Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item INFERENCE AND CONTROL IN NETWORKS FAR FROM EQUILIBRIUM.(2022) Sharma, Siddharth; Levy, Doron Prof.; Biophysics (BIPH); Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis focuses on two problems in biophysics.1. Inference in networks far from equilibrium. 2. Optimal transitions between network steady-states of unequal dimensions. The system used for development of the theory and design of computational algorithms is the fully connected and asymmetric version of the widely used Ising model. We begin with the basic concepts of biological networks and their emergence as an analytical paradigm over the last two decades due to advancements in high-throughput experimental methods. Biological systems are open and exchange both energy and matter with their environment. Their dynamics are far from equilibrium and don’t have well characterized steady-state distributions. This is in stark contrast to equilibrium dynamics with the Maxwell-Boltzmann distribution describing the histogram of microstates. The development of inference and control algorithms in this work is for nonequilibrium steady-states without detailed balance. Inferring the Ising model far from equilibrium requires solving the inverse problem in statistical mechanics. As opposed to using a known Hamiltonian to solve for the macroscopic averages, we calculate the couplings and fields, i.e., model parameters, given the microstates or stochastic snapshots as inputs. We first demonstrate a time-series calculation for the inverse problem and use Poisson and Polya-Gamma latent variables to construct a quadratic likelihood function which is then maximized using the expectation-maximization algorithm. In addition to the main calculation, properties of the Polya-Gamma variables are used to solve logistic regression on a Gaussian mixture. This has applications to problems like clustering and community detection. Not all available data in biology is time-ordered. In fact for some systems, e.g., gene-regulatory networks, most of the data is not in time-series. The solution to the inverse problem for such systems (data) is qualitatively different as it involves solving for the thermodynamic arrow of time. The present work uses the definition of a sufficient statistic based on equivalence classes to design a likelihood function through the disjoint cycles of the permutation group. The geometric intuition is provided using dihedral group of the same order. We state and prove that our likelihood function is minimally sufficient and present an optimization algorithm with computational results. The second problem, i.e., optimal network control is solved using optimal transport. We recognize that biological networks have the property to grow and shrink while remaining functional and robust. Recent works that have continued the progress made by earlier sem- inal results have concentrated on systems which do not undergo transitions that alter their dimensions. For example, a network increasing or decreasing its number of nodes. The connection between thermodynamics and optimal transport is well established through the Wasserstein metric being the minimal dissipation for stochastic dynamics. This result depends on narrow convergence which requires that the system size remains the same. Recently introduced Gromov-Wasserstein metric defined on a space of metric measure spaces, makes it possible to design optimal paths between probability distributions of different sizes. In context of networks, the GW metric can define geodesics between two network nonequilibrium steady-states with different number of vertices. The last two chapters discuss the mathematical concepts and results that are required to develop the GW metric on networks and the computational algorithms that follow as a result. We define the probability measures and loss functions as per the physical properties of the Ising model and demonstrate a geodesic calculation between two networks of different sizes.Item THE PHYSICS OF IDEAS: INFERRING THE MECHANICS OF OPINION FORMATION FROM MACROSCOPIC STATISTICAL PATTERNS(2016) Burghardt, Keith A.; Girvan, Michelle; Rand, William; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In a microscopic setting, humans behave in rich and unexpected ways. In a macroscopic setting, however, distinctive patterns of group behavior emerge, leading statistical physicists to search for an underlying mechanism. The aim of this dissertation is to analyze the macroscopic patterns of competing ideas in order to discern the mechanics of how group opinions form at the microscopic level. First, we explore the competition of answers in online Q&A (question and answer) boards. We find that a simple individual-level model can capture important features of user behavior, especially as the number of answers to a question grows. Our model further suggests that the wisdom of crowds may be constrained by information overload, in which users are unable to thoroughly evaluate each answer and therefore tend to use heuristics to pick what they believe is the best answer. Next, we explore models of opinion spread among voters to explain observed universal statistical patterns such as rescaled vote distributions and logarithmic vote correlations. We introduce a simple model that can explain both properties, as well as why it takes so long for large groups to reach consensus. An important feature of the model that facilitates agreement with data is that individuals become more stubborn (unwilling to change their opinion) over time. Finally, we explore potential underlying mechanisms for opinion formation in juries, by comparing data to various types of models. We find that different null hypotheses in which jurors do not interact when reaching a decision are in strong disagreement with data compared to a simple interaction model. These findings provide conceptual and mechanistic support for previous work that has found mutual influence can play a large role in group decisions. In addition, by matching our models to data, we are able to infer the time scales over which individuals change their opinions for different jury contexts. We find that these values increase as a function of the trial time, suggesting that jurors and judicial panels exhibit a kind of stubbornness similar to what we include in our model of voting behavior.Item MODELING OF INTERFACES: APPLICATIONS IN SURFACE AND POLYMER PHYSICS(2013) Patrone, Paul Nathan; Einstein, Theodore L.; Margetis, Dionisios; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, I give an overview of my work on multiscale modeling of interfaces in crystalline and block-copolymer systems. I focus on two distinct interface systems: steps on vicinal surfaces and microdomain interfaces in block- copolymers melts. For each system, I consider how to (i) define the interface, (ii) derive a coarse-grained model of the interface, and (iii) use the model to study morphological features of the interface. For vicinal surfaces, we define a step by means of ensemble averages, which leads to a Burton-Cabrera-Frank (BCF) -type model of surface evolution. Using the BCF model, we study the combined effects of step interactions and fluctuations. For block-copolymers, we define the microdomain interfaces in terms of the relative density of monomers and use the Leibler-Ohta- Kawasaki phase-field Hamiltonian to study the line-edge roughness.Item Theoretical Methods in the Non-Equilibrium Quantum Mechanics of Many Bodies(2011) Robertson, Andrew Benjamin; Galitski, Victor M; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A toolbox of theoretical methods pertinent to the study of non-equilibrium many-body quantum mechanics is presented with an eye to specific applications in cold atoms systems and solids. We discuss the generalization from unitary quantum mechanics to the non-unitary framework of open quantum systems. Theoretical techniques include the Keldysh close-time-path integral and its associated correlation functions, the quantum kinetic equation, and numerical integration of equations of motion both unitary and non-unitary. We explore how the relaxation of the assumption of equilibrium yields a whole new array of sometimes counterintuitive effects. We treat such examples as the non-equilibrium enhancement of BCS superfluidity by driving, bistability and coherent population transfer in Feshbach coupled fermions, and the dynamic stimulation of quantum coherence in bosons confined to a lattice. These systems are considered with an eye to enhancing some useful quantum properties and making them available in wider parameter regimes.Item Modeling the Anisotropy of Step Fluctuations on Surfaces: Theoretical Step Stiffness Confronts Experiment(2006-08-29) Stasevich, Timothy John; Einstein, Theodore L; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we study the anisotropy of step stiffness: an important parameter describing the fluctuations of surface steps within the continuum step model. Using a lattice-gas framework, we derive many practical formulas for the anisotropy of step stiffness on face centered cubic {001} and {111} surfaces. We compare our formulas to experiments on Ag and Cu surfaces and thereby predict the size of nearest-neighbor, next-nearest-neighbor, and three-adatom, non-pairwise "trio" interactions between adatoms. To further corroborate our theory, we perform a series of first-principle calculations of the relevant adatom interactions. We also incorporate our formulas into simulations and model the relaxation of a Ag step initially pinned by surface impurities. Finally, we extend our theory to model Ag steps decorated by C_60 molecules. Together, our work provides a consistent picture of step stiffness anisotropy from an experimental, theoretical, and numerical perspective.