VictorJuiz/thesis huggingface dataset:
Baroclinic Critical Layers and Zombie Vortex Instability in Stratified Rotational Shear Flow

Without instabilities, the gas in the protoplanetary disk around a forming protostar remains in orbit rather than falling onto the protostar and completing its formation into a star. Moreover without instabilities in the fluid flow of the gas, the dust grains within the disk's gas cannot accumulate, agglomerate, and form planets. Keplerian disks are linearly stable by Rayleigh’s theorem because the angular momentum of the disk increase/ns with increasing radius. This has led to the belief that there exists a large region in protoplanetary disks, known as the dead zone, which is stable to pure hydrodynamic disturbances. The dead zone is also believed to be stable against magneto-rotational instability (MRI) because the disks' cool temperatures inhibit ionization and therefore prevent the MRI./nA recent study shows the existence of a new hydrodynamic instability called the Zombie Vortex Instability (ZVI), where successive generations of self replicating vortices (\textit{zombie vortices}) may fill the disk with turbulence and destabilize it. The instability is triggered by finite amplitude perturbations, including weak Kolmogorov noise, in stratified (with Brunt-Vasala frequency N) flows, rotating with angular velocity and shear./nSo far there are no observational evidences of the Zombie Vortex Instability and there are very few laboratory experiments of stratified plane Couette flow with background rotation in the literature./nWe perform systematic simulations exploring existence of Zombie Vortex Instability in terms of control parameters (Reynolds number, shear, rotation and stratification). We present a parameter map showing two regimes where ZVI occurs, and interpret the physics that determines the boundaries of the two regimes. We also discuss the effects of viscosity and the existence of a threshold for $Re$. Our study on viscous effect, parameter map and its underlying physics provide guidance for designing practical laboratory experiments in which ZVI could be observed.

Advisor: Marcus, Philip Steven
String Theory, Strongly Correlated Systems, and Duality Twists

In the first part of this dissertation (Chapter 1), I present a construction of a six dimensional (2,0)-theory model that describes the dynamics of the Fractional Quantum Hall Effect (FQHE). The FQHE appears as part of the low energy description of the Coulomb branch of the A_1 (2,0)-theory formulated on a geometry (S^1 x R^2)/Z_k. At low-energy, the configuration is described in terms of a 4+1D supersymmetric Yang-Mills (SYM) theory on a cone (R^2/Z_k) with additional 2+1D degrees of freedom at the tip of the cone that include fractionally charged particles. These fractionally charged "quasi-particles" are BPS strings of the (2,0)-theory wrapped on short cycles. In this framework, a W-boson can be modeled as a bound state of k quasi-particles, which can be used to understand the dynamics of the FQHE./nIn the second part of this dissertation (Chapters 2-3), I investigate the N=4 SYM theory compactified on a circle, with a varying coupling constant (Janus configuration) and an S-duality twist. I relate this setup to a three dimensional topological theory and to a dual string theory. The equality of these descriptions is exhibited by matching the operator algebra, and the dimensions of the Hilbert space. Additionally, this dissertation addresses a classic result in number theory, called quadratic reciprocity, using string theory language. I present a proof that quadratic reciprocity is a direct consequence of T-duality of Type-II string theory. This is demonstrated by analyzing a partition function of abelian N=4 SYM theory on a certain supersymmetry-preserving four-manifold with variable coupling constant and a SL(2,Z)-duality twist.

