VictorJuiz/thesis huggingface dataset:
The Doob-Martin compactification of Markov chains of growing words

We study the limiting behavior of Markov chains that iteratively generate a sequence of random finite words./nIn the first part of thesis, we consider a Markov chain such that the $n^{\mathrm{th}}$ word is uniformly distributed over the set $\bW_n$ of words of length $2n$ in which $n$ letters are $a$ and $n$ letters are $b$: at each step an $a$ and a $b$ are shuffled in uniformly at random among the letters of the current word. We also consider a Markov chain such that the $n^{\mathrm{th}}$ word takes values in the set of words in $\bB_n$ such that the number of letters $a$ in the first $k$ letters is at least the number of letters $b$ in those positions for any $1 \le k \le 2n$: at each step an $a$ and a $b$ are shuffled uniformly at random into the existing word so that the $a$ precedes the $b$. We obtain a concrete characterization of the respective Doob-Martin boundaries of these Markov chains and thereby delineate all the ways in which the Markov chains can be conditioned to behave at large times. We exhibit a bijective correspondence between the points in the respective boundaries of Markov chains and ergodic random total orders on the set $\{a_1, b_1, a_2, b_2, \ldots \}$ that have the specific properties determined by the Markov chains. We establish for the first Markov chain a further bijective correspondence between the set of such random total orders and the set of pairs $(\mu,\nu)$ of diffuse probability measures on $[0,1]$ such that $\frac{1}{2}(\mu+\nu)$ is Lebesgue measure: the restriction of the random total order to $\{a_1, b_1, \ldots, a_n, b_n\}$ is obtained by taking $X_1, \ldots, X_n$ (resp. $Y_1, \ldots, Y_n$) i.i.d. with common distribution $\mu$ (resp. $\nu$), letting $(Z_1, \ldots, Z_{2n})$ be $\{X_1, Y_1, \ldots, X_n, Y_n\}$ in increasing order, and declaring that the $k^{\mathrm{th}}$ smallest element in the restricted total order is $a_i$ (resp. $b_j$) if $Z_k = X_i$ (resp. $Z_k = Y_j$)./nThe second part of thesis focuses on the mixing time of a Markov chain of words in $\bW_n$ that arises from removing a letter $a$ and a letter $b$ uniformly at random followed by inserting the letter $a$ and the letter $b$ uniformly at random back into one of the slots defined by the remaining letters. We present an upper bound of the form $n \log n + (\log 8)n$ and a lower bound of the form $(1 - \alpha) n\log n - c_{\alpha} n, \alpha > \frac12$.

Advisor: Evans, Steven N
Fast Approximation Algorithms for Positive Linear Programs

Positive linear programs (LPs), or equivalently, mixed packing and covering LPs, are LPs formulated with/nnon-negative coefficients, constants, and variables. Notable special cases of positive LPs include packing LPs and covering LPs. Positive LPs model a wide range of fundamental problems both in theory of computation as well as in practice, thus have long drawn interest in theoretical computer science, operations research, and optimization communities./nIn this work, we study iterative methods for approximately solving positive LPs efficiently. Given a positive LP of size $N$, we are interested in iterative methods that can converge to a $(1\pm \epsilon)$-approximate optimal solution with complexity that is nearly linear in $N$, and polynomial in $\frac{1}{\epsilon}$./nFor the special cases of packing LPs and covering LPs, we design improved sequential and parallel approximate solvers, both using first-order (i.e. gradient based) descent methods from (continuous) convex optimization. In particular, we build upon the linear coupling framework introduced by Allen-Zhu and Orecchia. The performance of first-order methods are sensitive to the geometry of the problem space, as well as properties of the objective function. At a high level, we design (discrete) techniques that exploit the combinatorial structures of the LPs, which lead to signiﬁcantly improved theoretical behavior of the optimization method. More specifically, our sequential (i.e., non-parallelizable) solver is based on a $\tilde{O}(N/\epsilon)$ algorithm for packing LPs in a previous breakthrough by Allen-Zhu and Orecchia, and we provide a unified method with running time $\tilde{O}(N/\epsilon)$ for both packing LPs and covering LPs. Our parallel algorithm has depth (i.e., parallel running time) $\tilde{O}(1/\epsilon^2)$, which is $\Omega(1/\epsilon)$ faster than the previous best algorithm./nFor general positive LPs, we take a more combinatorial framework, called Lagrangian relaxation, but we crucially adapt the framework to leverage insights from continuous convex optimization. The incorporation of continuous optimization techniques provides a primal-dual perspective of the method, and leads to faster convergence. More specifically, we develop a $\tilde{O}(1/\epsilon^3)$ depth parallel algorithm, improving a long-standing bound of $\tilde{O}(1/\epsilon^4)$ for positive LPs./n/nAt a high level, we benefit from a integrated view of continuous and combinatorial techniques to obtain the improved results in this work. This combination brings intriguing new perspectives to algorithm design, and is promising for further exciting progress.

