Physics Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2800
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Item Mathematical Modeling of Cellular Exhaustion to Guide Future Immunotherapy Research(2024) Simmons, Tyler; Levy, Doron; Biophysics (BIPH); Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Cellular exhaustion is a dysfunction found in various adaptive immune cells. In chronic settings, like cancer, antigen persistence and prolonged stimulation initiates the development of T cell exhaustion. The exhausted T cell population is a distinct lineage consisting of progenitor exhausted CD8+ T cells and terminally exhausted CD8+ T cells and is characterized by an upregulation of inhibitory receptor frequencies and diminished effector functions. The hypofunctionality of exhausted T cells prevents proper immunity and fails to eradicate the tumor. Recent years have shown a growing interest in targeting T cell exhaustion, attempting to reinvigorate effector functions, as a form of immunotherapy. Though beneficial responses have been reported in clinical settings, patient responses are inconsistent. Complementing the current biological understanding of T cell exhaustion and to advance immunotherapeutic efforts, novel research using mathematical modeling offers valuable insight. Constructing a foundational framework of an exhausted immune response to cancer provides an alternative approach to understanding the tumor-immune system. Presented here is the construction of a mathematical model detailing the development of progenitor and terminally exhausted CD8+ T cell populations in response to a growing tumor. Parameterization and simulation of this model captures biological dynamics observed in experimental and clinical settings. Analysis and conclusions of this model suggest population size and maintenance of progenitor exhausted CD8+ T cells should be a pillar of immunotherapy efforts. Stemming from these conclusions, it was theorized that targeting exhausted CD4+ helper T cells, which, under normal non-chronic conditions, contribute heavily to CD8+ T cell responses, would be a new and effective approach for immunotherapy. To test this hypothesis, the previously constructed model of CD8+ T cell exhaustion was expanded to incorporate CD4+ helper 1 T cells as well as immunosuppressive regulatory T cells. Simulation and analysis of this expanded model further emphasize the need to maintain progenitor exhausted CD8+ T cell numbers. Additionally, model analysis also indicated that the functionality of CD4+ T cells, both regulatory and exhausted CD4+ helper 1 T cells, played a crucial role in tumor persistence. From this work, research regarding CD4+ T cell exhaustion is strongly encouraged. With a better understanding of this dysfunction, CD4+ T cells may be a potentially effective target for future immunotherapy strategies.Item QUANTUM SIMULATION OF BOSONIC SYSTEM AND APPLICATION OF MACHINE LEARNING(2023) Kuo, En-Jui; Hafezi, Mohammad; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)First, we introduce the notion of "generalized bosons," whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^{\dagger}]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so the results regarding the difficulty of sampling carry over directly. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms. In the rest of the thesis, we move on to different topics. Firstly, we incorporate machine learning techniques in quantum information. We use machine learning to classify rational two-dimensional conformal field theories (CFTs). We first use the energy spectra of these minimal models to train a supervised learning algorithm. In contrast to conventional methods that are typically qualitative and involve system size scaling, our method quantifies the similarity of the spectrum of a system at a fixed size to candidate CFTs. Such an approach allows us to correctly predict the nature and value of critical points of several strongly correlated spin models using only their energy spectra. Our results are also relevant for the ground-state entanglement Hamiltonian of certain topological phases of matter described by CFTs. Remarkably, we achieve high prediction accuracy by only using the lowest few Rényi entropies as the input. Finally, using autoencoders, an unsupervised learning algorithm, we find a hidden variable that has a direct correlation with the central charge and discuss prospects for using machine learning to investigate other conformal field theories, including higher-dimensional ones. Next, we demonstrate how machine learning techniques, especially unsupervised learning algorithms, can be used to study Symmetry-Protected Topological (SPT) phases of matter. SPT phases are short-range entangled phases of matter with a non-local order parameter that are preserved under a local symmetry group. Here, we use an unsupervised learning algorithm, namely diffusion maps, to differentiate between symmetry-broken phases and topologically ordered phases and between non-trivial topological phases in different classes. Specifically, we show that phase transitions associated with these phases can be detected in various bosonic and fermionic models in one dimension, including the interacting SSH model, the AKLT model and its variants, and weakly interacting fermionic models. Our approach provides a cost-effective computational method for detecting topological phase transitions associated with SPT systems, which can also be applied to experimental data