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Controlling the Dynamics of Microstructure Formation in Mixed-Matrix Polymeric-Particle Membranes
Get PDFPolymer membranes are increasingly important in energy generation, water purification, and resource recovery. Control over chemistry, morphology, and mechanical properties gives organic polymers unparalleled advantages for membrane technology—but only if these complementary functions can be married into a cohesive material. Herein I have sought to expand upon the chemical tools for integrating diverse polymers into multifunctional membrane materials, making them easily tunable to various applications. To overcome a fundamental challenge in polymer science—namely, that polymers with different functions often do not mix—the functional polymer is grown in situ in a solution containing a preformed scaffold polymer, a method pioneered by co-advisor Mamadou Diallo. The hierarchical structure of the resulting mixed matrix polymeric-particle (M2P2) membrane is governed by the kinetic competition between polymerization and phase separation of the functional polymer from the scaffold polymer. This competition is quenched by immersion in a nonsolvent, which rapidly solidifies the material to trap the metastable structure formed during synthesis.
In my quest to understand how these competing processes interact to inform multifunctional membrane design, I developed a general method for studying transient structure using ultra-small angle neutron scattering (Chapter II), working closely with Kornfield Group alumnus Dr. Joey Kim. I then investigated the synergistic effects of incorporating different functional polymer architectures in M2P2 membranes (Chapter III), working with fellow graduate student Orland Bateman. By combining low-generation dendrimers with randomly hyperbranched oligomers bearing similar chemical functionality, we can systematically tune the characteristic length of domains formed during synthesis. In the final chapter I discuss the main conclusions and describe future directions for understanding structure during processing in M2P2 membranes. My thesis ultimately provides a broadly relevant platform for membrane design and synthesis, one in which the favorable properties of different polymers may be combined to strike a balance between function, stability, and ease of fabrication.</p
Data-Driven Protein Engineering
Get PDFDirected evolution has enabled the adaptation of natural protein sequences for an endless variety of human applications. Given a starting point - a sequence with measurable activity - directed evolution is able to improve protein sequences by iteratively accumulating beneficial mutations. However, directed evolution requires investing large experimental effort, which continues to be the major bottleneck in efficient protein optimization. To this end, we describe a framework for incorporating machine learning in the directed evolution process to maximize the utility of generated experimental data in Chapter 2. In Chapter 3, we then show that this framework outperforms traditional directed evolution methods on an empirical fitness landscape. However, directed evolution is fundamentally limited by its need for a starting point, or a sequence with measurable activity. To tackle this issue, we test the ability of nascent deep learning techniques for generating short, functional amino acid sequences in Chapter 4. Encouraged by this success, we attempted to generate full length enzymatic sequences for desired substrates without success. However, we were able to apply this deep learning approach to model other aspects of enzymatic protein sequences in Chapter 5. Finally, the field of data-driven protein sequence generation is enjoying a recent surge in interest, and we provide an updated review of protein engineering with machine learning, focusing on recent work in deep generative modeling in Chapter 1.</p
Views of an Ocean World: The Signatures of Internal and External Processes on the Surface of Europa
Get PDFBeneath a comparatively thin ice shell, Europa harbors a global, salty, liquid-water ocean in contact with a rocky seafloor, making it an exciting target for exploring habitability in the Solar System. The potential habitability of Europa's ocean depends on its composition, which may be reflected in that of Europa's geologically young, fractured surface. However, two intertwined uncertainties are the degree to which the ocean and the surface are in contact, and the degree to which surface materials truly represent oceanic signatures. The latter is complicated by the fact that Europa’s surface is continuously altered by sulfur plasma and particle irradiation due to its location within Jupiter’s magnetosphere. In this thesis, I utilize a variety of multi-spectral, Earth-based observations of Europa to explore the balance and interplay of internal and external processes in shaping its surface.
Chapters II and III focus on using visible-wavelength spectroscopy from the Hubble Space Telescope (HST) to understand the chemistry of Europa's surface salts. In Chapter II, I present the detection of irradiated sodium chloride (NaCl) and show that its distribution correlates with geologically disrupted chaos terrain, suggesting an ocean source. In Chapter III, I investigate multiple spectral features across Europa's sulfur-bombarded trailing hemisphere. In comparing their geographies with the distributions of large-scale geology, magnetospheric particle bombardment, and surface color, I identify some features as reflective of purely exogenous sulfur radiolysis products and others as indicative of radiolysis products formed from a mixture of endogenous material and magnetospheric sulfur.
