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Facilitating Miniaturized Bioanalytical Assays in Microfluidic Devices
Get PDFThis work describes several efforts in making microfluidic lab-on-a-chip technology more convenient to use for bioanalysis in limited-resource settings (Chapters 2-3), and describes a device for miniaturized multistep process execution (Chapter 4). One underlying theme of these projects is the streamlining of the 'chip-to-world' interfacing to help bring this technology from specialized labs of its developers into more widespread utilization by potential users in other disciplines. Chapter 2 outlines a portable method for achieving stable fluid pumping for sample loading and flow control in microfluidic devices. Chapter 3 details a method for digital nucleic acid test readout with unmodified smartphone cameras. Chapter 4 demonstrates a lab-on-a-chip platform capable of carrying out complex multiplexed biochemical reactions requiring multiple sequential additions of reagents by performing RNA barcoding for multiplexed cDNA library generation.</p
Synthesis, Characterization, and Reactivity of Thiolate-Supported Metalloradicals
Get PDFReactive metalloradical intermediates have been implicated in both biological and synthetic catalyst systems for small molecule activation processes, including proton reduction and ammonia oxidation. Towards a greater mechanistic understanding of such transformations on well-defined model complexes, this thesis explores relevant H–H and N–N bond-forming reactions mediated by trivalent Fe and Ni species, as well as catalytic N–N bond cleavage mediated by an open-shell VFe bimetallic complex. First, a pair of thiolate-supported, S = ½ iron and nickel hydrides are synthesized and spectroscopically characterized at low temperatures (Chapters 2, 3). Paramagnetic iron and nickel hydrides have been proposed as catalytic intermediates of [NiFe] hydrogenase and nitrogenase, but characterization of such molecular species are limited. For both the FeIII and NiIII hydride complexes described herein, spin delocalization onto the thiolate ligand is proposed to stabilize the formal 3+ metal oxidation state. Furthermore, both the FeIII–H and NiIII–H species are demonstrated to undergo the bimolecular reductive elimination of dihydrogen upon warming, albeit with distinct activation parameters consistent with different proposed pathways for H–H bond formation. Chapter 4 expands upon the H–H bond forming chemistry demonstrated on the Ni system to demonstrate related N–N bond formation from an analogous NiIII–NH2 species, resulting in the formation of a NiII2(N2H4) complex. Given the diverse mechanistic possibilities for the overall 6e-/6H+ transformation to oxidize ammonia to dinitrogen, identification of the active M(NHx) intermediate and pathway for N–N bond formation is a central mechanistic question. While the homocoupling of M–NH2 species to form hydrazine has been hypothesized as the key N–N bond forming step in ammonia oxidation systems, stoichiometric examples of this transformation from M–NH2 complexes are rare. Lastly, Chapter 5 details the synthesis of a heterobimetallic VFe complex featuring a bridging thiolate, inspired by the structure of the VFe nitrogenase cofactor. This VFe species is demonstrated to be an active catalyst for the disproportionation of hydrazine to dinitrogen and ammonia. Notably, the heterobimetallic complex is appreciably more active than monometallic analogues of the individual V and Fe sites, suggesting that bimetallic cooperativity may facilitate the observed catalysis.</p
Gravitational Wave Polarizations: A Test of General Relativity Using Binary Black Hole Mergers
Get PDFGeneral Relativity predicts that gravitational radiation is purely tensor polarized and thus, gravitational waves are composed of linear combinations of two transverse polarization modes, referred to as plus (+) and cross (×) tensor modes. However, alternate gravitational theories predict the existence of up to four additional vector and scalar longitudinal GW polarization modes.
In this thesis, we develop a test of the gravitational wave (GW) polarization prediction of general relativity by searching for small admixtures of vector and/or scalar polarization components in transient GWs from binary black hole mergers. We use a network of five non-co-oriented GW detectors available in the near future, Bayesian inference parameter estimation, and nested sampling to quantify the detection sensitivity for such non-tensor GW polarization components.</p
Cavity Optomechanics for Hybrid Quantum Systems
Get PDFRecent advances in optomechanical systems have led to a series of scientific and technical advances. In addition, they have demonstrated macroscopic quantum phenomena, including probabilistic preparation of quantum states, squeezed light, and coherent transduction between photons with different energies. There are advantages in using phonons within a quantum information network. Within the solid state, all optical and electronic phenomena strongly depend on the local distortions of the crystal lattice, i.e. mechanical phonons, hence could connect dissimilar degrees of freedom such as superconducting qubits operating at gigahertz frequencies with atomic/optical states. Also, unlike photons, phonons do not radiate into free space. Energy damping of phonon can occur through radiation into bulk structure which support the mechanical resonator, through impurities and defects in the material, and due to the inherent anharmonic motion of atoms within solid-state materials.
