current fossil energy use. However, existing photovoltaic and solar thermal technologies cannot be scaled infinitely due to the temporal and geographic intermittency of sunlight. Therefore efficient and inexpensive methods for storage of solar energy in...

### Coupled Effects of Mechanics, Geometry, and Chemistry on Bio-Membrane Behavior

Ha Thanh Giang
Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes. We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes....

### Earthquake Geology of Myanmar

Yu Wang
This thesis describes the active structures of Myanmar and its surrounding regions, and the earthquake geology of the major active structures. Such investigation is needed urgently for this rapidly developing country that has suffered from destructive earthquakes in its long history. To archive a better understanding of the regional active tectonics and the seismic potential in the future, we utilized a global digital elevation model and optical satellite imagery to describe geomorphologic evidence for the...

### Developing Peptide Based Capture Agents for Diagnostics and Therapeutics

Arundhati Nag
Iterative in situ click chemistry (IISCC) is a robust general technology for development of high throughput, inexpensive protein detection agents. In IISCC, the target protein acts as a template and catalyst, and assembles its own ligand from modular blocks of peptides. This process of ligand discovery is iterated to add peptide arms to develop a multivalent ligand with increased affinity and selectivity. The peptide based protein capture agents (PCC) should ideally have the same degree...

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