Chapters IV and V further consider the effects of radiolytic processing through the analysis of infrared spectra obtained with Keck NIRSPEC. In Chapter IV, I report a previously unseen spectral feature at 3.78 µm in disk-integrated spectra of the trailing hemisphere. Using Hapke spectral modeling, I demonstrate that it represents an unidentified radiolytic product of potential relevance to understanding the alteration of endogenic material. Chapter V considers a radiolytic species thought to be independent of endogenic material -- hydrogen peroxide (H₂O₂), a species relevant to the oxidation state and habitability of the ocean in the case of mutual exchange through the ice shell. Contrary to laboratory expectations, I observe the largest H₂O₂ absorptions within salty, low-latitude chaos terrain. I hypothesize that this distribution may reflect decreased hydrogen peroxide destruction due to electron scavenging by CO₂ within these same regions, which would suggest an internal carbon source.
Finally, Chapters VI and VII present preliminary studies of Europa's thermal emission using four images obtained with the Atacama Large Millimeter Array (ALMA) and a global thermophysical model developed to simulate Europa's expected thermal emission. In Chapter VI, I combine a single ALMA image with an observation from the Galileo Photopolarimeter Radiometer (PPR) to show that a thermal anomaly seen by the PPR and associated with two potential plume detections is better explained by a locally high thermal inertia than by geologic heating. Chapter VII considers all four ALMA images. While much of the large-scale thermal structure can be readily attributed to albedo variation, modeling of the images reveals a number of localized anomalies, which may indicate variations in geothermal heat flow, thermal inertia, or millimeter emissivity. In the absence of the additional observations needed to distinguish between such possibilities, I construct hypothetical maps presenting the ranges of possible thermal inertia and emissivity values.</p
Thermal Bioswitches for Non-Invasive Control of Cellular Therapies
Get PDFTemperature is a unique input signal that could be used by engineered therapeutic cells to sense and respond to host conditions or spatially targeted external triggers such as focused ultrasound. To enable these possibilities, I present here a new class of thermal bioswitches that enables thermal control over bacterial and mammalian cells. For bacterial applications, we developed two new families of tunable, orthogonal, temperature-dependent transcriptional repressors providing switch-like control of bacterial gene expression at thresholds spanning the biomedically relevant range of 32–46 °C. We integrated these molecular bioswitches into thermal logic circuits and demonstrated their utility in three in vivo microbial therapy scenarios, including spatially precise activation using focused ultrasound, modulation of activity in response to a host fever, and self-destruction after fecal elimination to prevent environmental escape. This technology provides a critical capability for coupling endogenous or applied thermal signals to cellular function in basic research, biomedical and industrial applications.
To apply this technology in a relevant clinical scenario, we sought to engineer microbial immunotherapies that can be thermally controlled with focused ultrasound. This technology was enabled by rapid advances in synthetic biology that are driving the development of genetically modified microbes as therapeutic agents for a multitude of human diseases, including cancer. In particular, the reduced immune surveillance within the core of some solid tumors creates an ideal environment for microbes to engraft and release therapeutic payloads. However, these therapeutic payloads could be harmful if released in healthy tissues where microbes tend to also engraft in smaller numbers. As described in Chapter 2, my colleagues and I introduced a temperature-actuated state switch that enables tight spatiotemporal control over the activity of therapeutic microbes when combined with focused ultrasound hyperthermia. Through a combination of rational design and high throughput screening, we optimized the behavior of this switch to minimize leakage and maximize inducibility. When tested in a clinically relevant in vivo model, engineered microbes, successfully switched states, and induced a marked suppression of tumor growth upon focal activation. This bioswitch provides a critical tool to attain selective and sustained activity of therapeutic microbes in vivo.
Encouraged by the successful development of thermally actuated circuits in microbes, we aimed to establish equivalent technologies for thermal control of human T cells. Genetically engineered T cells are actively being developed to perform a variety of therapeutic functions with great clinical promise. However, no robust mechanisms exist to externally control the activity of T cells at specific locations within the body. Such spatiotemporal control could help mitigate potential off-target toxicity due to incomplete molecular specificity in applications such as T-cell immunotherapy against solid tumors. In Chapter 4, my colleagues and I tested the ability of heat shock promoters to mediate thermal actuation of genetic circuits in primary human T cells in the well-tolerated temperature range of 37−42 °C, and we introduced genetic architectures enabling the tuning of the amplitude and duration of thermal activation. We demonstrated the use of these circuits to control the expression of chimeric antigen receptors and cytokines, and the killing of target tumor cells. Overall, the technologies developed here provide critical tools to direct control therapeutic cells after they have been deployed deep inside the body.</p
Gravitational Wave Signatures of Black Hole Physics
Get PDFGravitational wave observations are opening the door to test general relativity in regimes far less common than the weak gravitational fields that we experience in the solar system. The first part of this thesis addresses the broad issue of how different exotic predictions of general relativity imprint themselves in gravitational waves.
