VictorJuiz/thesis huggingface dataset:
Veering triangulations and pseudo-Anosov flows

We prove a correspondence theorem between veering triangulations and pseudo-Anosov flows that takes a more dynamical approach compared to Schleimer and Segerman's work. We introduce the notion of a veering branched surface, which provides an equivalent, yet more natural way of studying veering triangulations with pseudo-Anosov flows in mind. This sets up a theory that allows one to study questions regarding the dynamics of pseudo-Anosov flows using the combinatorial tool of veering triangulations/branched surfaces./nWe demonstrate some applications of this theory.
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Unknown environment 'enumerate'/nIn joint work with Eriko Hironaka, we show that if $f$ is a fully-punctured pseudo-Anosov map with at least two puncture orbits, then the normalized dilatation of $f$ is greater or equal to $\mu^4 \approx 6.854$, where $\mu = \frac{1+\sqrt{5}}{2}$ is the golden ratio. Combining this result with a refinement of the argument in (iii), as well as an exhaustive computation, we show that the minimum element of the set of normalized dilatations of fully-punctured pseudo-Anosov maps is $\mu^2$, and that the minimum accumulation point of the set is $\mu^4$./nIn joint work with Michael Landry, we generalize the theory of veering branched surfaces to the setting of sutured manifolds. In particular, we show that for every endperiodic map, the unstable Handel-Miller lamination on its compactified mapping torus is carried by a veering branched surface which is unique up to an explicit set of moves. Furthermore, from this veering branched surface, one can compute the foliation cone in which the associated depth one foliation belongs to.

Advisor: Agol, Ian
“Chiral Pool” Based Routes to Terpenoids, Jungermatrobrunin A and Xishacorene B, and Oxidative Coupling Approaches to Scholarinine A and Pleiocarpamine

Total synthesis is often pursued for one of two motivations: to showcase a strategy and/or methodology or to investigate the function of a natural product. The work described in this dissertation will span an array of natural products but focus on both of these motivations.Chapter 1 briefly discusses “chiral pool” syntheses to give context for some of the work outlined in Chapters 2, 3, and 4 of this dissertation. Chapter 2 discloses work toward rearranged ent-kaurene jungermatrobrunin A, utilizing a “chiral pool” starting material. We employed a “chiral pool” building block to synthesize a common decalin intermediate in enantioenriched fashion. Several potential routes to carry the decalin on to the jungermatrobrunin A framework are discussed. Additionally, the formal synthesis of two natural products, erigerol and forskolin, from the decalin intermediate are described. Chapters 3 and 4 outline the work completed toward the terpene xishacorene B. Chapter 3 focuses on the rearrangements of chrysanthenone derivatives that were discovered while attempting to forge the [3.3.1]bicyclic core of the natural product. These rearrangements were studied experimentally and computationally. The mechanism and underlying principles that were elucidated then aided in the synthesis of the [3.3.1]bicyclic core. Chapter 4 focuses on efforts to take the [3.3.1]bicyclic core to the natural product, highlighting key directed C–H functionalization efforts. Chapter 5 outlines efforts toward the alkaloid scholarinine A through a key oxidative coupling route. An efficient synthesis of scholarinine A would enable our collaborators, Corteva AgriSciences, to probe insecticidal activity of the natural product. Several attempted routes to the carbocyclic framework of scholarinine A are discussed in addition to a potential route to the alkaloid pleiocarpamine. Overall, this dissertation spans an array of targets, detailing work toward both terpene and alkaloid derived natural products.

Advisor: Sarpong, Richmond
Applications of Semiclassical Analysis on the Quantized Torus

The quantized torus is a finite-dimensional Hilbert space that represents quantum mechanicswith periodic phase space. The space can act as a toy model for many quantum effects, and it has the benefit of admitting numerical illustrations. Taking the dimension to infinity corresponds to taking a semiclassical limit, and allows us to visualize the quantum-classical correspondence in a simple setting. In this thesis, we examine several instances of such a semiclassical limit. We begin in the setting of quantum dynamics, and consider eigenvalues of a quantized cat map (i.e. hyperbolic symplectic integer matrix), cut off in phase space to include a fixed point as its only periodic orbit on the torus. We prove a simple formula for the eigenvalues on both the quantized real line and the quantized torus in the semiclassical limit as h → 0. We then consider the case with no fixed points, and prove a superpolynomial decay bound on the eigenvalues. We then study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between mea- surements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by propagation of a semiclassical defect mea- sure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is “less chaotic”. Finally, we apply semiclassical analysis to the field of quantum simulation, and improve bounds on the basic Trotterization algorithm in the setting of the semiclassical Schr ̈odinger equation. We show that the number of Trotter steps used for the observable evolution can be O(1). We then apply the theory of the quantized torus to extend our results to the discretized case, which is amenable to quantum computation models.

