Physical Sciences and Mathematics Commons^™

On Adaptivity And Randomness For Streaming Algorithms, Manuel Stoeckl

Dartmouth College Ph.D Dissertations

A streaming algorithm has a limited amount of memory and reads a long sequence (data stream) of input elements, one by one, and computes an output depending on the input. Such algorithms may be used in an online fashion, producing a sequence of intermediate outputs corresponding to the prefixes of the data stream. Adversarially robust streaming algorithms are required to give correct outputs with a desired probability even when the data stream is adaptively generated by an adversary that can see all intermediate outputs of the algorithm. This thesis binds together research on a variety of problems related to the …

Probing Central Spin Decoherence Dynamics Of Electronic Point Defects In Diamond And Silicon, Ethan Que Williams

Dartmouth College Ph.D Dissertations

Electron spins of point defects in diamond and silicon can exhibit long coherence times, making them attractive platforms for the physical implementation of qubits for quantum sensing and quantum computing. To realize these technologies, it is essential to understand the mechanisms that limit their coherence. Decoherence of these systems is well described by the central spin model, wherein the central electron spin weakly interacts with numerous electron and nuclear spins in its environment. The dynamics of the resultant dephasing can be probed with pulse electron paramagnetic resonance (pEPR) experiments.

Using a 2.5 GHz pEPR spectrometer built in-house, we performed multi-pulse …

Probing And Enhancing The Reliance Of Transformer Models On Poetic Information, Almas Abdibayev

Dartmouth College Ph.D Dissertations

Transformer models have achieved remarkable success in the widest variety of domains, spanning not just a multitude of tasks within natural language processing, but also those in computer vision, speech, and reinforcement learning. The key to this success is largely attributed to the self-attention mechanism, particularly its ability to scale in performance as it grows in the number of parameters. Extensive effort has been underway to study the major linguistic properties learned by these models during the course of their pretraining. However, the role of certain finer linguistic phenomena present in language and their utilization by Transformers has not been …

Equilibrium And Quench-Dynamical Studies Of Ultracold Fermions In Ring-Shaped Optical Traps, Daniel Gordon Allman

Dartmouth College Ph.D Dissertations

The unique capability to precisely tune the few and many-body configurations of
ultracold Fermi gases provides a multi-dimensional platform for studying novel, ex-
otic aspects of quantum systems. These aspects include superfluid/superconducting
phenomena supported by potentially exotic pairing mechanisms, non-equilibrium and
critical dynamics, and proposed quantum sensing or computing applications based on
atomtronics.
Ring geometries provide natural arenas for probing transport properties of super-
fluids. Metastable states of quantized superfluid flow —persistent currents— exhibit
remarkable properties, and the manner in which they form is an incredibly rich sub-
ject. Studies of quenched superfluids demonstrate that persistent currents can form
from …

Rough Numbers And Variations On The Erdős--Kac Theorem, Kai Fan

Dartmouth College Ph.D Dissertations

The study of arithmetic functions, functions with domain N and codomain C, has been a central topic in number theory. This work is dedicated to the study of the distribution of arithmetic functions of great interest in analytic and probabilistic number theory.

In the first part, we study the distribution of positive integers free of prime factors less than or equal to any given real number y>=1. Denoting by Phi(x,y) the count of these numbers up to any given x>=y, we show, by a combination of analytic methods and sieves, that Phi(x,y)<0.6x/\log y holds uniformly for all 3<=y<=sqrt{x}, improving upon an earlier result of the author in the same range. We also prove numerically explicit estimates of the de Bruijn type for Phi(x,y) which are applicable in wide ranges.