Advisor: Ganor, Ori J
Growth and Characterization of Silicon Carbide Thin Films and Nanowires

Silicon carbide (SiC) based electronics and sensors hold promise for pushing past the limits of current technology to achieve small, durable devices that can function in high-temperature, high-voltage, corrosive, and biological environments. SiC is an ideal material for such conditions due to its high mechanical strength, excellent chemical stability, and its biocompatibility. Consequently, SiC thin films and nanowires have attracted interest in applications such as micro- and nano-electromechanical systems, biological sensors, field emission cathodes, and energy storage devices./nIn terms of high-temperature microdevices, maintaining low-resistance electrical contact between metal and SiC remains a challenge. Although SiC itself maintains structural and electrical stability at high temperatures, the metallization schemes on SiC can suffer from silicide formation and oxidation when exposed to air. The second chapter presents efforts to develop stable metallization schemes to SiC. A stack consisting of Ni-induced solid-state graphitization of SiC and an atomic layer deposited layer of alumina is shown to yield low contact resistivity of Pt/Ti to polycrystalline n-type 3C-SiC films that is stable in air at 450 ºC for 500 hours./nThe subsequent chapters focus on the growth and structural characterization of SiC nanowires. In addition to its structural stability in harsh-environments, there is interest in controlling SiC crystal structure or polytype formation. Over 200 different polytypes have been reported for SiC, with the most common being 3C, 4H, and 2H. In terms of SiC nanowire growth, the 3C or cubic phase is the most prevalent. However, as the stacking fault energy for SiC is on the order of a few meV, it is common to have a high density of stacking faults within a given SiC crystal structure. Thus, to enable reliable performance of SiC nanowires, a growth method that can promote a specific polytype or reduce stacking faults is of importance. Ni-catalyzed chemical vapor deposition method is employed for the growth of the nanowires. The effects of substrate structure and quality as well as the various growth parameters such as temperature, pressure, and post-deposition annealing are investigated. Most significant has been the growth and characterization of vertically aligned hexagonal phase (or 4H-like) SiC nanowires grown on commercially available 4H-SiC (0001)./nThe studies presented in this thesis tackle issues in SiC metallization and nanowire growth in efforts to expand the versatility of SiC as a material platform for novel devices.

Advisor: Maboudian, Roya
Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations

I study the geometry and the conservation laws of second-order partial differential equations of parabolic type. The general strategy is to replace the differential equation with an exterior differ- ential system—a smooth manifold with extra geometric structure that keeps track of the solutions—and then use geometric methods./nI use Cartan’s method of equivalence to determine the essential geometric curvatures of parabolic equations. I then explain the geometric significance of these curvatures, including some normal form results. The study of these curvatures also leads me naturally to a nice class of equations, the parabolic Monge-Ampe`re equations./nIn the second half, I study the relationship between the geometry and the conservation laws of parabolic equations. In particular, I prove that for a specific class of parabolic equations, the gen- erating function of any conservation law depends on at most second derivatives of solutions. This is in contrast to examples such as the KdV equation, which have conservation laws of arbitrarily high order.

Advisor: Bryant, Robert L
Design of the RISC-V Instruction Set Architecture

The hardware-software interface, embodied in the instruction set architecture (ISA), is arguably the most important interface in a computer system. Yet, in contrast to nearly all other interfaces in a modern computer system, all commercially popular ISAs are proprietary. A free and open ISA standard has the potential to increase innovation in microprocessor design, reduce computer system cost, and, as Moore’s law wanes, ease the transition to more specialized computational devices./nIn this dissertation, I present the RISC-V instruction set architecture. RISC-V is a free and open ISA that, with three decades of hindsight, builds and improves upon the original Reduced Instruction Set Computer (RISC) architectures. It is structured as a small base ISA with a variety of optional extensions. The base ISA is very simple, making RISC-V suitable for research and education, but complete enough to be a suitable ISA for inexpensive, low-power embedded devices. The optional extensions form a more powerful ISA for general-purpose and high-performance computing. I also present and evaluate a new RISC-V ISA extension for reduced code size, which makes RISC-V more compact than all popular 64-bit ISAs.

