VictorJuiz/thesis huggingface dataset:
SL_2(C)-holonomy invariants of links

The Reshetikhin-Turaev construction is a method of obtaining invariants of links (and other topological objects) via the representation theory of quantum groups.It underlies quantum invariants such as the Jones polynomial and its many generalizations. These invariants are algebraic in nature but are conjectured to detect important information about the geometry of links. In this thesis we explore these connections using an enhanced version of the RT construction./nThe geometry of a link complement can be described by a representation of its fundamental group into a Lie group, equivalently the holonomy of a flat Lie algebra-valued connection.Our invariants take this data as input, so we call them holonomy invariants. The case of trivial holonomy recovers the ordinary RT construction./nWe consider holonomy representations into $\operatorname{SL}_2(\mathbb C)$, which are closely related to hyperbolic geometry.In order to define our invariants we consider a particular coordinate system on the space of representations in terms of diagrams we call shaped tangles. We show that these coordinates are closely related to the shape parameters of a certain ideal triangulation (the octahedral decomposition) of the link complement./nUsing shaped tangles we define a family of holonomy invariants $\mathrm{J}_N$ indexed by integers $N \ge 2$, which we call the nonabelian quantum dilogarithm.They can be interpreted as a noncommutative deformation of Kashaev's quantum dilogarithm (equivalently, the $N$th colored Jones polynomial at a $N$th root of unity) or of the ADO invariants, depending on the eigenvalues of the holonomy. Our construction depends in an essential way on representations of quantum $\mathfrak{sl}_2$ at $q = \xi$ a primitive $2N$th root of unity. We show that $\mathrm{J}_N$ is defined up to a power of $\xi$ and does not depend on the gauge class of the holonomy./nAfterwards we introduce a version of the quantum double construction for the holonomy invariants.We show that the quantum double $\mathrm{T}_N$ of the nonabelian dilogarithm $\mathrm{J}_N$ admits a canonical normalization with no phase ambiguity. Finally, we prove that in the case $r = 2$ the doubled invariant $\mathrm{T}_2$ computes the Reidemeister torsion of the link complement twisted by the holonomy representation.

Advisor: Reshetikhin, Nicolai
Principled Statistical Approaches For Sampling and Inference in High Dimensions

The growth in the number of algorithms to identify patterns in modern large-scale datasets has introduced a new dilemma for practitioners: How does one choose between the numerous methods? In supervised machine learning, accuracy on a hold-out dataset is the flagship for choice making. This dissertation presents research that can provide principled guidance for making choices in three popular settings where such a flagship measure is not readily available. (I) Convergence of Markov chain Monte Carlo sampling algorithms, used commonly in Bayesian inference, Monte Carlo integration, and stochastic simulation: We provide explicit non-asymptotic guarantees for state-of-the-art sampling algorithms in high dimensions that can help the user pick a sampling method and the number of iterations based on the computational budget at hand. (II) Statistical-computational challenges with mixture model estimation used commonly with heterogeneous data: We provide non-asymptotic guarantees with Expectation-Maximization for parameter estimation when the number of components is not known, and characterize the number of samples and iterations needed for the desired accuracy, that can inform the user of the potential two-edged price when dealing with noisy data in high dimensions. (III) Reliable estimation of heterogeneous treatment effects (HTE) in causal inference, crucial for decision making in medicine and public policy: We introduce a data-driven methodology StaDISC that is useful for validating commonly used models for estimating HTE, and for discovering interpretable and stable subgroups with HTE using calibration. While we illustrate its usefulness in precision medicine, we believe the methodology to be of general interest in randomized experiments.

Advisor: Wainwright, Martin
Yu, Bin
Molecular Precursors to Actinide Oxide and Nitride Nanomaterials