In the second part, we turn …

Development Of Single-Crystalline And 3d-Printable Porous Organic Materials, Mingshi Zhang

Dartmouth College Ph.D Dissertations

Porous organic materials with designable structures, large surface areas, low densities, and unique electronic and optical properties have found widespread applications in adsorption, separation, energy storage, and catalysis. However, the majority of organic porous materials are synthesized as fluffy powders, which poses two fundamental challenges for them. Firstly, they lack a single-crystal structure at the microscopic scale, making it difficult to study the specific pore size, shape, and potential substrate binding sites at the atomic level and further establish the structure-property relationship. Secondly, they lack the general processing method and macroscopic shape design, making it difficult to manufacture suitable components …

Self-Supervised Pretraining And Transfer Learning On Fmri Data With Transformers, Sean Paulsen

Dartmouth College Ph.D Dissertations

Transfer learning is a machine learning technique founded on the idea that knowledge acquired by a model during “pretraining” on a source task can be transferred to the learning of a target task. Successful transfer learning can result in improved performance, faster convergence, and reduced demand for data. This technique is particularly desirable for the task of brain decoding in the domain of functional magnetic resonance imaging (fMRI), wherein even the most modern machine learning methods can struggle to decode labelled features of brain images. This challenge is due to the highly complex underlying signal, physical and neurological differences between …

Rhodium-Catalyzed Asymmetric Synthesis Of P-P And P-C Bonds, Sarah T. Chachula

Dartmouth College Ph.D Dissertations

Chapter 1: Synthesis, Structure, Dynamics, and Enantioface-Selective η3-Benzyl Coordination in the Chiral Rhodium Complexes Rh(diphos*)(η3-CH2Ph) Abstract: The rhodium benzyl complexes Rh(diphos*)(η3-CH2Ph) (1-14, diphos* = chiral bis(phosphine)) were prepared either by treatment of Rh(COD)(η3-CH2Ph) (15, COD = 1,5-cyclooctadiene) with diphos*, or from the reaction of [Rh(diphos*)(Cl)]2 (16- 20) with PhCH2MgCl. For C2-symmetric diphos*, observation of one set of NMR signals for complexes 1-12 suggested that the two diastereomers in which different 3-benzyl enantiofaces were coordinated to rhodium interconverted rapidly on the NMR time scale via suprafacial shifts; observation of five inequivalent aryl 1H NMR signals showed that antarafacial shifts were slow …

System-Characterized Artificial Intelligence Approaches For Cardiac Cellular Systems And Molecular Signature Analysis, Ziqian Wu

Dartmouth College Ph.D Dissertations

The dissertation presents a significant advancement in the field of cardiac cellular systems and molecular signature systems by employing machine learning and generative artificial intelligence techniques. These methodologies are systematically characterized and applied to address critical challenges in these domains. A novel computational model is developed, which combines machine learning tools and multi-physics models. The main objective of this model is to accurately predict complex cellular dynamics, taking into account the intricate interactions within the cardiac cellular system. Furthermore, a comprehensive framework based on generative adversarial networks (GANs) is proposed. This framework is designed to generate synthetic data that faithfully …

Cosmological Vector Fields And Constraining The Neutrino Masses, Avery J. Tishue

Dartmouth College Ph.D Dissertations

In this thesis I explore two main topics: the role and consequences of cosmological vector fields, and new ideas for constraining fundamental physics with state-of-the-art experiments. These topics are disparate in content and technique but unified in their attempt to leverage novel approaches to better understand longstanding questions in cosmology. These questions, such as ``What is causing the universe to accelerate today?'' and ``What are the neutrino masses?'', underpin the modern cosmological paradigm. They play a key role in our understanding of cosmic history, the formation of structure, and the fate of our universe. Answers to or hints about these …

Jones Polynomial Obstructions For Positivity Of Knots, Lizzie Buchanan

Dartmouth College Ph.D Dissertations

The fundamental problem in knot theory is distinguishing one knot from another. We accomplish this by looking at knot invariants. One such invariant is positivity. A knot is positive if it has a diagram in which all crossings are positive. A knot is almost-positive if it does not have a diagram where all crossings are positive, but it does have a diagram in which all but one crossings are positive. Given a knot with an almost-positive diagram, it is in general very hard to determine whether it might also have a positive diagram. This work provides positivity obstructions for three …

Effective Non-Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics, Vincent Paul Flynn

Dartmouth College Ph.D Dissertations

Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an "effective non-Hermiticity" intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search …

Brill--Noether Theory Via K3 Surfaces, Richard Haburcak

Dartmouth College Ph.D Dissertations

Brill--Noether theory studies the different projective embeddings that an algebraic curve admits. For a curve with a given projective embedding, we study the question of what other projective embeddings the curve can admit. Our techniques use curves on K3 surfaces. Lazarsfeld's proof of the Gieseker--Petri theorem solidified the role of K3 surfaces in the Brill--Noether theory of curves. In this thesis, we further the study of the Brill--Noether theory of curves on K3 surfaces.