The ringdown portion of a binary black hole merger is dominated by superposition of quasinormal modes, the resonant modes of a perturbed black hole. The quasinormal mode spectrum of a perturbed black hole mostly reflects the spacetime geometry near the photon orbits. Chapter 2 of this thesis develops a new method for calculating quasinormal mode frequencies for weakly charged, rotating black holes. Chapter 3 uses a variety of analytic approximations to calculate the charged, rotating quasinormal mode frequencies in other cases, including nearly extremal black holes.
The event horizon is one of the most unique predictions of general relativity and it unsurprisingly does not imprint itself in gravitational wave emission. However, alternatives to black holes known as exotic compact objects do leave a unique signature in the form of echoes following the initial signal. Chapter 4 develops a formalism to understand and calculate these echoes.
The second part of this thesis focuses on reducing the noise in gravitational wave measurements using neural networks. Chapter 5 demonstrates on mock data how simple neural networks can use auxiliary measurements from the detector to predict unmodeled noise which can be subtracted offline.</p
Optimizing Cloud AI Platforms: Resource Allocation and Market Design
Get PDFThe numerous applications of data-driven algorithms and tools across diverse industries have led to tremendous successes in recent years. As the volume of massive data that is created, collected, and consumed continues to grow, there are many new imposed challenges faced by today's cloud AI platforms that support the deployment of machine learning algorithms on a large scale. In this thesis, we tackle the emerging challenges within cloud AI systems and beyond by adopting approaches from the fields of resource allocation and market design.
First, we propose a new scheduler, Generalized Earliest Time First (GETF), and provide the provable, worst-case approximation guarantees for the goals of minimizing both makespan and total weighted completion time of tasks with precedence constraints on related machines with machine-dependent communication times. These two results address long-standing open problems. Further, we adopt the classic speed scaling function to model power consumption and use mean response time to measure the performance. We propose the concept of pseudo-size to quantify importance of tasks and design a family of two-stage scheduling frameworks based on the approximation of pseudo-size. Assuming a good approximation of pseudo-size, we are able to provide the first provable bound of a linear combination of performance and energy goals under this setting.
Second, we study the design of mechanisms for data acquisition in settings with information leakage and verifiable data. We provide the first characterization of an optimal mechanism for data acquisition if agents are concerned about privacy and their data is correlated with each other. Additionally, the mechanism allows, for the first time, a trade-off between the bias and variance of the estimator. Transitioning from the data market into the energy market, we propose a new pricing scheme, which is applicable to general non-convex costs, and allows using general parametric pricing functions. Optimizing for the quantities and the price parameters simultaneously, and the ability to use general parametric pricing functions allows our scheme to find prices that are typically economically more efficient and less discriminatory than those of the existing schemes while still supporting a competitive equilibrium. In addition, we supplement the proposed method with a computationally efficient polynomial-time approximation algorithm, which can be used to approximate the optimal quantities and prices for general non-convex cost functions.</p
Inference, Computation, and Games
Get PDFIn this thesis, we use statistical inference and competitive games to design algorithms for computational mathematics.
In the first part, comprising chapters two through six, we use ideas from Gaussian process statistics to obtain fast solvers for differential and integral equations. We begin by observing the equivalence of conditional (near-)independence of Gaussian processes and the (near-)sparsity of the Cholesky factors of its precision and covariance matrices. This implies the existence of a large class of dense matrices with almost sparse Cholesky factors, thereby greatly increasing the scope of application of sparse Cholesky factorization. Using an elimination ordering and sparsity pattern motivated by the screening effect in spatial statistics, we can compute approximate Cholesky factors of the covariance matrices of Gaussian processes admitting a screening effect in near-linear computational complexity. These include many popular smoothness priors such as the Matérn class of covariance functions.
