VictorJuiz/thesis huggingface dataset:
Quantum Simulation: Upper and Lower Bounds

Quantum computers now exist, and will likely continue to get bigger and better. But will theyever be useful? That is, are there real-world problems that future quantum computers will be able to solve well enough in a reasonable amount of time, but for which classical computers cannot do the same? This thesis presents a collection of results that together address this question from different directions. The first part limits the utility of quantum computers. We show how to characterize and minimize the cost (in time and memory) of simulating quantum computations on a classical computer in terms of the congestion (a graph property) of a graphical representation of the quantum computation. Therefore, for a quantum computation to have an advantage over classical computation, it must have large congestion. Even when that is the case, better classical simulations, costly though they may be, can help validate and develop quantum computers. We also prove that the fundamental problem of quantum chemistry, the electronic structure problem, is QMA-complete. Therefore, under standard complexity-theoretic assumptions, the solution must be represented using a quantum state, and yet still even quantum computers cannot efficiently find it. The second part includes methods for applying and compiling quantum algorithms in order to maximize the utility of the hardware we have, now and in the future. We introduce the strategy of generalized swap networks and show how to use them to compile quantum algorithms for quantum chemistry and classical optimization. We combine quantum computation with constraint programming in two ways: we show how to combine existing quantum algorithms to speed up the solution of constraint programming problems, which capture a wide range of realistic application domains, and also discuss the application of constraint programming to compiling quantum algorithms. We also present a framework for generalizing the Quantum Approximate Optimization Algorithm to what we call the Quantum Alternating Operator Ansatz. Many of the algorithms are heuristic, but by improving the efficiency of their implementation on actual devices, we improve our chances of successfully trying them out and seeing if they work or not.

Advisor: Vazirani, Umesh
Whaley, Katherine B
Why do Gradient Methods Work in Optimization and Sampling?

Modern machine learning models are complex, hierarchical, and large-scale and are trained using non-convex objective functions. The algorithms used to train these models, however, are incremental, first-order gradient-based algorithms like gradient descent and Langevin Monte Carlo. Why and when do these seemingly simple algorithms succeed?/nThis question is the focus of this thesis. We will consider three problems. The first problem involves the training of deep neural network classifiers using the logistic loss function with gradient descent. We establish conditions under which gradient descent drives the logistic loss to zero, and prove bounds on the rate of convergence. Our analysis applies for smoothed approximations to the ReLU activation function, such as Swish and the Huberized ReLU, proposed in previous applied work. We provide two sufficient conditions for convergence. The first is simply a bound on the loss at initialization. The second is a data separation condition used in prior analyses./nThe second pertains to the problem of sampling from a strongly log-concave density. We provide an information theoretic lower bound on the number of stochastic gradient queries of the log density needed to generate a sample. Several popular sampling algorithms (including many Markov chain Monte Carlo methods) operate by using stochastic gradients of the log density to generate a sample; our results establish an information theoretic limit for all of these algorithms./nThe final problem involves sampling from a distribution whose log-density is non-smooth. We show that a slight modification of the Langevin Monte Carlo algorithm can be used to generate samples from such distributions in polynomial-time. We also provide non-asymptotic guarantees on the rate of convergence of this algorithm.

Advisor: Bartlett, Peter L.
DeWeese, Michael R.
Statistics of Certain Automorphic Representations through the Stable Trace Formula

Since Automorphic representations for general groups are very difficult to study individually, they are often studied in families instead. The Arthur-Selberg trace formula lends itself naturally to answering questions about averages of various parameters of the local components of automorphic representations in so-called harmonic families. In their 2016 work, Shin and Templier realized that, in the special case of representations with discrete series at infinity, the trace formula simplified dramatically enough to compute statistics with good error bounds. These bounds were good enough for applications: first, an averaged Sato-Tate law analogous to Sato-Tate for families of elliptic curves and second, computations of the specific random-matrix statistics that low-lying zeros of $L$-functions in the family follow. Following Shin-Templier's idea, we solve two further problems about discrete-at-infinity families./nFirst, Shin-Templier's work used the invariant trace formula which disallowed families that distinguish representations with infinite component in the same $L$-packet. However, which member of this $L$-packet a representation might correspond to determines some important characteristics---whether the representation is holomorphic or quaternionic for example. Methods related to the stable trace formula can remove this restriction. The key idea is applying a certain "hyperendoscopy" formulation of stabilization used first by Ferrari, though many technical difficulties come up./nSecond, while the equidistribution results achieved are interesting in their own right, they also provide a proof-of-concept that the tools developed for proving them are sufficient for studying very general questions about discrete-at-infinity families. As a further demonstration, we also use these methods to solve a very different problem of computing explicit dimensions of spaces of quaternionic forms on the exceptional group $G_2$.