We prove results concerning lifting line bundles from curves to K3 surfaces. Via an analysis of the stability of Lazarsfeld--Mukai bundles, we deduce a bounded version …

New Physics In The Age Of Precision Cosmology, Vivian I. Sabla

Dartmouth College Ph.D Dissertations

The Lambda-cold dark matter (LCDM) model has become the standard model of cosmology because of its ability to reproduce a vast array of cosmological observations, from the earliest moments of our Universe, to the current period of accelerated expansion, which it does with great accuracy. However, the success of this model only distracts from its inherent flaws and ambiguities. LCDM is purely phenomenological, providing no physical explanation for the nature of dark matter, responsible for the formation and evolution of large-scale structure, and giving an inconclusive explanation for dark energy, which drives the current period of accelerated expansion.

Furthermore, cracks …

Synthetic, Catalytic, And Mechanistic Studies Of Supermesityl Phosphiranes And Phosphines, Ryan M. Tipker

Dartmouth College Ph.D Dissertations

Methylation of P-stereogenic phosphiranes Mes*PCH2CH(R) (Mes* = 2,4,6-(t-Bu)3C6H2, R = Me, Ph) with MeOTf gave P-stereogenic phosphiranium cations; [Mes*P(Me)CH2CH(Ph)][OTf] underwent syn-anti isomerization via P-epimerization. Mechanistic studies suggested ring opening gave a hyperconjugation-stabilized carbocation in which pyramidal inversion at P was promoted by s-interaction with the pendant cation. Attempted phosphirane protonation with HOTf resulted in ring opening and C-H activation of an o-t-Bu group to give phospholanium cations. Treatment of [Mes*P(Me)CH2CH(Ph)][OTf] with LiPPh2 gave bis(phosphino)ethanes. Copper- catalyzed P-alkylation of the secondary phosphine PHPh(Mes*) with benzyl bromides gave P-stereogenic tertiary phosphines with a supermesityl substituent.

The Extremes Of Galaxy Formation & Evolution, Kelly E. Whalen

Dartmouth College Ph.D Dissertations

Galaxy populations are shaped by the physical processes that regulate their star formation and central black hole growth throughout cosmic time. The primary aim of this thesis is to understand how these processes occur and how they shape evolution in some of the most extreme galaxies in the Universe including quasars, compact starbursts, and ultra-diffuse dwarfs. Gas-rich major mergers funnel large amounts of gas towards the nucleus, triggering rapid AGN accretion and compact star formation. In this work, I study powerful quasars and extreme, massive, compact starburst galaxies within the context of merger-driven galaxy evolution scenarios. One aim of this …

Counting Elliptic Curves With A Cyclic M-Isogeny Over Q, Grant S. Molnar

Dartmouth College Ph.D Dissertations

Using methods from analytic number theory, for m > 5 and for m = 4, we obtain asymptotics with power-saving error terms for counts of elliptic curves with a cyclic m-isogeny up to quadratic twist over the rational numbers. For m > 5, we then apply a Tauberian theorem to achieve asymptotics with power saving error for counts of elliptic curves with a cyclic m-isogeny up to isomorphism over the rational numbers.

Spectral Sequences And Khovanov Homology, Zachary J. Winkeler

Dartmouth College Ph.D Dissertations

In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant MKh(L) for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the Asaeda-Pryzytycki-Sikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a Z^n-filtration on the Khovanov complex, and as a result we will get various spectral sequences relating MKh(L) to Kh(L), AKh(L), and APS(L). Our …

Triangular Modular Curves Of Low Genus And Geometric Quadratic Chabauty, Juanita Duque Rosero

Dartmouth College Ph.D Dissertations

This manuscript consists of two parts. In the first part, we study generalizations of modular curves: triangular modular curves. These curves have played an important role in recent developments in number theory, particularly concerning hypergeometric abelian varieties and approaches to solving generalized Fermat equations. We provide a new result that shows that there are only finitely many Borel-type triangular modular curves of any fixed genus, and we present an algorithm to list all such curves of a given genus.