Advisor: Zworski, Maciej R
Transport and Spectral Functions in Low-dimensional Quantum Spin Systems

Non-equilibrium properties of quantum materials are examined in low-dimensional systems using matrix product state (MPS) simulations. The spectral function known as the dynamical structure factor, which is directly observed in neutron scattering experiments, is studied for two classes of novel quantum systems. First, recent work has demonstrated that the Heisenberg spin chain exhibits anomalous super-diffusive transport at infinite temperature called Kardar-Parisi-Zhang (KPZ) hydrodynamics. Here, it is demonstrated that signatures of KPZ physics are present in the low-energy spectrum at experimentally relevant temperatures, and this has been detected in KCuF_3 with neutron scattering. The crossover from the ground state physics described by the Tomonaga-Luttinger liquid theory to KPZ hydrodynamics at high temperatures is explored./nSecond, the spectral function of the J_1-J_2 Heisenberg model is studied using MPS simulations. Signatures for the three primary classes of quantum spin liquid (QSL) states in the spectral function are discussed. Our findings point to a U(1) Dirac spin liquid ground state in this model. The calculated spectrum is then compared with the triangluar lattice compounds KYbSe_2 and YbZn_2GaO_5. We find that KYbSe_2 is well modelled by the J_1-J_2 Heisenberg model in close proximity to the QSL phase. Additionally, we find that the QSL phase of the J_1-J_2 Heisenberg model captures the essential features of the YbZn_2GaO_5, suggesting a realization of a Dirac spin liquid in this material./nLastly, the effect of using an MPS to study quantum dynamics is explored. Using an MPS places a restriction on the entanglement in the system, and we study how this modifies time dynamics in a Kibble-Zurek process.We derive that the effect of finite entanglement on a Kibble-Zurek process is captured by a dimensionless scaling function of the ratio of two length scales, one determined dynamically and one by the entanglement restriction. This result is verified numerically in the transverse field Ising model and the 3-state Potts model.

Advisor: Moore, Joel E
From home ranges to range-level connectivity: conservation and behavioral insights from GPS telemetry data

Understanding how animals use space and access key resources can offer critical insights that can inform management and conservation actions. This dissertation explores space use and movement behavior for three large mammalian species in South America at different scales and with different emphases. In Chapter 1, I study vicuña space use in the southern end of the species’ range and compare this with results from other parts of the vicuña range. My study offers the first estimates of vicuña home range sizes using telemetry data and compares these with results from previous studies. Additionally, I assess how vicuñas at my study site share space with conspecifics from other families, and if vicuñas display the strong territorial behavior displayed by the species in other parts of their range. Finally, I investigate how environmental factors may affect vicuña space use, including home range sizes, space-sharing and diel migration patterns. In Chapter 2, I study puma space use in three protected areas in the high Andean and Patagonian steppes and answer questions about the linkages between heterogeneity in the landscape and how pumas use space and move around in their home ranges. As a carnivore species known for its flexibility in adapting to very different habitat conditions, do pumas respond to differences in habitats and terrain factors with changes in behavior? What are the specific ways in which varying landscape variables affect this space use? Do different landscape factors affect behavior across study sites? Does changing landscape heterogeneity affect other factors such as distances moved by pumas? Chapter 3 comprises an assessment of connectivity between key jaguar habitats. First, I use a large, publicly available jaguar GPS telemetry dataset to develop a movement resistance layer, incorporating key environmental and anthropogenic variables known to facilitate or impede jaguar movement across the species’ range in the Americas. Next, I identify corridor areas connecting key jaguar habitats and other protected areas that are likely to be important from a jaguar conservation perspective across the jaguar range. These identified corridors may offer important strategic inputs towards range-level jaguar conservation strategies to ensure connectivity and dispersal between jaguar populations. Together, these analyses offer behavioral and ecological insights that can inform conservation and management actions for continued persistence of these species and their movement across landscapes.