Advisor: Patterson, David
Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis

As the amount of data collected in our world increases, reliable compression algorithms are needed when datasets become too large for practical analysis, when significant noise is present in the data, or when the strongest signals in the data are needed. In this work, two data compression algorithms are presented. The main result is a low-rank approximation algorithm (a type of compression algorithm) that uses modern techniques in randomization to repurpose a classic algorithm in the field of linear algebra called the LU decomposition to perform data compression. The resulting algorithm is called Spectrum-Revealing LU (SRLU)./nBoth rigorous theory and numeric experiments demonstrate the effectiveness of SRLU. The theoretical work presented also develops a framework with which other low-rank approximation algorithms can be analyzed. As the name implies, Spectrum-Revealing LU seeks to capture the entire spectrum of the data (i.e. to capture all signals present in the data)./nA second compression algorithm is also introduced, which seeks to compression graphs. Called a sparsification algorithm, this algorithm can accept a weighted or unweighted graph and produce an approximation without changing the weights (or introducing weights in the case of an unweighted graph). Theoretical results provide a bound on the quality of the results, and a numeric example is also explored.

Advisor: Gu, Ming
Persson, Per-Olof
Fixing Gauge Redundancies in Quantum Gravity

Evidence has accumulated that descriptions of systems in quantum gravity depend strongly on various choices of gauge-fixing including a choice of "reference frame." We discuss several explicit examples of this reference frame dependence and, in doing so, clarify a number of general features of quantum gravity including the thermodynamics of spacetime, the holographic principle, and black hole complementarity./nOur discussion focuses on two superficially independent subjects. The first of these is that of holographic screens. These are codimension-one surfaces that are preferred from the perspective of the holographic principle. They are generated by a choice of null foliation and, in particular, can be fixed by the light cones of a worldline. We will study a class of holographic screens called past and future holographic screens and strengthen a recently proven area law for these surfaces. We then introduce a definition of holographic entanglement entropy associated with past and future holographic screens and, in doing so, provide new evidence for the importance of screens in quantum gravity. Our second major emphasis is on the black hole information paradox and the firewall paradox. We give a set of hypotheses for the microscopic structure of black holes that appears to be self-consistent and admit a smooth horizon despite the AMPS arguments. Our model relies on the principle that the quantum information associated with spacetime is both delocalized and reference frame dependent.

Advisor: Nomura, Yasunori
A Search for Lepton-Flavor-Violating Decays of the 125 GeV Higgs Boson with Hadronically Decaying Tau Leptons in the 20.3 fb^{-1}, \sqrt{s} = 8 TeV Dataset Collected in 2012 by the ATLAS Detector at the Large Hadron Collider

This dissertation presents a search for lepton-flavor-violating (LFV) decays of the 125 GeV Higgs boson in final states of \mu\tau_{\mathrm{had}} and e\tau_{\mathrm{had}} in the full dataset collected by the ATLAS detector in 2012. The search is based on data samples of proton--proton collisions at \sqrt{s} = 8 TeV, corresponding to an integrated luminosity of 20.3 fb^{-1}. The topology of LFV events is exploited through an optimized selection of objects and events, with signal and control regions defined by event kinematics. A binned likelihood fit searching for the presence of LFV Higgs decays is performed using the reconstructed Higgs boson mass as the discriminating variable. No such decays are observed. The expected (observed) upper limits at 95% confidence on the branching ratios for the muon and electron final states are found to be Br(H \rightarrow \mu\tau) = 1.24% (1.85%) and Br(H \rightarrow e\tau) = 2.07% (1.81%).

Advisor: Shapiro, Marjorie D
Cold Pools, Effective Buoyancy, and Atmospheric Convection

‘Cold pools’ are pools of air that have been cooled by rain evaporation, and which subsequently slump down and spread out across the Earth’s surface due to their negative buoyancy. Such cold pools, which typically arise from rain produced by convection, also feed back upon convection by kicking up new convection at their edges./nThis thesis studies the interaction of cold pools and convection at two levels of detail: on one end, we study the dynamics and thermodynamics of a single, idealized cold pool, and on the other, we study the interplay between a steady-state ensemble of convection and the many cold pools that accompany it. A recurring notion is that of ‘effective buoyancy’, which is the net acceleration experienced by a density anomaly such as a cold pool, including the back-reaction of the environment (i.e. the ‘virtual mass effect’) which reduces the net acceleration from its Archimedean value. We derive analytical formulae for the effective buoyancy of cold pools and other roughly cylindrical density anomalies, and use the same framework to understand the forces at play when cold pools trigger new convection. We also analyze the sizes and lifetimes of cold pools, and examine the impact of cold pools on the organization (i.e. clustering) of convection.