In the second part of the manuscript, we explore the problem of computing the set of rational points on a smooth, …

Combating Fake News: A Gravity Well Simulation To Model Echo Chamber Formation In Social Media, Jeremy E. Thompson

Dartmouth College Ph.D Dissertations

Fake news has become a serious concern as distributing misinformation has become easier and more impactful. A solution is critically required. One solution is to ban fake news, but that approach could create more problems than it solves, and would also be problematic from the beginning, as it must first be identified to be banned. We initially propose a method to automatically recognize suspected fake news, and to provide news consumers with more information as to its veracity. We suggest that fake news is comprised of two components: premises and misleading content. Fake news can be condensed down to a …

The Multiset Partition Algebra: Diagram-Like Bases And Representations, Alexander N. Wilson

Dartmouth College Ph.D Dissertations

There is a classical connection between the representation theory of the symmetric group and the general linear group called Schur--Weyl Duality. Variations on this principle yield analogous connections between the symmetric group and other objects such as the partition algebra and more recently the multiset partition algebra. The partition algebra has a well-known basis indexed by graph-theoretic diagrams which allows the multiplication in the algebra to be understood visually as combinations of these diagrams. My thesis begins with a construction of an analogous basis for the multiset partition algebra. It continues with applications of this basis to constructing the irreducible …

Oh The Places Snow Blows: Observations And Impacts Of Snow Redistribution On Arctic Sea Ice, David Clemens-Sewall

Dartmouth College Ph.D Dissertations

Arctic sea ice has declined dramatically due to climate change. This decline impacts Arctic communities, ecosystems, international trade, and the world's climate. However, due to uncertain physical processes, climate models generally do not capture the severity of the observed decline---adding uncertainty to projections of future climate change. A major uncertainty in the Arctic sea ice component of climate models is how much heat passes through the snow on top of the ice in the winter. This heat flux controls how much ice grows each winter, impacting how much ice survives the summer melt. Snow is an excellent thermal insulator (about …

Quantifying The Economic Costs Of Global Warming, Christopher W. Callahan

Dartmouth College Ph.D Dissertations

Climate change poses a threat to the well-being of people across the globe. Rising global temperatures will increase the frequency and magnitude of extreme climate events, threatening the lives and livelihoods of vulnerable people. Yet the magnitude and persistence of these economic impacts are poorly understood, making it difficult both to design equitable mitigation and adaptation strategies and to hold emitters accountable for the impacts of their emissions. In this thesis, I combine methods from detection and attribution, climate projection, and causal inference to understand the global economic consequences of past and future climate change. I show that two extreme …

Fermion Encodings And Algorithms For Quantum Simulation, Riley W. Chien

Dartmouth College Ph.D Dissertations

The study of the properties of quantum mechanical systems of many particles occupies a central role in condensed matter physics, high-energy physics, and quantum chemistry. In recent decades, developments in quantum information theory have suggested that quantum computers could become an especially useful tool for studying such quantum systems.

In this thesis, we address the additional challenges for quantum simulations posed by particles which are fermionic in nature, namely those caused by the nonlocal fermionic statistics. In particular, we study the encodings of fermionic degrees of freedom into the qubits of a quantum computer. We focus on finding a scheme …

Metallacycle-Mediated Cross-Coupling As An Enabling Tool For Studies In Carbocycle Synthesis And Functionalization, Adam Barry Millham