Advisor: Middleton, Arthur D
Development of Site-Selective Protein and Peptide Modification Strategies

The goal of protein modification is to take advantage of the structural complexity and bindingspecificity of a protein and pair it with the additional properties that a synthetic molecule can provide. Many strategies have been developed that target native amino acids present on the protein surface, such as lysine, but these modification methods tend to produce heterogeneous mixtures of products since there are often multiples copies of the residue displayed. To better control the level of modification, the N-terminus has become a popular target since each protein has only one. Our lab has recently developed an N-terminal modification strategy that uses 2-pyridinecarboxaldehyde (2PCA) to form an imidazolidine product. The reaction proceeds through an imine intermediate, which is then cyclized with the second amino acid residue to form the product. The reaction can be performed with all 20 native amino acids at the N-terminus, and high levels of conversion can be obtained. Despite this generality, we have found that over time the imidazolidinone conjugate with 2PCA can reverse to liberate the free, unmodified protein, and that the rate of reversal is dependent on the identity of the N-terminal residue. To better understand the factors that influence product stability, we undertook a mechanistic study of the reaction, using NMR kinetics and DFT calculations, to explore the most likely pathway leading to product formation. Through these studies, we found that N-terminal proline residues create the most stable product, and that glycine at position two can also have a secondary stabilizing effect. DFT calculations supported these findings and allowed for structural analysis of the reactive species and transition states that contributed to this stabilization. With a better understanding of how the reaction proceeds, future goals will be toward the development of 2PCA derivatives that can capitalize on these effects to form irreversible conjugates./nIn addition to N-terminal modification, our lab has also developed several methods forsite-selective tyrosine modification using a tyrosinase enzyme. Tyrosinase is able to oxidize the phenol of tyrosine to a reactive quinone intermediate, which can then be captured by a variety of nucleophiles. Our goal was to use this chemistry and apply it toward the synthesis of cyclic peptides. We have demonstrated that linear peptides bearing a tyrosine and cysteine residue are able to be oxidized with tyrosinase, and the subsequently formed quinone can be coupled with the cysteine thiol to form a cyclic product. In addition to peptide substrates, we have also demonstrated that this chemistry works on peptide sequences displayed at the N- or C-terminus of a protein. Initial work has shown that the level of tyrosinase activity and selectivity is heavily influenced by the identity of the amino acids next to the tyrosine residue, and future work will be focused on engineering new tyrosinase variants that are less sequence dependent.

Advisor: Francis, Matthew
Attosecond Four-Wave Mixing: A Tabletop Nonlinear Spectroscopy in the Extreme Ultraviolet

Nonlinear spectroscopies employ multiple short coherent pulses to generate higher-order polarization signals. The rich degrees of freedom available for controlling the properties of each beam enable highly selective measurements in both the frequency and time domains. Despite their widespread use with optical pulses, nonlinear spectroscopies have been relatively unexplored in the extreme ultraviolet (XUV) or X-ray spectral regions due to the lack of strong coherent light sources until recently. The objective of this project is to develop nonlinear spectroscopies in these short wavelength regions. A table-top technique, attosecond FWM spectroscopy, has been successfully demonstrated, which utilizes a short attosecond XUV pulse and two noncollinear, few-cycle near-infrared pulses to generate background-free third-order polarization signals. The work detailed in this dissertation has broadened the scope of attosecond FWM spectroscopy and thus has taken the development of nonlinear spectroscopy in the XUV one step further. It includes the successful demonstration of probing ultrafast dynamics in molecules, such as O2 and CO2, and exploring the potential of non-resonant FWM process in a wave packet dynamic in Ar. Looking ahead, the upcoming implementation of attosecond FWM experiments at the carbon K-edge will offer new avenues for investigating chemically and biologically significant organic molecules with nonlinear spectroscopies. Ultimately, attosecond FWM spectroscopy will serve as a solid foundation for future explorations in nonlinear spectroscopy at short wavelength, opening doors to innovative applications in various scientific fields.

Advisor: Leone, Stephen R.
Neumark, Daniel M.
Comonadicity for Localizations

The Barr-Beck-Lurie comonadicity theorem characterizes when an adjunction $
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$ can be used to present $\mathcal{C}$ as the category of comodules in $\mathcal{D}$ for the coalgebra object \mbox{$L\circ R \in End(\mathcal{D})$}; loosely speaking, the comodule structure supplies the instructions for how to assemble object in $\mathcal{C}$ from an object in $\mathcal{D}$. This thesis explores the proofs and applications in a number of contexts of this method for endowing categories of interest $\mathcal{C}$ with this tautological algebraically-flavored description, in the hopes of being a kind of handbook and toolkit for someone looking to demonstrate a comandicity result./nThe toolkit grew out of an investigation of a fundamental comonadicity result: Zariski descent for quasicoherent sheaves. Our main effort, joint with Peng Zhou, is in (1) presenting comonadicity statements in the case where $mathcals{C}\xrightarrow{L}\mathcal{D}$ is a product of reflective localizations, and (2) applying it to deduce a descent statement for those closed covers of Lagrangian skeleta which are locally modeled on ones that arise in the coherent-constructible correspondence of Fang-Liu-Treumann-Zaslow.