In this thesis, we explore the limits of acoustic damping and coherence of a microwave-frequency acoustic nanocavity with a phononic crystal shield that possesses a wide bandgap for all polarizations of acoustic waves. The nanocavity is formed from an optomechanical crystal (OMC) nanobeam resonator. It supports an acoustic breathing mode at ~ 5 GHz and a co-localized telecom optical resonant mode which allows us to excite and readout mechanical motion using radiation pressure from a pulsed laser source. This minimally invasive pulsed measurement technique avoids a slew of parasitic damping effects - typically associated with electrode materials and mechanical contact, or probe fields for continuous readout - and allows for the sensitive measurement of motion at the single phonon level. The results of acoustic ringdown measurements at millikelvin temperatures show that damping due to radiation is effectively suppressed by the phononic shield, with breathing mode quality factors reaching mechanical quality factor Q = 4.9 x 1010, corresponding to an unprecedented frequency-Q product of f-Q = 2.6 x 1020 and an effective phonon propagation length of several kilometers. Measurement of the frequency jitter of the acoustic resonance is also performed, indicating telegraph-like noise corresponding to a coherence time of ~ 130 µs. The observed breathing mode behavior can be explained by TLS interactions when taking into account the highly modified density of phonon states in the shielded OMC cavity, which are most likely present in the amorphous etch-damaged region of the silicon surface. In particular, we find that damping due to nearly resonant TLS is suppressed due to the bandgap of the phononic shield, and that relaxation damping from non-resonant TLS can explain the magnitude, low temperature dependence of the breathing mode damping, and lack of saturation of the damping with both temperature and acoustic amplitude.
The extremely small motional mass and narrow linewidth of the OMC cavity make it ideal for precision mass sensing and in exploring limits to alternative quantum collapse models.
Our mechanical modes exist in the same frequency range as common superconducting qubits, suggesting a possibility for creating a hybrid quantum architecture consisting of acoustic and superconducting quantum circuits, where the small scale, reduced cross-talk, and ultralong coherence time of quantum acoustic devices may provide significant improvements in connectivity and performance of current quantum hardware. A proposal of mechanical quantum memory based on ultra-high-Q mechanical model and piezo-electrical coupling is also discussed in this work.
One remaining roadblock, which significantly compromises the utility of OMCs integration with superconducting circuits, is the very weak, yet non-negligible parasitic optical absorption, which is thought to occur due to surface defect states, and together with inefficient thermalization can yield significant heating of the hypersonic mechanical mode of the device at ultralow temperatures, where microwave systems can be reliably operated as quantum devices. In 1D OMC experiments, the quantum cooperativity (Ceff), which corresponds to the standard photon-phonon cooperativity divided by the Bose factor of the thermal bath and is the most relevant figure-of-merit for operation of optomechanical systems at ultralow temperatures, was lower than unity for all but a microsecond around the time an optical pulse is applied. This limits quantum optomechanical experiments to schemes with short pulses. Increased Ceff can be achieved with improved thermalization, for example, by employing a two-dimensional (2D) OMC cavity.
In this thesis, we demonstrate an improved silicon quasi-2D OMC with an over 50-fold improvement in back-action per photon over previous reports. We are able to measure the dynamics of the internal cavity acoustic modes of both 1D nanobeam and quasi-2D OMCs. Quasi-2D OMC shows much lower bath occupancy compared to 1D structures. Most importantly, quasi-2D OMCs demonstrated a Ceff greater than unity under steady-state optical pumping, a crucial threshold for realizing a variety of optomechanical applications. For example, bi-directional transduction or amplification of continuous quantum signals require the optomechanical device to be operated in a continuous mode. An analysis of piezo-optomechanical bi-directional microwave to optics transducer is also presented in this thesis.</p
Scalable Synthesis and Verification: Towards Reliable Autonomy
Get PDFWe have seen the growing deployment of autonomous systems in our daily life, ranging from safety-critical self-driving cars to dialogue agents. While impactful and impressive, these systems do not often come with guarantees and are not rigorously evaluated for failure cases. This is in part due to the limited scalability of tools available for designing correct-by-construction systems, or verifying them posthoc. Another key limitation is the lack of availability of models for the complex environments with which autonomous systems often have to interact with. In the direction of overcoming these above mentioned bottlenecks to designing reliable autonomous systems, this thesis makes contributions along three fronts.