Advisor: Romps, David M
Wurtele, Jonathan
Small Sample Inference

Multiple comparisons and small sample size, common characteristics of many types of "Big Data" including those that are produced by genomic studies, present specific challenges that affect reliability of inference. Use of multiple testing procedures necessitates estimation of very small tail probabilities and thus approximation of distal tails of a test statistic distribution. Results based on large deviation theory provide a formal condition that is necessary to guarantee error rate control given practical sample sizes, linking the number of tests and the sample size; this condition, however, is rarely satisfied. Using methods that are based on Edgeworth expansions (relying especially on the work of Peter Hall), we explore what it might translate into in terms of actual error rates. Our investigation illustrates how far the actual error rates can be from the declared nominal levels, indicating poor error rate control./nEdgeworth expansions, providing higher order approximations to the sampling distribution, also offer a promising direction for data analysis that could ameliorate the situation. In Chapter 1, we derive generalized expansions for studentized mean-based statistics that incorporate ordinary and moderated one- and two-sample t-statistics as well as Welch t- test. Fifth-order expansions are generated with our developed software that can be used to produce expansions of an arbitrary order. In Chapter 2, we propose a data analysis method based on these expansions that includes tail diagnostic procedure and small sample adjustment. Using the software algorithm developed for generating expansions, we also obtain results for unbiased moment estimation of a general order. Chapter 3 introduces a general linear combination (GLC) bootstrap, which is specifically tailored for small sample size. A stabilized variance version of GLC bootstrap, based on empirical Bayes approach, is developed for high-dimensional data. Applying these methods to clustering, we propose an inferential procedure that produces pairwise clustering probabilities.

Advisor: Hubbard, Alan E
Detection, Quantification, and Characterization of Diverse RNA Transcript Isoforms

RNA sequencing (RNA-Seq) is a powerful technique to assess gene expression and to characterize RNA transcripts, as it allows for high-throughput study of RNA at a nucleotide resolution. It can provide transcriptome-wide information on alternative splicing, novel transcripts, tissue-specific and allele-specific expression, and RNA- DNA differences. While high-throughput sequencing has revolutionized RNA research, there are several challenges associated with its application. The limiting factors in the utility of any RNA-Seq experiment are two-fold: (1) at the experimental stage, correctly isolating and preparing the sample so as to capture all transcripts of interest, and (2) at the data analysis stage, utilizing the right computational methods to accurately assign sequencing reads to the correct transcripts. Non-canonical isoforms can easily be missed by standard methods at either stage. As RNA exists in a multitude of forms corresponding to its diverse functions, with variations in sequence, length, shape, and number, it is important to develop sequencing methods that are capable of capturing this diversity./nHerein, we describe methods for performing RNA sequencing experiments and data analysis, illustrate their utility in experimental studies using Drosophila melanogaster, and present novel methods for the detection, quantification, and characterization of two non-canonical transcript isoforms: the fusion transcript and circular RNA.