Advisor: Rao, Satish
Efficient Algorithms for Markov Random Fields, Isotonic Regression, Graph Fused Lasso, and Image Segmentation

Markov random field (MRF) is a multi-label clustering model with applications in image segmentation, image deblurring, isotonic regression, graph fused lasso, and semi-supervised learning. It is a convex optimization problem on an arbitrary graph of objective function consisting of functions defined on the nodes (called deviation functions) and edges (called separation functions) of the graph. There exists a provably fastest MRF-algorithm for arbitrary graphs and a broad class of objective functions. This MRF-algorithm uses the technique of graph minimum cut. Although MRF of this class of objective functions generalizes isotonic regression and graph fused lasso, this MRF-algorithm has lower time complexity than those specialized algorithms for isotonic regression and graph fused lasso./nSome problems in time series and gene sequence signal processing are special cases of MRF on a path graph. We present three efficient algorithms to solve MRF on a path graph for different classes of objective functions. The algorithms are the fastest algorithms for the respective classes of objective functions. The first algorithm uses graph minimum cut technique inspired by the provably fastest MRF-algorithm. The second algorithm is based on a relationship with a lot-sizing problem in production planning. The third algorithm is based on the technique of Karush-Kuhn-Tucker (KKT) optimality conditions./nMRF is used in image segmentation to identify multiple salient features in an image. The Hochbaum Normalized Cut (HNC) model is a binary clustering model that is also applicable to image segmentation, with the goal to separate the foreground from the background. We compare the empirical performance between the HNC model and the spectral method in image segmentation. Both HNC and the spectral method can be viewed as heuristics for the NP-hard normalized cut criterion, which is another binary clustering criterion often used for image segmentation. We present experimental evidence that the HNC model provides solutions which not only better approximate the optimal normalized cut solution, but also have better visual segmentation quality over those provided by the spectral method. The experimental evidence further suggests that HNC should be the preferred image segmentation criterion over normalized cut.

Advisor: Hochbaum, Dorit S.
Polynomial Proof Systems, Effective Derivations, and their Applications in the Sum-of-Squares Hierarchy