Chapter 1. The overarching hypothesis and goals of this work are stated. Actinide molecules and nanomaterials are introduced as model systems for nuclear fuels and nuclear forensics. Routes to develop new actinide molecules and materials from bespoke molecular precursors are described./nChapter 2. The current state of nuclear forensic chemistry is reviewed, with discussion of pre- and post-detonation scenarios. Advances in synthetic chemistry and actinide nanomaterials are emphasized, and their relevance to modern nuclear forensic capabilities is highlighted. Numerous real-world case studies from nuclear smuggling and weapons fallout are analyzed and discussed./nChapter 3. Volatile uranium(IV) amidate complexes are synthesized as single-source molecular precursors to uranium oxide films. These complexes are found to decompose to UO2 through an alkene elimination mechanism, enabling epitaxial stabilization of stoichiometric UO2 on {111} silicon substrates. Chemical vapor deposition (CVD) of these single-source precursors yields crystalline, phase-pure UO2 films with a fir tree-like microstructure and a high surface area./nChapter 4. Thorium(IV) amidate complexes are synthesized as volatile single-source molecular precursors for thorium dioxide. The effects of different ligand substituents towards the thermal properties and decomposition mechanism of the precursors are explored. Using X-ray diffraction and spectroscopy to characterize the decomposition products, the purity and crystallinity of ThO2 samples formed from these precursors are compared./nChapter 5. The syntheses of the first homoleptic uranium(III) and uranium(IV) amidate complexes are described. These can be interconverted by chemical reduction/oxidation, showing an unusual change in coordination number from four in the uranium(III) complex to eight in the uranium(IV) complex in the solid state structures./nChapter 6. Three new bridging uranium nitride complexes are synthesized from amidinate-supported precursors and their structural and magnetic properties are explored. The amidinate ligand substituents are seen to affect the composition and nuclearity of the nitride products. Using 15N labeling and acid hydrolysis, the nitrido ligands in all three complexes are proven to form via two-electron reduction of azide. Uranium complexes in the +3, +4, and +5 oxidation states are synthesized and magnetically characterized to provide a reference for the magnetic behavior of the nitrides, all three of which are found to contain uranium(IV) at each metal center./nAppendix. Various projects that have not yet been published are discussed. These include uranium(IV) and uranium(VI) amidate precursors, uranium(IV) heterometallic complexes, actinide triazenide complexes, and precursors for thorium nitride materials.

Advisor: Arnold, John
Learning and Planning for Industrial Robotic Manipulation

Industrial robot manipulators are widely deployed in various manufacturing tasks. Compared with human workers, industrial robot manipulators have advantages in terms of precision, efficiency, and repeatability. But it often requires tremendous engineering efforts to set up and program the manipulator for a specific task. The deficiency of intelligence restricts robots from broader applications. Therefore, it becomes more and more important to enable robots to acquire skills that can accomplish complex tasks and generalize across different scenarios. This dissertation aims to develop skill learning and planning methods for industrial robotic manipulation. We study 1) how to learn manipulation skills when there are uncertainties in the object state estimation, 2) how to generalize the manipulation skills across different scenarios, 3) how to achieve high-level task planning for long-horizon manipulation tasks./nRobotic manipulation of both rigid and deformable objects is studied in this dissertation. To manipulate rigid objects, a contact pose identification method is proposed to compensate for the pose uncertainties in the peg-in-hole assembly. In addition to rigid objects, the manipulation of deformable objects is also studied. A tracking and manipulation framework is proposed to robustly estimate the state of the cable and manipulate the cable to desired shapes. For more complex cable manipulation tasks, which often require long-horizon planning, a spatial representation is proposed to model the spatial relationship between the cable and environment fixtures. Multiple manipulation primitives are efficiently learned to configure the cable to desired states. For the task that combines both assembly and deformable object manipulation, a trajectory optimization with complementarity constraints is formulated to model the hybrid dynamics in belt drive units assembly. The problem is solved as a mathematical program with complementarity constraints to obtain feasible and efficient assembly trajectories.

Advisor: Tomizuka, Masayoshi MT
Systematic Mutagenesis of MS2 Virus-Like Particles for Engineered Properties and Computational Models of Assembly

Virus-like particles (VLPs) are nanoscale proteinaceous materials that show promise as scaffolds for a plethora of applications, including vaccine development, targeted drug delivery, and nanoreactor production. These self-assembling structures are based on viral architectures, but lack genetic material to cause infection. Though theoretically particle features may be finely tailored via genetic manipulation, the phenotypic consequences of mutations to self-assembling proteins remains hard to predict. Throughout this work, advancements in both the functional engineering of VLPs and the fundamental understanding of VLP design constraints are described. A method for selection of chemically modifiable capsids was developed and applied to a systematic library of N-terminally extended bacteriophage MS2 VLPs, resulting in highly reactive capsids for site-specific bioconjugation. The one-dimensional fitness landscape of a non-native MS2 assembly configuration was also constructed and used to develop machine learning models for assembly state prediction. This work highlights the utility of fitness landscaping in producing materials with applications-driven properties and explores the possibilities of in silico modeling for targeted engineering of VLPs. Furthermore, efforts to assess and improve the equity of the Chemistry academic community for marginalized populations are discussed. An annual survey framework was developed for generating quantitative understanding of departmental climate over time, and longitudinal improvements in departmental inclusivity were observed. This method was also used to critically assess how academicvalues of underrepresented graduate students are not well represented in faculty modes of evaluation. The developed framework is readily adaptable to other institutions aiming to improve the inclusion of historically minoritized groups in STEM.