obtained from quantum simulators.Item Analysis of models of superfluidity(2022) Jayanti, Pranava Chaitanya; Trivisa, Konstantina; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis deals with the rigorous analysis of two models of superfluidity. One of them is a macro-scale description of the interacting dynamics of a mixture of superfluid Helium and normal Helium. The equations used are modifications of the incompressible Navier-Stokes equations in 2D, with a nonlinear \textit{mutual friction} that couples the two fluids. We show global well-posedness of strong solutions (with high-regularity data) to this model, by proving a Beale-Kato-Majda-type condition. This work has been published in the Journal of Nonlinear Science. \\ Next, we study a micro-scale model (the ``Pitaevskii’’ model) of superfluid-normal fluid interactions, derived by Lev Pitaevskii in 1959. This involves the nonlinear Schr\"odinger equation and incompressible inhomogeneous Navier-Stokes equations. Mass and momentum exchange between the two fluids is mediated through a nonlinear and bidirectional coupling. We establish the existence of local solutions (strong in wavefunction and velocity, weak in density) that satisfy an energy equality. The analysis of this model has been published in the Journal of Mathematical Fluid Mechanics. \\ Finally, we prove a weak-strong type uniqueness theorem for the solutions of the Pitaevskii model. We begin by arguing that the standard weak-strong uniqueness argument does not seem to work in the case of weak solutions whose regularity is governed purely by the energy balance equation, even if the strong solution is as smooth as one wishes. Thus, we are forced to consider slightly less weak solutions obtained from a higher-order energy bound. Owing to their better regularity, we can compare them to \textit{moderate} solutions $-$ which are rougher than conventional strong solutions used for this purpose $-$ and establish a \textit{weak-moderate uniqueness} theorem. Relative to the solutions actually constructed in the earlier part of this thesis, only some of the regularity properties are used, allowing room for improved existence theorems in the future, while maintaining compatible uniqueness results. The uniqueness results have been accepted for publication in Nonlinearity.Item Spectral graph theory with applications to quantum adiabatic optimization(2016) Baume, Michael Jarret; Jordan, Stephen P; Childs, Andrew; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.Item Patterns and Complexity in Biological Systems: A Study of Sequence Structure and Ontology-based Networks(2010) Glass, Kimberly; Girvan, Michelle; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Biological information can be explored at many different levels, with the most basic information encoded in patterns within the DNA sequence. Through molecular level processes, these patterns are capable of controlling the states of genes, resulting in a complex network of interactions between genes. Key features of biological systems can be determined by evaluating properties of this gene regulatory network. More specifically, a network-based approach helps us to understand how the collective behavior of genes corresponds to patterns in genetic function. We combine Chromatin-Immunoprecipitation microarray (ChIP-chip) data with genomic sequence data to determine how DNA sequence works to recruit various proteins. We quantify this information using a value termed "nmer-association.'' "Nmer-association'' measures how strongly individual DNA sequences are associated with a protein in a given ChIP-chip experiment. We also develop the "split-motif'' algorithm to study the underlying structural properties of DNA sequence independent of wet-lab data. The "split-motif'' algorithm finds pairs of DNA motifs which preferentially localize relative to one another. These pairs are primarily composed of known transcription factor binding sites and their co-occurrence is indicative of higher-order structure. This kind of structure has largely been missed in standard motif-finding algorithms despite emerging evidence of the importance of complex regulation. In both simple and complex regulation, two genes that are connected in a regulatory fashion are likely to have shared functions. The Gene Ontology (GO) provides biologists with a controlled terminology with which to describe how genes are associated with function and how those functional terms are related to each other. We introduce a method for processing functional information in GO to produce a gene network. We find that the edges in this network are correlated with known regulatory interactions and that the strength of the functional relationship between two genes can be used as an indicator of how informationally important that link is in the regulatory network. We also investigate the network structure of gene-term annotations found in GO and use these associations to establish an alternate natural way to group the functional terms. These groups of terms are drastically different from the hierarchical structure established by the Gene Ontology and provide an alternative framework with which to describe and predict the functions of experimentally identified groups of genes.Item An Epistemic Framing Analysis of Upper Level Physics Students' Use of Mathematics(2008-07-11) Bing, Thomas Joseph; Redish, Edward F.