Dartmouth College Ph.D Dissertations

Natural products, specifically complex, carbocyclic natural products, have served as the inspiration for novel methods development for decades. Over that time, metallacycle-mediated cross-coupling has arisen as a powerful means for the synthesis of fused carbocycles. This work details three methods for the synthesis and functionalization of carbocyclic motifs that have been enabled by Ti-mediated cross-coupling reactions. The first of these studies include a complementary method to the Pauson–Khand reaction for the synthesis of highly substituted cyclopentenones via Ti-mediated alkyne–β-ketoester coupling. The second project, a modern approach to steroidal tetracycles, will be discussed that features: (1) an alkoxide-directed metallacycle-mediated [2+2+2] annulation …

Efforts Towards The Asymmetric De Novo Synthesis Of Lanostanes And Euphanes, Htoo Tint Wai

Dartmouth College Ph.D Dissertations

Tetracyclic triterpenoids are ubiquitous in nature and biology, with members displaying a wide range of medically relevant properties and occupying rather distinct regions of chemical space. Members of this large class include well-known steroid hormones and sterols as well as structurally interesting subclasses such as lanostanes and euphanes, among others. Comprised of the tetracyclic skeleton with three stereodefined quaternary centers at ring-junction positions, lanostanes and euphanes present synthetic challenges that are different from those encountered in efforts targeting the structurally less complex steroid hormones. Lanostanes, in particular, stand as a historically important class of compounds as significant attention has been …

Converting Hydrazone-Based Photoswitches Into Functional Materials, Sirun Yang

Dartmouth College Ph.D Dissertations

The development of new classes of molecular switches with enhanced performance and brand-new functionalities enables practitioners to push the frontiers of adaptive materials. In the realm of photoswitches, the bistability of hydrazones (i.e., molecules that incorporate the C=N-NH functional group) allows for the kinetic trapping of polymer and supramolecular assemblies resulting in multistate actuation and emergent phenomena that are not tractable with other photoswitches. This property has transformed hydrazone photoswitches into powerful tools that can be used in understanding fundamental molecular interactions and how to apply them in modulating the physicochemical properties of materials.

Progressing from disordered to …

On The Thom Isomorphism For Groupoid-Equivariant Representable K-Theory, Zachary J. Garvey

Dartmouth College Ph.D Dissertations

This thesis proves a general Thom Isomorphism in groupoid-equivariant KK-theory. Through formalizing a certain pushforward functor, we contextualize the Thom isomorphism to groupoid-equivariant representable K-theory with various support conditions. Additionally, we explicitly verify that a Thom class, determined by pullback of the Bott element via a generalized groupoid homomorphism, coincides with a Thom class defined via equivariant spinor bundles and Clifford multiplication. The tools developed in this thesis are then used to generalize a particularly interesting equivalence of two Thom isomorphisms on TX, for a Riemannian G-manifold X.

Space-Efficient Algorithms And Verification Schemes For Graph Streams, Prantar Ghosh

Dartmouth College Ph.D Dissertations

Structured data-sets are often easy to represent using graphs. The prevalence of massive data-sets in the modern world gives rise to big graphs such as web graphs, social networks, biological networks, and citation graphs. Most of these graphs keep growing continuously and pose two major challenges in their processing: (a) it is infeasible to store them entirely in the memory of a regular server, and (b) even if stored entirely, it is incredibly inefficient to reread the whole graph every time a new query appears. Thus, a natural approach for efficiently processing and analyzing such graphs is reading them as …

Cysteine Metallochemistry And Metal Binding: Quantification Of The Thermodynamic Foundations Of Cellular Homeostasis, Matthew R. Mehlenbacher

Dartmouth College Ph.D Dissertations

Metals are required for life. Many metalloproteins contain cysteine in their metal-binding site (MBS) and cysteines are unique in that they are reactive, and strongly bind certain metals, which aid in metal selectivity and specificity. Using isothermal titration calorimetry (ITC), the thermodynamic foundation for metal binding, cellular protection, and transcriptional regulation, which all utilize cysteines in their MBS, are quantified.

In bacteria there are metalloprotein pathways that actively uptake mercury, which are regulated by the metalloregulatory protein MerR. MerR de-represses the transcription of these mer proteins in a metal-dependent manner. Using ITC, the thermodynamic foundation of the negative allosteric coupling …