Advisor: Francis, Matthew B.
Design and Deployment of the Simons Array Cosmic Microwave Background Polarization Instrument

The cosmic microwave background (CMB) provides a powerful tool for study of the history and evolution of the universe. Several decades of CMB measurements have yielded an increasingly clearer picture of the contents, structure, history, and fate of the cosmos. While some information channels in the CMB have been measured to their fundamental sensitivity limit, a host of physics remains to be extracted from the faint polarization anisotropies and small-scale angular correlations of the CMB. To such an end, a vibrant field of complementary measurements has developed over time. Adding to these is the Simons Array, a new ground-based telescope array in the Chilean Atacama desert designed to simultaneously search for signatures of cosmic inflation and precisely characterize the gravitational lensing of the CMB by large-scale cosmic structure./nThis thesis describes the Simons Array design as well as several developments that have enabled its sensitivity and their implementation in the experiment. After a brief overview of the scientific motivations and measurement strategies of CMB polarization imaging surveys, an overview of the design and construction of the Simons Array instruments is given. The development of optimized packaging and assembly of close-packed detector hardware and developments in the cryomechanical support of large cryogenic detector arrays are then described. Additionally, advances in the frequency division multiplexed readout of CMB detector arrays representing a factor of several increase in multiplexing capability are presented. Finally, the integration and field commissioning of the first Simons Array telescope is described, and a summary of its initial performance during observations is given.

Advisor: Lee, Adrian T
Structural and Functional Studies of Escherichia coli Ribosomes and Their Polymerization of Unnatural Monomers

The ribosome catalyzes the synthesis of polypeptides with high efficiency and sequence specificity. Repurposing the ribosome as a platform for manufacturing other sequence defined polymers could access a wide variety of previously unattainable molecules and bulk materials. In this work, we aim to understand both engineered and wild type ribosomes through structural and biochemical analysis. We reveal limitations of previous engineering efforts on the ribosome, highlighting the importance of careful mutation and selection techniques. The ribosome we study is poorly assembled and nonfunctional in vitro despite improved polymerization of β-amino acids in vivo. We identify key regions of the ribosome that are disrupted by mutations and offer suggestions for more targeted engineering that will preserve efficient ribosome assembly. We also characterize the structure of the wild type ribosome bound to an unnatural, non-α-amino acid monomer for the first time. This monomer is correctly accommodated into the P site of the ribosome, explaining previously observed activity as an initiator substrate. Lastly, we assess a new, short peptide luciferase-complementing reporter in defined in vitro translations as a better readout of mutant ribosome activity. Using this assay, we show activity of purified active site mutant ribosomes in vitro for the first time, reconciling often observed differences from in vivo systems. These projects underscore the importance of detailed characterization of both the input to and results of ambitious bioengineering efforts.

Advisor: Cate, Jamie
Scalable Machine Learning Algorithms for Biological Sequence Data

Recent advances in sequencing and synthesis technologies have sparked extraordinary growth in large-scale biological experimentation and data collection. This explosive growth necessitates the development of scalable yet accurate methods to investigate increasingly complex biological questions. Machine learning has become a vital tool for addressing the needs of computational biology blending complex statistical models with efficient computation to uncover the underpinnings of biology./nIn this dissertation, I develop three novel machine learning algorithms tailored towards biological sequence data to aid in answering such biological questions. The first method is a general-purpose statistical framework for inference of population genetic parameters. Previous methods focused on developing model approximation methods for a restricted class of models or reducing datasets to a set of hand-crafted summary statistics and comparing them against simulated data. Our framework uses a exchangeable neural network which respects the permutation-invariant symmetries of the data to learn the mapping from simulated datasets to the population genetic parameters of interest./nThe second method extends the ideas from the first method to a more challenging setting where segmentation of the genotypes is necessary to determine tracts of archaic admixture. In this setting, the data are permutation-equivariant requiring a neural network architecture that results in accurate segmentation of archaic admixture tracts./nFinally, the third method focuses on the problem of search in protein engineering to discover high fitness protein sequences of interest. Standard bandit optimization methods often focus on experimental feedback that is purely sequential. In protein engineering, advances in high-throughput synthesis and experimentation can often lead to large batches of size as large as 10^5 where the size of the batch can often be much larger than the number of rounds of experimentation. We propose a family of parallel contextual linear bandit algorithms and analyze their regret bounds.