Semidenite programming (SDP) relaxations have been a popular choice for approximation/nalgorithm design ever since Goemans and Williamson used one to improve the best approximation/nof Max-Cut in 1992. In the effort to construct stronger and stronger SDP relaxations,/nthe Sum-of-Squares (SOS) or Lasserre hierarchy has emerged as the most promising/nset of relaxations. However, since the SOS hierarchy is relatively new, we still do not know/nthe answer to even very basic questions about its power. For example, we do not even know/nwhen the SOS SDP is guaranteed to run correctly in polynomial time!/nIn this dissertation, we study the SOS hierarchy and make positive progress in/nunderstanding the above question, among others. First, we give a sufficient, simple criteria/nwhich implies that an SOS SDP will run in polynomial time, as well as confirm that our/ncriteria holds for a number of common applications of the SOS SDP. We also present an/nexample of a Boolean polynomial system which has SOS certificates that require exponential time to find, even though the certificates are degree two. This answers a conjecture of [54]./nSecond, we study the power of the SOS hierarchy relative to other symmetric SDP relaxations/nof comparable size. We show that in some situations, the SOS hierarchy achieves/nthe best possible approximation among every symmetric SDP relaxation. In particular, we/nshow that the SOS SDP is optimal for the Matching problem. Together with an SOS lower/nbound due to Grigoriev [32], this implies that the Matching problem has no subexponential/nsize symmetric SDP relaxation. This can be viewed as an SDP analogy of Yannakakis'/noriginal symmetric LP lower bound [72]./nAs a key technical tool, our results make use of low-degree certificates of ideal membership/nfor the polynomial ideal formed by polynomial constraints. Thus an important step in our/nproofs is constructing certificates for arbitrary polynomials in the corresponding constraint/nideals. We develop a meta-strategy for exploiting symmetries of the underlying combinatorial/nproblem. We apply our strategy to get low-degree certificates for Matching, Balanced CSP, TSP, and others.

Advisor: Raghavendra, Prasad
Development of Diverse Hydrogels from the Protean Polymer, Elastin-like Polypeptide

Hydrogels have been used to develop scaffolds to address challenges in tissue engineering and drug delivery for several decades. The major advantage of using hydrogels is that their high water content and low stiffness enables them to mimic tissue-like environments. In my work, I develop four unique hydrogels using a single polymer, elastin-like polypeptide. The first challenge I address is that of hydrogel extensibility. Typical hydrogels cannot undergo large strains, which limits their durability and applicability to active tissues such as muscles. I use ELP to create a rubber-like elastic hydrogel that can stretch to 15 times its original length. Unlike most previous ELP hydrogels, our gels can reach such high strains due to the well-defined structure of our materials with minimal crosslinks. Next, I focus on developing an adhesive hydrogel using ELP. Unlike most adhesives, especially protein-based adhesives, our adhesive hydrogels are flexible and deswell in physiological conditions. This improves their potential for success in practical applications. We also developed a self-healing hydrogel by combining ELP with bioglass. Unlike other strategies that use reversible physical bonds, we use pH driven reversible Schiff base formation to synthesize hydrogels. Bioglass raises the localized pH to yield ideal conditions that favor gelling in our system. We also show that our materials can self-heal after being severed, which makes them durable and ideal for topical applications. Finally, we employ our efforts in the design and synthesis of protein-based beads for biolaser development. These devices are stimuli-responsive, which makes them ideal for optical sensing applications for biomolecule sensing and the flexibility of the hydrogels also makes them suitable for studying cellular biophysics. Through my dissertation, I hope to convey the versatility of ELP and the potential of structural design that can lead to the development of hydrogels with diverse functions.

Advisor: Lee, Seung-Wuk
Biotransformation discovery enabled by high-throughput mass-spectrometric enzyme activity screening and comparative genomics

The potential of replacing unsustainable petroleum feedstocks with the biological production of small molecules is stipulated on access to a wide array of enzyme-catalyzed transformations. In this dissertation, we have taken two distinct approaches to expanding the biocatalytic toolbox. In one case, we develop a high-throughput mass spectrometry-based assay for detecting enzyme activity. We lay out in detail the chemical synthesis, software development, assay optimization and benchmarking that has allowed the assay to become a robust method. We then showcase our technology to the screening of a cytochrome P450 mutant library, allowing us to identify enzyme variants with desired altered substrate specificity. In a complimentary enzyme discovery approach, we turn to the diversity of fascinating reactions already present in nature. Through comparative genomics of the marine bacterium Pseudoalteromonas rubra, we identify an enzyme responsible for catalyzing the impressive feat of regioselective C–H activation and C–C bond-formation in the biosynthesis of cycloprodigiosin.