Advisor: Shin, Sug Woo
Anima

Mixed ensemble piece for Pierrot Ensemble and Drone Machine./nAnima ("soul" in Italian) explores drama, space, and intimacy through the relationship between acoustic and electronic sound sources. The orchestral instruments of the ensemble are amplified, allowing them to fuse with the electronic sounds produced by an analog drone pedal in real time. The sound quality of the drone machine is reminiscent of an organ or bagpipe, with long, sustained tones that are brought to life and warped by a series of guitar effects pedals. The meditative nature of the drone brings a calm, spiritual element to the piece, but when pushed to its sonic limits, the machine is able to produce sounds that are forceful, powerful and intense, in an exploration of extremes that is mirrored by the other instruments of the ensemble.

Advisor: Ueno, Ken
The structure and dynamics of the Syk family kinases

The amino acid sequence of a protein dictates its function. This function is informed not only by the folded shape(s) adopted by the protein but also the dynamic equilibria between these different shapes, or conformations. Evolution modulates the conformational dynamics of proteins in order to optimize existing functions or select for new functions. Here I characterize the conformational dynamics of the regulatory tandem SH2 domain in the Syk family of kinases. I find that in the T-cell specific Syk family kinase, ZAP-70, this domain is predominantly in an ‘inactive’ conformation while its B-cell paralog, Syk, is found in the ‘active’ conformation, even in the absence of the activating ITAM peptide. The long- and short-time scale dynamics of the C-terminal SH2 domains are found to be particularly different between the two proteins. Residues which form stabilizing interactions in the C-SH2 are found in Syk but not in ZAP-70. Significantly, these residues are highly conserved in the Syk lineage but variable in the ZAP-70 linage. These data suggest that the differences in the conformational dynamics of the regulatory tandem SH2 domain are a result of evolutionary selection in both Syk and ZAP-70. In order to explore how the conformational dynamics of the catalytic domains in Syk family kinases may also have diverged I developed a high-throughput assay to probe kinase activity in bacteria. This assay, based on a bacterial two-hybrid, allowed for the screening of the relative activities of a saturation mutagenesis library of a bacterially expressed Syk family kinase. The loss of function mutations identified in this screen correlate well to residues identified in other kinases as critical to function and/or structure. Activating mutations in the regulatory hydrophobic spine, catalytic hydrophobic spine, and activation loop suggest that single point mutants can shift the conformational equilibria of the kinase. These positions may be critical to the tuning of the catalytic activity of Syk and ZAP-70. The data presented in this thesis describe how the conformational dynamics of the paralogous Syk family of kinases have diverged and specialized in order to fulfill their related, yet distinct roles in the adaptive immune system.

Advisor: Marqusee, Susan
Kuriyan, John
Reproductive, Metabolic, and Autonomic Networks Across the Female Lifespan

Mammalian physiology is exquisitely tuned to anticipate and synchronize with environmental oscillations. These oscillations appear to occur in a networked fashion across systems and timescales, such that information about difficult-to-measure systems (e.g., reproductive) may be garnered from easy-to-measure systems (e.g., autonomic, and thermoregulatory). These network dynamics and their implications for health require deep exploration. The goals of this dissertation are to 1) investigate the relationship among reproductive, metabolic, and autonomic rhythms at the hourly to ovulatory timescales, and 2) investigate the conditions under which peripheral timeseries features may serve as proxies for hormonal status. This dissertation traverses discrete stages of reproductive life: adolescence, adulthood, and menopause; as well as the impacts of exogenous network perturbations at each stage of life. Chapter 1 reviews central mechanisms of coupled oscillations in the reproductive and thermoregulatory systems. Chapters 2 and 3 investigate the development of thermoregulatory rhythms across adolescence, their dependence on endogenous and exogenous reproductive hormones, their interaction with natural and artificial environments, and derive peripheral features to monitor reproductive development in the rat. Chapter 4 extends these findings to adult women and investigates shared rhythmicity among autonomic and thermoregulatory outputs and sex hormones for the purposes of LH surge prediction or identification of its absence in menopause. With an eye toward future developments in sex hormone replacement, Chapter 5 compares the effects of the most advanced forms of continuous hormone replacement therapy on biological rhythms in metabolic output. These studies inform our understanding of the structure of reproductive, metabolic, and autonomic networks across life, and reveal translational tools for reproductive health.