Advisor: Song, Yun S
Sharp Switching in Tunnel Transistors and Physics-based Machines for Optimization

In this thesis, I report my work on two different projects in the field of energy-efficient computation:/nPart 1 (Device Physics): Tunnel Field-Effect Transistors (tFETs) are one of the candidate devices being studied as energy-efficient alternatives to the present-day MOSFETs. In these devices, the preferred switching mechanism is the alignment (ON) or misalignment (OFF) of two energy levels or band edges. Unfortunately, energy levels are never perfectly sharp. When a quantum dot interacts with a wire, its energy level is broadened. Its actual spectral shape controls the current/voltage response of such transistor switches, from on (aligned) to off (misaligned). The most common model of spectral line shape is the Lorentzian, which falls off as reciprocal energy offset squared. Unfortunately, this is too slow a turnoff, algebraically, to be useful as a transistor switch. Electronic switches generally demand an ON/OFF ratio of at least a million. Steep exponentially falling spectral tails would be needed for rapid off-state switching. This requires a new electronic feature, not previously recognized: narrowband, heavy-effective mass, quantum wire electrical contacts, to the tunneling quantum states./nPart 2 (Systems Physics): Optimization is built into the fundamentals of physics. For example, physics has the principle of least action, the principle of minimum power dissipation, also called minimum entropy generation, and the adiabatic principle, which, in its quantum form, is called quantum annealing. Machines built on these principles can solve the mathematical problem of optimization, even when constraints are included. Further, these machines become digital in the same sense that a flip–flop is digital when binary constraints are included. A wide variety of machines have had recent success at approximately optimizing the Ising magnetic energy. We demonstrate that almost all those machines perform optimization according to the principle of minimum power dissipation as put forth by Onsager. Moreover, we show that this optimization is equivalent to Lagrange multiplier optimization for constrained problems.

Advisor: Yablonovitch, Eli
Methodology development in medical and genomics data

Data that quantify various aspects of medicine and biology are constantly improving and changing. As new techniques become available, opportunities arise to improve our understanding of diseases and other biological properties. With these ever changing data modalities new statistical techniques are required to do proper analysis. In this thesis we analyze, and develop new methods when necessary, for three types of biological data, bulk and single cell RNA-sequencing as well as magnetic resonance imaging (MRI)./nFirst, we develop a statistic for analyzing high-throughput RNA-sequencing data in the context of drug discovery. Changes in gene expression between disease and normal tissues can be used to understand the genomic signature of a disease. When those diseased cells are exposed to a large number of drugs and other perturbations, we can systematically search for the perturbations that reverse the expression of the genes which are altered in the disease. In Chapter 2, we present a new method for quantifying this relationship between disease and drug that outperforms existing methods in simulation, decreases computation time, and is comparable in real data. Additionally, we show an improved ability to quantify the involvement of individual genes in effective drugs. An accompanying software package makes this method easily applicable to new data./nIn the second study we extend an existing semi-supervised learning method called GeneFishing for application to single cell RNA-sequencing data (scRNA-seq). Single cell data has unique properties that make its analysis different from the bulk data used in Chapter 2. While direct application of GeneFishing was not always possible in scRNA-seq, due to dissimilar sources of variation and a marked increase in technical noise, the provided modifications allowed for the analysis to be possible. In addition to using GeneFishing as an effective gene prioritization method in single cell data, we show that it can be used as a way to understand how to measure gene-gene co-expression and as a context specific feature selection method for downstream analyses. Again, we present the accompanying software package, scGeneFishing, for performing GeneFishing in a variety of datasets, including scRNA-seq./nFinally in Chapter 4 of this dissertation we analyze a different type of medical data, brain images. We use MRI scans of patients with primary progressive multiple sclerosis to study the association of regional brain volume at baseline with disease progression. We find that statistics summarizing volume in pre-defined regions of interest (ROIs) are not more predictive of progression than using traditional clinical and MRI variables. However, by deriving data-driven ROIs through voxel-level clustering we are able to achieve better predictive performance.

Advisor: Huang, Haiyan
Bickel, Peter J