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Mathematics is central to a professional physicist's work and, by extension, to a physics student's studies. It provides a language for abstraction, definition, computation, and connection to physical reality. This power of mathematics in physics is also the source of many of the difficulties it presents students. Simply put, many different activities could all be described as "using math in physics". Expertise entails a complicated coordination of these various activities. This work examines the many different kinds of thinking that are all facets of the use of mathematics in physics. It uses an epistemological lens, one that looks at the type of explanation a student presently sees as appropriate, to analyze the mathematical thinking of upper level physics undergraduates. Sometimes a student will turn to a detailed calculation to produce or justify an answer. Other times a physical argument is explicitly connected to the mathematics at hand. Still other times quoting a definition is seen as sufficient, and so on. Local coherencies evolve in students' thought around these various types of mathematical justifications. We use the cognitive process of framing to model students' navigation of these various facets of math use in physics. We first demonstrate several common framings observed in our students' mathematical thought and give several examples of each. Armed with this analysis tool, we then give several examples of how this framing analysis can be used to address a research question. We consider what effects, if any, a powerful symbolic calculator has on students' thinking. We also consider how to characterize growing expertise among physics students. Framing offers a lens for analysis that is a natural fit for these sample research questions. To active physics education researchers, the framing analysis presented in this dissertation can provide a useful tool for addressing other research questions. To physics teachers, we present this analysis so that it may make them more explicitly aware of the various types of reasoning, and the dynamics among them, that students employ in our physics classes. This awareness will help us better hear students' arguments and respond appropriately.Item Applications of Superspace Techniques to Effective Actions, Complex Geometry, and T Duality in String Theory(2007-04-26) Merrell, Willie; Gates, Sylvester J; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We describe the use of superspace techniques to discuss some of the issues in string theory. First we use superspace techniques to derive the effective action for the 10D N=1 Heterotic string perturbatively to first order in the parameter alpha prime. Next we demonstrate how to use the superspace description of the supersymmetric gauge multiplet for chiral superfield in 2d N=(2,2) to discuss T duality for sigma models that realizes a particular case of generalized Kahler geometry. We find that the salient features of T duality are captured but at the cost of introducing unwanted fields in dual sigma model. Fortunately the extra fields decouple from the relevant fields under consideration. This leads us to introduce a new supersymmetric gauge multiplet that will eliminate the need to introduce extra fields in the dual sigma model.Item Numerical studies of constraints and gravitational wave extraction in general relativity(2004-08-04) Fiske, David Robert; Misner, Charles W; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Within classical physics, general relativity is the theory of gravity. Its equations are non-linear partial differential equations for which relatively few closed form solutions are known. Because of the growing observational need for solutions representing gravitational waves from astrophysically plausible sources, a subfield of general relativity, numerical relativity, has a emerged with the goal of generating numerical solutions to the Einstein equations. This dissertation focuses on two fundamental problems in modern numerical relativity: (1) Creating a theoretical treatment of the constraints in the presence of constraint-violating numerical errors, and (2) Designing and implementing an algorithm to compute the spherical harmonic decomposition of radiation quantities for comparison with observation. On the issue of the constraints, I present a novel and generic procedure for incorporating the constraints into the equations of motion of the theory in a way designed to make the constraint hypersurface an attractor of the evolution. In principle, the prescription generates non-linear corrections for the Einstein equations. The dissertation presents numerical evidence that the correction terms do work in the case of two formulations of the Maxwell equations and two formulations of the linearized Einstein equations. On the issue of radiation extraction, I provide the first in-depth analysis of a novel algorithm, due originally to Misner, for computing spherical harmonic components on a cubic grid. I compute explicitly how the truncation error in the algorithm depends on its various parameters, and I also provide a detailed analysis showing how to implement the method on grids in which explicit symmetries are enforced via boundary conditions. Finally, I verify these error estimates and symmetry arguments with a numerical study using a solution of the linearized Einstein equations known as a Teukolsky wave. The algorithm performs well and the estimates prove true both in simulations run on a uniform grid and in simulations that make use of fixed mesh refinement techniques.