First, we develop an approach for parallelized synthesis from linear-time temporal logic Specifications corresponding to the generalized reactivity (1) fragment. We begin by identifying a special case corresponding to singleton liveness goals that allows for a decomposition of the synthesis problem, which facilitates parallelized synthesis. Based on the intuition from this special case, we propose a more generalized approach for parallelized synthesis that relies on identifying equicontrollable states.
Second, we consider learning-based approaches to enable verification at scale for complex systems, and for autonomous systems that interact with black-box environments. For the former, we propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. For the latter, we present a data-driven approach based on chance-constrained optimization that allows for a system to be evaluated for specification conformance without an accurate model of the environment. We demonstrate this approach on several tasks, including a lane-change scenario with real-world driving data.
Lastly, we consider the problem of interpreting and verifying learning-based components such as neural networks. We introduce a new method based on Craig's interpolants for computing compact symbolic abstractions of pre-images for neural networks. Our approach relies on iteratively computing approximations that provably overapproximate and underapproximate the pre-images at all layers. Further, building on existing work for training neural networks for verifiability in the classification setting, we propose extensions that allow us to generalize the approach to more general architectures and temporal specifications.</p
On The Hecke Orbit Conjecture for PEL Type Shimura Varieties
Get PDFThe Hecke orbit conjecture plays an important role in understanding the geometric structure of Shimura varieties. First postulated by Chai and Oort in 1995, the Hecke orbit conjecture predicts that prime-to-p Hecke correspondences on mod p reductions of Shimura varieties characterize the foliation structure formed by Oort's central leaves. In other words, every prime-to-p Hecke orbit is Zariski dense in the central leaf containing it. Roughly speaking, a central leaf is the locus in a Shimura variety consisting of all points whose corresponding Barsotti-Tate groups belong to a fixed geometric isomorphism class. On the other hand, the prime-to-p Hecke orbit of a closed point x is the (countable) set consisting of all points y such that there is a prime-to-p quasi-isogeny from x to y.
In 2005, Chai and Yu proved the Hecke orbit conjecture for Hilbert modular varieties, followed by a proof for Siegel modular varieties by Chai and Oort in the same year. The major purpose of the present work is to generalize the method of Chai and Oort to Shimura varieties of PEL type. We show that the Hecke orbit conjecture holds for points in certain irreducible components of Newton strata under our assumptions.</p
Synthesis of Enantioenriched (Poly)Fluorinated Building Blocks, 2,2-Disubstituted Pyrrolidines and [7,7]Paracyclophanes
Get PDFThe Stoltz group, and moreover the synthetic community at large, has long been interested in the synthesis of enantioenriched compounds with interesting biological activities. This thesis presents three projects unified in an attempt to access compounds with relevance to the medicinal chemistry and natural products communities, encompassing reaction development, synthetic strategy and natural product synthesis.
A general method for the enantioselective synthesis of carbo- and heterocyclic carbonyl compounds bearing fluorinated α-tetrasubstituted stereocenters using palladium-catalyzed allylic alkylation is described. These fluorinated, stereochemically rich building blocks hold potential value in medicinal chemistry and are prepared using an orthogonal and enantioselective approach into such chiral moieties compared to traditional approaches, often without the use of electrophilic fluorinating reagents.
The synthesis of a variety of enantioenriched 2,2-disubstituted pyrrolidines is described. A stereogenic quaternary center is first formed utilizing an asymmetric allylic alkylation reaction of a benzyloxy imide, which can then be reduced to a chiral hydroxamic acid. This compound can then undergo a thermal "Spino" ring contraction to afford a carbamate protected 2,2-disubstituted pyrrolidine stereospecifically, allowing access to new molecules that could be useful in the medicinal chemistry community.
Finally, we have developed a synthesis of an enaptioenriched [7,7]paracyclophane compound using sequential C-H functionalization reactions, including selective Rh-catalyzed C-H insertion reactions developed by the Davies group at Emory University. Investigations are currently ongoing into potential antimicrobial activity of different [7,7]paracyclophanes and the total synthesis of naturally occurring [7,7]paracyclophanes.</p
Optimizing Deep Neural Networks for Single Cell Segmentation
Get PDFAnalysis of live-cell imaging experiments at the resolution of single cells provides exciting insights into the inner workings of biological systems. Advances in biological imaging and computer vision allow for segmentation of natural images with a high degree of accuracy. However, automation of the segmentation pipeline at the single cell resolution remains a challenging task. Complex deep learning models require large, well-annotated datasets that are rarely available in biology. In this research, we explore various methods that optimize state of the art deep learning frameworks, despite limited resources. We trained a large permutation of models to quantify their capacity and to measure the effects of temporal information, spatial awareness and transfer learning on model performance. We find that, although training set size is most impactful in improving model accuracy, we can leverage techniques like spatial awareness and transfer learning to compromise for the lack of data. These insights show that, with an abundance of data, light-weight models can be as performant as their heavy-weight counterparts in cellular analysis
Universality Laws and Performance Analysis of the Generalized Linear Models
Get PDFIn the past couple of decades, non-smooth convex optimization has emerged as a powerful tool for the recovery of structured signals (sparse, low rank, etc.) from noisy linear or non-linear measurements in a variety of applications in genomics, signal processing, wireless communications, machine learning, etc.. Taking advantage of the particular structure of the unknown signal of interest is critical since in most of these applications, the dimension p of the signal to be estimated is comparable, or even larger than the number of observations n. With the advent of Compressive Sensing there has been a very large number of theoretical results that study the estimation performance of non-smooth convex optimization in such a high-dimensional setting.