Advisor: Keasling, Jay D
Klinman, Judith P
Robust Estimation in Linear Model With Many Instruments

The first chapter of this dissertation considers a new class of robust estimators in a linear instrumental variables (IV) model with many instruments. The estimators are generalized method of moments (GMM) estimators, and the class includes the limited maximum likelihood estimator (LIML) as a special case. Each estimator in the class is consistent and asymptotically normal under many instruments asymptotics, and this chapter provides consistent variance estimators that are of the ``sandwich'' type and can be used to conduct asymptotically correct inference. Furthermore, this chapter characterizes an optimal robust estimator among the members of the class. Compared to LIML, the optimal robust estimator is less influenced by outliers and more efficient under thick-tailed error distributions. In an empirical example (Angrist and Krueger, 1991), the optimal robust estimator is approximately 80 percent more efficient than LIML./n/nThe second chapter of this dissertation provides a central limit theorem based on Stein's method (Stein, 1972) which is an integral component in the proof of the main theorem in the first chapter. It also appears to be general enough in its scope that it can be applied to a variety of other problems.

Advisor: Jansson, Michael
Prenatal Referrals, Access and Quality in the Public Health Sector of Two Mexican States

Over half of all births in Mexico are attended in the public health care system. Prenatal care for these women is overwhelmingly at the primary healthcare clinics staffed by general practice physicians, medical residents, and in a few instances, professional midwives. Access to specialty care for those women who need it is dependent on the effective functioning of the referral system./nThis dissertation seeks to understand the functioning of referral systems, the quality of care provided to women with obstetric-related referrals and aspects of care coordination to facilitate care of referred patients using a mixed methods study of a network of public health primary care clinics and secondary-level hospitals in Oaxaca and Guerrero, two of the poorest Mexican states./nChapter 1 found that having insurance coverage, in this case, the public health insurance coverage Seguro Popular, led to greater odds of referral and therefore presents a policy solution to help break down barriers to accessing specialty care. Chapter 2 assessed the quality of care delivered in the prenatal period, measured as the proportion of screenings and preventive care actions carried out. No significant difference in the quality of care delivered was observed between referred and non-referred women. Chapter 3 assessed the change in visit-level quality of care pre- and post-referral for referred versus non-referred women. We found significant declines in quality of care over time in both referred and non-referred women, with referred women experiencing a significantly greater decline than their non-referred counterparts. Qualitative data highlight areas of process losses and potential gains with referred women and shared prenatal care between primary care providers and specialists./nWhile the referral system elements of physical infrastructure and human resources tend to be a focus of initiatives to strengthen systems in resource-constrained settings, failing to strengthen care coordination hamper the development of strong referrals systems that can successfully care for women who require access to more specialized care.

Advisor: Rodriguez, Hector P
Astral Visuality in the Chinese and Inner Asian Cult of Tejaprabhā Buddha, ca. 900-1300 AD

The Song dynasty (960-1279) and its northern neighbors of the "conquest dynasties" witnessed the circulation of new knowledge and techniques in divination and the astral sciences, and the widespread worship of astral deities. These elements cohered within the cult of the Tejaprabhā Buddha, controller of the visible heavens. This dissertation examines how this cult transformed Chinese and Inner Asian visual culture. The corpus of materials it addresses, in particular from the Inner Asian kingdom of the Tangut Xixia (1038-1227), sheds new light on cultural development and interaction across Eurasia. In vivid detail, the paintings, sculptures, prints, and decorated grottoes reveal complex processes of reception, appropriation, translation, and world-making. They connect with a rich body of texts within the astral sciences, including Buddhist scriptures that are here studied closely. Examining not only the symbolic meaning of astral art but also its semiotic mechanisms, this dissertation demonstrates how the visible heavens as represented on earth came to constitute unique forms of visuality, and revisits foundational promises of art history as a modern discipline.