Advisor: Pachter, Lior
Fun with Fields

This dissertation is a collection of results in model theory, related in one way or another to fields, NIP theories, and elimination of imaginaries. The most important result is a classification of dp-minimal fields, presented in Chapter 9. We construct in a canonical fashion a non-trivial Hausdorff definable field topology on any unstable dp-minimal field. Using/nthis we classify the dp-minimal pure fields and valued fields up to elementary equivalence. Furthermore we prove that every VC-minimal field is real closed or algebraically closed./nIn Chapter 11, we analyze the theories of existentially closed fields with several valuations and orderings, as studied by van den Dries. We show that these model complete theories are NTP2, and analyze forking, dividing, and burden in these theories. The theory of algebraically closed fields with n independent valuation rings turns out to be an example of such a theory. This provides a new and natural example of an NTP2 theory which is neither/nsimple nor NIP, nor even a conceptual hybrid of something simple and something NIP./nIn Chapter 8, we exhibit a bad failure of elimination of imaginaries in a dense o-minimal structure. We produce an exotic interpretable set which cannot be put in definable bijection with a definable set, after naming any amount of parameters. However, we show that these exotic interpretable sets are still amenable to some of the tools of tame topology: they must/nadmit nice definable topologies locally homeomorphic to definable sets./nChapter 12 proves the existence of Z/nZ-valued definable strong Euler characteristics on pseudofinite fields, which measure the non-standard “size” of definable sets, mod n. The non-trivial result is that these “sizes” are definable in families of definable sets. This could probably be proven using etale cohomology, but we give a more elementary proof relying heavily on the theory of abelian varieties./nWe also present simplified and new proofs of several model-theoretic facts, including the definability of irreducibility and Zariski closure in ACF (Chapter 10), and elimination of imaginaries in ACVF (Chapter 6). This latter fact was originally proven by Haskell, Hrushovski, and Macpherson. We give a proof that is drastically simpler, inspired by Poizat’s proofs of elimination of imaginaries in ACF and DCF.

Advisor: Scanlon, Thomas
Erasure Coding for Big-data Systems: Theory and Practice

Big-data systems enable storage and analysis of massive amounts of data, and are fueling the data revolution that is impacting almost all walks of human endeavor today. The foundation of any big-data system is a large-scale, distributed, data storage system. These storage systems are typically built out of inexpensive and unreliable commodity components, which in conjunction with numerous other operational glitches make unavailability events the norm rather than the exception./nIn order to ensure data durability and service reliability, data needs to be stored redundantly. While the traditional approach towards this objective is to store multiple replicas of the data, today's unprecedented data growth rates mandate more efficient alternatives. Coding theory, and erasure coding in particular, offers a compelling alternative by making optimal use of the storage space. For this reason, many data-center scale distributed storage systems are beginning to deploy erasure coding instead of replication. This paradigm shift has opened up exciting new challenges and opportunities both on the theoretical as well as the system design fronts. Broadly, this thesis addresses some of these challenges and opportunities by contributing in the following two areas:/n(1) Resource-efficient distributed storage codes and systems:/nAlthough traditional erasure codes optimize the usage of storage space, they result in a significant increase in the consumption of other important cluster resources such as the network bandwidth, input-output operations on the storage devices (I/O), and computing resources (CPU). This thesis considers the problem of constructing codes, and designing and building storage systems, that reduce the usage of I/O, network, and CPU resources while not compromising on storage efficiency./n(2) New avenues for erasure coding in big-data systems:/nIn big-data systems, the usage of erasure codes has largely been limited to disk-based storage systems, and furthermore, primarily towards achieving space-efficient fault tolerance---in other words, to durably store "cold'' (less-frequently accessed) data. This thesis takes a step forward in exploring new avenues for erasure coding---in particular for "hot'' (more-frequently accessed) data---by showing how erasure coding can be employed to improve load balancing, and to reduce the (median and tail) latencies in data-intensive cluster caches./nAn overarching goal of this thesis is to bridge theory and practice. Towards this goal, we present new code constructions and techniques that possess attractive theoretical guarantees. We also design and build systems that employ the proposed codes and techniques. These systems exhibit significant benefits over the state-of-the-art in evaluations that we perform in real-world settings, and are also slated to be a part of the next release of Apache Hadoop.

Advisor: Ramchandran, Kannan