A popular approach for estimating an unknown signal β₀ ϵ ℝᵖ in a generalized linear model, with observations y = g(Xβ₀) ϵ ℝⁿ, is via solving the estimator β̂ = arg minβ L(y, Xβ + λf(β). Here, L(•,•) is a loss function which is convex with respect to its second argument, and f(•) is a regularizer that enforces the structure of the unknown β₀. We first analyze the generalization error performance of this estimator, for the case where the entries of X are drawn independently from real standard Gaussian distribution. The precise nature of our analysis permits an accurate performance comparison between different instances of these estimators, and allows to optimally tune the hyperparameters based on the model parameters. We apply our result to some of the most popular cases of generalized linear models, such as M-estimators in linear regression, logistic regression and generalized margin maximizers in binary classification problems, and Poisson regression in count data models. The key ingredient of our proof is the Convex Gaussian Min-max Theorem (CGMT), which is a tight version of the Gaussian comparison inequality proved by Gordon in 1988. Unfortunately, having real iid entries in the features matrix X is crucial in this theorem, and it cannot be naturally extended to other cases.
But for some special cases, we prove some universality properties and indirectly extend these results to more general designs of the features matrix X, where the entries are not necessarily real, independent, or identically distributed. This extension, enables us to analyze problems that CGMT was incapable of, such as models with quadratic measurements, phase-lift in phase retrieval, and data recovery in massive MIMO, and help us settle a few long standing open problems in these areas.</p
Derivation of Realistic Forcing Schemes to Reproduce Turbulent Characteristics of Round Jets on Centerline
Get PDFTurbulence forcing techniques are often required in the numerical simulation of statistically stationary turbulent flows. However, the existing forcing techniques are not based on physics, but rather arbitrary numerical methods that sustain the turbulent kinetic energy. In this work, a realistic forcing technique is devised to reproduce the centerline turbulent characteristics of round jets in a triply periodic box.
A velocity forcing term is derived from the Navier-Stokes equations by applying a Reynolds decomposition with the mean velocity of the axisymmetric jet. The result is an anisotropic linear forcing term. A series of direct numerical simulations (DNS) are performed over a range of Reynolds numbers by applying the derived velocity forcing term in a 3D cubic box. The budget of the terms in the kinetic energy equation is found to be very close to the experimental measurement on the centerline. The anisotropy ratio, kinetic energy, and dissipation rate of the simulations are also comparable to experimental values. Finally, the kinetic energy spectrum in the axial direction is presented. With appropriate normalizations, the spectrum agrees well with the round jet spectrum on its centerline.
A similar procedure is applied to passive scalars to derive a scalar forcing term to simulate the centerline mixing properties of round jets. The term is derived from the scalar transport equation using a Reynolds-like decomposition of the scalar field. The equation is closed by applying the known mean velocity and scalar profiles of axisymmetric jets. The result is a combination of a mean gradient term and a linear scalar term. DNS at different Reynolds numbers have been performed with these source terms for unity Schmidt number. Scalar flux values and scaling exponents of scalar energy spectra from simulations are comparable to experimental values. In addition, a dimensional analysis shows that the normalized scalar statistics, such as variance, flux, and dissipation rate, should only be a function of Reynolds number; indeed, such quantities computed from our simulations approach constant values as the Reynolds number increases. The effects of velocity forcing on scalar fields are also investigated; changing velocity forcing terms may result in unstable scalar fields even under the same scalar forcing.
More computations on higher Schmidt number scalars are performed with the same velocity and scalar forcing terms. It is found that the scalar flux values decrease with increasing Schmidt number for low Reynolds number flows, and reach plateaus as the Schmidt number increases. The flux values also increase with the Reynolds number for all non-unity Schmidt numbers. The scaling exponents of scalar energy spectra are found to decrease with increasing Schmidt number for all Reynolds numbers.</p