In the special case of Green's matrices of elliptic boundary value problems (with possibly unknown elliptic operators of arbitrarily high order, with possibly rough coefficients), we can use tools from numerical homogenization to prove the exponential accuracy of our method. This result improves the state-of-the-art for solving general elliptic integral equations and provides the first proof of an exponential screening effect. We also derive a fast solver for elliptic partial differential equations, with accuracy-vs-complexity guarantees that improve upon the state-of-the-art. Furthermore, the resulting solver is performant in practice, frequently beating established algebraic multigrid libraries such as AMGCL and Trilinos on a series of challenging problems in two and three dimensions.
Finally, for any given covariance matrix, we obtain a closed-form expression for its optimal (in terms of Kullback-Leibler divergence) approximate inverse-Cholesky factorization subject to a sparsity constraint, recovering Vecchia approximation and factorized sparse approximate inverses. Our method is highly robust, embarrassingly parallel, and further improves our asymptotic results on the solution of elliptic integral equations. We also provide a way to apply our techniques to sums of independent Gaussian processes, resolving a major limitation of existing methods based on the screening effect. As a result, we obtain fast algorithms for large-scale Gaussian process regression problems with possibly noisy measurements.
In the second part of this thesis, comprising chapters seven through nine, we study continuous optimization through the lens of competitive games. In particular, we consider competitive optimization, where multiple agents attempt to minimize conflicting objectives. In the single-agent case, the updates of gradient descent are minimizers of quadratically regularized linearizations of the loss function. We propose to generalize this idea by using the Nash equilibria of quadratically regularized linearizations of the competitive game as updates (linearize the game). We provide fundamental reasons why the natural notion of linearization for competitive optimization problems is given by the multilinear (as opposed to linear) approximation of the agents' loss functions. The resulting algorithm, which we call competitive gradient descent, thus provides a natural generalization of gradient descent to competitive optimization. By using ideas from information geometry, we extend CGD to competitive mirror descent (CMD) that can be applied to a vast range of constrained competitive optimization problems. CGD and CMD resolve the cycling problem of simultaneous gradient descent and show promising results on problems arising in constrained optimization, robust control theory, and generative adversarial networks. Finally, we point out the GAN-dilemma that refutes the common interpretation of GANs as approximate minimizers of a divergence obtained in the limit of a fully trained discriminator. Instead, we argue that GAN performance relies on the implicit competitive regularization (ICR) due to the simultaneous optimization of generator and discriminator and support this hypothesis with results on low-dimensional model problems and GANs on CIFAR10.</p
Genetic Circuits for the Control of Multi-Strain Bacterial Populations
Get PDFMicrobial species rarely exist alone. Nearly everywhere you could think to look, microorganisms of various species live together in harmony. Microbes together in their communities are incredibly powerful actors wherever they are found; they perform small miracles---the conversion of milk into yogurt---and large ones---production of most of the planet's oxygen and organic carbon.
Our burgeoning knowledge of microbial life combined with modern technologies to manipulate it create a critical, exciting opportunity to harness microbial power for the betterment of technology, people, and the planet. This thesis presents a body of work which explores the manipulation of microbial communities using the intersectional bio-engineering approach of synthetic biology. We demonstrate how molecular tools evolved by bacteria can be repurposed to create rationally designed systems for controlling features of bacterial populations.
We begin by examining a genetic circuit that caps the size of a bacterial population by coordinating the deaths of population members -- the population capping or "pop cap" circuit. Briefly, E. coli cells in the pop cap circuit are engineered to synthesize a chemical -- a quorum sensing (QS) signal -- that reports the density of the population, sense this chemical, and produce the ccdB toxin to destroy themselves in response. The molecular tools that make up this circuit are drawn from organisms across the spectrum of bacterial diversity. Brought together, they create a feedback control circuit that controls population size by causing member cells to die when a target population size has been reached. To improve the performance of this population controller and reduce the influence of the environment on the circuit, we add the aiiA quorum sensing signal degradase to allow the experimenter control over the degradation rate of the QS density signal. Additionally, we explore RNA and protein mechanisms to sequester the death-causing toxin---inactivating it---allowing us to release a population cap. The resulting "cap and release" circuit is a flexible motif that can be scaled to control multi-strain populations, expanding the scope of control beyond the single-strain populations regulated by the base pop cap circuit.