Advisor: Kriegsfeld, Lance J
Wilbrecht, Linda
Insights and applications from data driven representation learning

This dissertation is an exploration of data-driven discovery, inspired by neuroscientific studies of the brain. Each of the three projects listed will describe a different domain of input data (self-driving video, medical image, and biological audio), and how investigating neural network behavior trained on that data can reveal insights for each underlying task. Chapter 2 assess motion selectivity in a self-driving network trained to predict two output tasks: steering and motor. We show how different control conditions can define temporal behavior, as well as how frame order is only implicitly learned if relevant for the task, even if the frame order is present in the input and output training data. Chapter 3 assesses self-supervisedly learned representations from retinal fundus images. We show how these learned representations can drive a voting scheme classifier to match supervised and human expert baselines for disease severity prediction in this field, minimizing the bias enforced from clinically relevant ground truth labels. These representations can be further probed to discover mislabeled or easily confused data, as well as phenotype groupings in retinal images that pertain to other pathology and physiology of the subject. These imply NPID and cluster analysis tools could aid clinicians organize and label data from multiple tasks, an expensive process that requires uncommon expertise. Similarly, Chapter 4 extends this idea about data-driven learning to the audio domain. Here, self-supervisedly learned representations from zebra finch data yielded feature encodings that were functionally relevant for classifying vocalization calls, driving a voting scheme classifier to match supervised baseline performance on a generally difficult task of intra-species audio discrimination. We convert audio waveforms to spectrogram image representations of sound signals, and train a CNN on these inputs, so we can probe these visually-defined audio features. To do so, we assessed how neuronal behavioral preferences can be described by a mid-level representation space of audio (the modulation power spectrum), as well as how these features compare to mid-level audio features correlated with zebra finch brain activity. Data-driven algorithms can learn representations with minimal bias, so commonalities between artificial and biological neural systems imply similar encodings are optimally learned. All in all, this dissertation has evaluated deep learning applied on a host of real world tasks aside from standard datasets curated for computer vision. Though each project requires a different lens for explaining functionally salient behavior, we offer data-driven insights into each underlying task that seem to be consistent with experimental findings in neuroscience and medicine.

Advisor: Yu, Stella X
Olshausen, Bruno A
Measuring Stereotype Threat

Stereotype threat is a situational experience, in which individuals feel vulnerable to the possibility of being judged because of a negative stereotype associated to their social group. This experience leads to decline in performance, even among highly skilled individuals. The objective of this research is to provide researchers with a comprehensive theoretical framework of measuring stereotype threat and develop and validate the stereotype threat instrument. To date, no instrument has completely been able to explain the amount of stereotype threat experienced by individuals, placed in different situations and belonging to different social groups./nIn Chapter 1, we review past research on stereotype threat and discuss various influential moderators of stereotype threat. We identify gaps in the pre-existing measures and explore ways of operationalizing the stereotype threat construct. In Chapter 2, we establish the stereotype threat balance framework and define a new stereotype threat construct. We develop the stereotype threat instrument using the four building blocks approach. In Chapter 3, we measure stereotype threat experienced by transfer students studying in four-year universities across the nation. We collect evidence in support of using the proposed instrument as a valid metric for measuring stereotype threat. In Chapter 4, using differential item functioning, we investigate for any potential item bias in the stereotype threat instrument for the different racial groups in our sample. Once we establish no measurement bias, we analyze differences in outcomes for the five racial groups, Asians, Blacks, Latinos, Whites and Others (American Indians or Native Americans, Bi-racial, Pacific Islanders)

Advisor: Wilson, Mark
A Laser Plasma Accelerator based Free-Electron Laser driven by a 100-TW-class laser

Free-Electron Lasers (FELs) with ultra-intense coherent beams have been widely used for a variety of research, such as interrogations of the inner structure of atoms, molecules, clusters, and tightly-spaced crystal structures. Unfortunately, X-ray light sources suffer from both a high cost and limited scientific beam time, due to their kilometer-scale accelerator. On the other hand, laser-plasma accelerators (LPAs), enabling the production of high-quality MeV to GeV electron beams, are compact, less expensive, and have the electron and secondary radiation beams synchronized with a femtosecond laser driver. Here we pursue the technology required for a compact LPA based FEL, which has the capability to deliver high intensity coherent radiation pulses. A state-of-the-art 100-TW-class laser system dedicated to demonstrating an LPA based FEL was constructed. As part of this system, a novel online, non-destructive laser diagnostic, capable of measuring the transverse position and pointing angle of the laser at focus was developed. The diagnostic is based on a unique double-surface-coated wedged-mirror design for the final steering optic in the laser beamline. It produces a witness beam highly correlated with the main beam. By propagating low-power kHz pulses to the focus, the spectra of the focal position and pointing angle fluctuations with their dominant frequencies below 70 Hz, were observed. This diagnostic was also used to characterize the excellent position and pointing angle correlation of the 1-Hz high-power laser pulses to this low-power kHz pulse train, opening a promising path to implementing fast non-perturbative feedback concepts, even on few-Hz-class high-power laser systems. Furthermore, new aspects of the design and physics of an LPA based FEL, which are unique to the electron beam generated by the LPA, were investigated. One method to achieve coherent radiation in an FEL driven by an LPA is to reduce the electron beam slice energy spread by stretching the beam in a chicane, producing a linear energy chirp. Seed radiation at the resonant wavelength propagating in an undulator with the energy chirped beam may then be coherently amplified. With such a linear-energy-chirped beam, it is observed in simulations using GENESIS that the peak frequency of the seeded FEL radiation redshifts linearly with the amount of electron beam chirp and the undulator propagation distance, and inversely with the undulator wavelength and electron energy. This observed FEL radiation redshifting is explained by the dispersion of the microbunching structures during propagation due to the energy chirp of the electron beam, and analyzed using the coupled Maxwell-Vlasov equations describing the FEL dynamics.