Advisor: Nadler, David E
Performative Prediction: Theory and Practice

When algorithmic predictions inform social decision-making, these predictions don’t just forecast the world around them: they actively shape it. Building models that influence the world is, in fact, often the primary goal of prediction. For example, in medicine, we predict the risk of a person developing a disease to hopefully minimize the likelihood that it occurs. In elections, we predict voting preferences with the goal of targeting information campaigns that are explicitly designed to influence people’s political beliefs. If done properly, social predictions are performative. They directly interact with the world around them and change it./nIn this thesis, we will first introduce a learning-theoretic framework, performative prediction, that places these problems on formal mathematical grounds. We will illustrate how the framework can be used to analyze common social prediction dynamics, such as repeated retraining in response to strategic effects. Furthermore, we will discuss how it can be used to design decision rules that embrace the distinction between forecasting future outcomes accurately and steering them towards socially desirable targets./nIn the second part of the thesis, we will use these theoretical ideas as a guiding lens to study early warning systems, a popular class of risk prediction tools used in over half of US public high schools. We will present the results of a collaboration with the Wisconsin Department of Public Instruction in which we performed the first large-scale evaluation of the long-term impacts of early warning systems on graduation rates. At the end, we will close with a discussion regarding the policy implications of our work.

Advisor: Bartlett, Peter L
Hardt, Moritz
Data and Label Efficient Representation Learning

Recent advances in unsupervised representation learning have led to a host of widely used AI tools, such as ChatGPT and Stable Diffusion. These tools have been the result of applying relatively simple training algorithms to massive models on massive GPU clusters, even larger amounts of unlabeled training data, and by tuning the algorithms on a host of labeled evaluation tasks. In this dissertation, we present methodologies to address removing each of these components when training models for representation learning, i.e. limited compute, limited training data, and limited evaluation data. This dissertation contains four main chapters that focus on data and label-efficient representation learning./nData efficient representation learning focuses on learning useful representations with less data (labeled or unlabeled), which as discussed throughout this dissertation, can be particularly important for applications with limited data availability. Label efficient representation learning focuses on learning useful representations with little or no human annotations for the training data. As will be discussed, this is important for applications where it is often difficult or impossible to obtain accurately labeled data, such as in privacy sensitive fields or for applications with highly ambiguous label definitions./nThe four chapters in this dissertation that address these topics include: (1) SelfAugment: Automatic Augmentation Policies for Self-Supervised Learning, which explored how to develop augmentation policies with little/no labeled training data and small amount of unlabeled data for unsupervised learning pipelines. (2) Data Efficient Self-Supervised Representation Learning, which explored how to leverage a form of hierarchical pretraining for 80x more data efficient pretraining. (3) Region Similarity Representation Learning, which explored one of the first methods for learning region-level representation by performing contrastive learning at a region (patch-based) level and let to substantial improvements for downstream tasks such as object detection/segmentation when few labeled data were available. (4) Scale-MAE: A Scale-Aware Masked Autoencoder for Multiscale Geospatial Representation Learning, which explored methods for leveraging known scale information for geospatial representation learning.

Advisor: Keutzer, Kurt
Design Methodologies and Automated Generation of Ultra High Speed Wireline SerDes Transmitters

With the ever increasing bandwidth demand in high performance computing, network and communications, machine learning applications, etc, wireline data transfer between multiple chips on the same package has been doubling in per-lane data rate every 3-4 years. The challenging design complexity of the analog and mixed signal front-end circuits necessitates the use of automated process portable layout generators and closed loop design scripts to reduce the turn-around time from circuit design to tape-outs in advanced FinFET technology nodes./nTo that end, this thesis introduces new feature improvements in the Berkeley Analog Generator (BAG) 3++, which is an open source framework for automating process portable circuit generation and encoding closed loop design methodologies. Then the thesis presents the design of a 160 Gbps NRZ transmitter (TX) targeting low loss (~3dB) ultra short reach channels for die-to-die data transfer, with 2 tap FFE for pre-equalization. Some major challenges in this effort are the design of a high speed 8:1 mux stage using inductor-based peaking topologies, and a novel method of creating the 1 UI delayed data stream for the FFE precursor using the available octature clock phases. The TX is taped out in Intel16 process as a part of a complete 160 Gbps NRZ transceiver design, and tested in loopback mode by serially transmitting data to the receiver over a 8.5 mm differential channel on package.

Advisor: Stojanovic, Vladimir
Alon, Elad