Using the scalable cap and release motif, we design a genetic circuit to regulate a multi-strain community. Two different cell strains expressing symmetric, interconnected cap and release systems form the "A=B" circuit, so named for its ability to control the composition of the community to a target ratio of A cells to B cells, or Apopulation = αBpopulation. Through dynamical system models of the system, we explore the effects of active QS signal degradation on composition control performance and perform a parameter sensitivity analysis of the system to help determine the best method for building a functioning A=B system in the laboratory. We use a high throughput construction and screening protocol to create variants of the A=B system with identical architectures, but slightly differing component production rates. We crown the most successful variant with a series of experiments to determine if it indeed recapitulates our model's predictions for its performance. Our implementation of the A=B circuit can successfully regulate the composition of a community, with interesting additional effects on total population density.
The cap and release and A=B circuits need parts that can do three things: 1) send a signal between cells to communicate information, 2) compare two signals, 3) regulate cell growth or death. We highlight bacteriocins, bacterial protein exotoxins that are released from a producer cell to kill other cells of similar species, as attractive tools for bacterial community engineering both for their multi-functionality and modular protein structure. By themselves, bacteriocins can perform all the functions needed for population control: they transmit themselves between cells, have unique high-affinity sequestering antitoxin proteins, and are toxins to receiver cells. We begin the process of their characterization and usage as synthetic biological "parts" by creating non-native expression systems that match native expression strengths. Using these experimenter-controlled systems we design preliminarily test a bacteriocin-based bacterial community control circuit. Additionally, given the E. coli colicin bacteriocins' unique, nearly plug-and-play modular domain structure, we explore possibilities for engineering colicin proteins themselves for increased functional diversity or uses outside of growth regulation.</p
Spacecraft Motion Planning and Control under Probabilistic Uncertainty for Coordinated Inspection and Safe Learning
Get PDFDuring a spacecraft mission design process, engineers often balance the following three criteria: science return, optimality in performance, and safety. Given a science criterion, engineers design the orbit parameters with predefined performance and safety. Often in this approach, the spacecraft has no understanding of the expected outcome or the knowledge of the mission safety criteria. Autonomous science-driven orbit (or goal) selection and planning for safety under uncertainty enable efficient and adaptable missions. To this end, we propose an architecture for information-based guidance and control for coordinated inspection, motion planning and control algorithms for safe and optimal guidance under uncertainty, and architecture for safe exploration.
In the first part of this thesis, we present an architecture for inspection or mapping of a target spacecraft in a low Earth orbit using multiple observer spacecraft. We use an information gain approach to directly consider the trade-off between gathered data and fuel/energy cost. The estimated information gain is a crucial input to the motion planner, which computes orbits and reconfiguration strategies for each of the observers to maximize the information gain from distributed observations of the target spacecraft. The resulting motion trajectories jointly consider observational coverage of the target spacecraft and fuel/energy cost. We validate our architecture in a mission simulation to visually inspect the target spacecraft and on the three degree-of-freedom robotic spacecraft dynamics simulator testbed.
In the second part of the thesis, we present gPC-SCP, Generalized Polynomial Chaos-based Sequential Convex Programming method, to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning and control of robotic systems under uncertainty. The proposed method involves two steps. The first step is to derive a deterministic nonlinear optimal control problem (DNOC) with convex constraints that are surrogate to the SNOC by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem using sequential convex programming (SCP) for trajectory generation and control. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC. We derive a stable stochastic model predictive controller using the gPC-SCP for tracking a potentially unsafe trajectory in the presence of uncertainty. We empirically demonstrate the efficacy of the gPC-SCP method for the following three test cases: 1) collision checking under uncertainty in actuation, 2) collision checking with stochastic obstacles, and 3) safe trajectory tracking under uncertainty in the dynamics and obstacle location by using a receding horizon control approach. We validate the effectiveness of the gPC-SCP method on the robotic spacecraft testbed.
In the third part of this thesis, we present a new approach for optimal motion planning for safe exploration that integrates the chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an Information-cost Stochastic Nonlinear Optimal Control problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has a higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.</p
Linear Codes with Constrained Generator Matrices
Get PDFDesigning good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be nonzero, has found many recent applications, including in distributed coding and storage, linear network coding, multiple access networks, and weakly secure data exchange. The dual problem, where the parity check matrix has a support constraint, comes up in the design of locally repairable codes. The central problem here is to design codes with the largest possible minimum distance, subject to the given support constraint on the generator matrix. When the distance metric is the Hamming distance, the codes of interest are Reed-Solomon codes, for which case, the problem was formulated as the "GM-MDS conjecture." In the rank metric case, the same problem can be considered for Gabidulin codes. This thesis provides solutions to these problems and discusses the remaining open problems.</p