Advisor: Schroeder, Carl
Wurtele, Jonathan
Limit shapes in two-dimensional lattice models arising from physics and combinatorics

In this thesis we study aspects of the limit shape phenomenon for two-dimensional lattice models. The three models that will be of greatest interest to us are the six vertex model, the dimer model on the hexagonal lattice, and bounded lecture hall tableaux. Chapter 1 presents a brief overview of the these objects and their relations to one another, as well as the techniques we will use to study them. In Chapter 2, we give a more detailed description of the six vertex model, and describe the Bethe ansatz method for computing the free energy in the thermodynamic limit. We show that there is an infinite family of commuting Hamiltonians governing the evolution of the limiting height function of the inhomogeneous six vertex model on a cylinder. In Chapter 3, we describe the Kasteleyn theory for dimer models on the hexagonal lattice. This dimer model can be seen as a degeneration of the six vertex model from the previous chapter. We study the asymptotic behavior of the dimer correlation functions. In Chapter 4, we turn to the study of an object arising from combinatorics known as bounded lecture hall tableaux. We show that these can be seen as a lattice model of non- intersecting paths on a certain graph. Equivalently, we show how they can be described as a dimer model. We study limit shape formation in the non-intersecting lattice path setting and conjecture formula for the arising Arctic curves. Throughout this thesis many numerical simulations of lattice models are presented. In Chapter 5, we describe an algorithm for numerically simulating lattice models utilizing the parallel processing capabilities of graphical processing units. This method of simulation applies to the previous models studied in this thesis, as well as to many other two-dimensional lattice models. Several examples are given.

Advisor: Reshetikhin, Nicolai
Essays in Development Economics

Big data promises to bring new opportunities of cost saving and data-driven decision making into the field of international development. This dissertation illustrates different ways of utilizing the ever growing repository of satellite imagery and crowd-sourced data to evaluate effectiveness of development programs, while achieving cost saving and timely delivery of insights. Chapter 2 leverages high-resolution daytime satellite imagery and deep learning methods to evaluate development aid programs entirely remotely, using an unconditional cash transfer program in western Kenya as a proof of concept. Chapter 3 shows how we compile crowd-sourced policy data to deliver timely insights on the effectiveness of international COVID-19 containment policies. Chapter 4 explores a new idea to quickly and relatively inexpensively gather more evidence on the long-term impacts of development programs - instead of implementing a new program and tracking the participants for decades to come, we revisit existing randomized control trials that were conducted in the past few decades and identify those that can be followed up for evaluation.

Advisor: Miguel, Edward
Gonzalez-Navarro, Marco
A Gift of the Dharma: The Life and Works of Vanaratna (1384-1468)

The fifteenth-century Buddhist monk and paṇḍita Vanaratna lived a remarkable life that unfolded across the length and breadth of South Asia and crossed the Himalayan range. As a teacher, author, and pilgrim, Vanaratna traveled through and lived among many of the diverse Buddhist communities of his time and witnessed a tumultuous yet vibrant period in the regions’ history. Vanaratna’s life is particularly compelling for the fact that he counts among the last of the Buddhist paṇḍitas of Indic descent to leave an impression in the historical record. Active in eastern India, Sri Lanka, southern and northern India, Nepal, and Tibet, Vanaratna’s life is accessible to us through a rich and extensive body of Sanskrit and Tibetan literature, as well as art-historical and material sources. This study is not the first to give Vanaratna the attention he merits, but it does aim to be the first to take into consideration this large body of material available on his life that has previously been underutilized or not considered at all. The primary witnesses for Vanaratna’s life examined closely here include the Tibetan biographies (rnam thar) of Vanaratna composed by his immediate disciples, the Tibetan biographies of his students and colleagues, his extant works preserved in Sanskrit and Tibetan translation, and art-historical materials that record his life and deeds. These materials will be coordinated with the broader historical record in order to remedy both the dearth of comprehensive studies of Vanaratna’s life and the scarcity of primary sources on the political and religious history of fifteenth-century South Asia, Nepal, and Tibet.

Advisor: von Rospatt, Alexander