Advisor: Berger, Patricia
The Role of HIF-1α and iNOS in IFN-γ Mediated Control of Mycobacterium tuberculosis Infection

Mycobacterium tuberculosis, the causative agent of tuberculosis, is responsible for an enormous burden of morbidity and mortality worldwide, and is responsible for nearly 2 million deaths annually. As a pathogen, M. tuberculosis is extraordinarily successful, infecting an estimated 2 billion people worldwide. M. tuberculosis is able to thrive in macrophages, an immune cell type that specializes in eating and killing bacteria. Despite the remarkable capabilities of M. tuberculosis to infect and persist in humans, the large majority of immunocompetent people are able to successfully control infection, and there is great interest in understanding what characterizes a successful immune response to M. tuberculosis infection. One of the key molecules in the immune response to M. tuberculosis is the cytokine Interferon gamma (IFN-γ), which is primarily produced by CD4+ T Cells during the adaptive response to infection. IFN-γ is thought to activate macrophages, allowing them to kill M. tuberculosis. Within this dissertation, I describe novel insights into the effects IFN-γ has on macrophages during M. tuberculosis infection./nMy dissertation work has focused primarily on two proteins, Hypoxia Inducible Factor 1 alpha (HIF-1α) and Inducible Nitric Oxide Synthase (iNOS), which are both activated by IFN-γ in macrophages during M. tuberculosis infection. First I demonstrate that HIF-1α activation during M. tuberculosis infection is IFN-γ dependent, and that this activation of HIF-1α is required for successful control of infection both in macrophages and in mice, and that HIF-1α regulates a variety of immune responses including aerobic glycolysis, eicosanoid production, inflammatory cytokine production, and nitric oxide production. Next, I explore the signaling roles of nitric oxide during M. tuberculosis infection. In the context of M. tuberculosis infection, nitric oxide has been assumed to primarily be a direct bactericidal effector. However, nitric oxide has well documented signaling roles in a variety of other contexts. Here, I show that nitric oxide plays key signaling roles during IFN-γ activation of M. tuberculosis infected macrophages. I find that nitric oxide is strongly anti-inflammatory via inhibition of NF-kB signaling, while at the same time nitric oxide activates antimicrobial responses via stabilization of HIF-1α.

Advisor: Stanley, Sarah A
RFID Reader Design for Neural Implants

Brain machine interfaces (BMI) have the ability to revolutionize both healthcare and neuroscience. Recent advances in neural interfaces have demonstrated the ability to control prosthetic limbs and to monitor and treat neurological diseases. Implants with the ability to acquire neural signals are the primary sources of information used to control these systems. To ensure low risk of infection, these implants should be powered wirelessly and communicate wirelessly to the outside world. An efficient, wearable RFID interrogator, sitting outside the skull delivering power to and receiving uplink data from these implants, is a critical component of a wireless BMI system that is convenient and safe for patients to use./nHowever, RFID readers have a classical problem of self-interference from the transmitted carrier leaking into the reader’s receive path, potentially saturating and desensitizing the RX amplifiers. Conventional methods of carrier rejection result in an RFID reader form factor that is too bulky and impractical to be worn on a human head. To solve these problems, we have developed a novel architecture for a fully integrated RFID transceiver that uses only 1 antenna and no bulky isolation components. We exploit the non-linearity of a class E/Fodd switching PA and use it as a demodulator to mix our received backscattered signal back to baseband. The reader is fabricated on a 1.2 mm x 1.5 mm CMOS Integrated Circuit and was tested with a proprietary implant through a channel of pig skin and bovine t-bone to mimic the channel characteristics of a human skull. The system achieves a data rate of 2 Mb/s, while delivering 790 uW of power to the implant at a TX power consumption of 35 mW for an overall link efficiency of 2.3%. This efficient reader is well-suited for BMI systems meant for long-term chronic neural recording for the purposes of monitoring neurological diseases such as epilepsy and Alzheimer’s disease.

Advisor: Rabaey, Jan M