Physics Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2800
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Item Analyzing the Dynamics of Biological and Artificial Neural Networks with Applications to Machine Learning(2024) Srinivasan, Keshav; Girvan, Michelle; Biophysics (BIPH); Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The study of the brain has profoundly shaped the evolution of computational learning models and the history of neural networks. This journey began in the 1940s with Warren McCulloch and Walter Pitts’ groundbreaking work on the first mathematical model of a neuron, laying the foundation for artificial neural networks. The 1950s and 60s witnessed a significant milestone with Frank Rosenblatt’s development of the perceptron, showcasing the potential of neural networks for complex computational tasks. Since then, the field of neural networks has witnessed explosive growth, and terms like “Artificial Intelligence” and “Machine Learning” have become commonplace across diverse fields, including finance,medicine, and science. This dissertation explores the symbiotic parallels between neuroscience and machine learning, focusing on the dynamics of biological and artificial neural networks. We begin by examining artificial neural networks, particularly in predicting the dynamics of large, complex networks—a paradigm where traditional machine learning algorithms often struggle. To address this, we propose a novel approach utilizing a parallel architecture that mimics the network’s structure, achieving scalable and accurate predictions. Shifting our focus to biological neuronal networks, we delve into the theory of critical systems. This theory posits that the brain, when viewed as a complex dynamical system, operates near a critical point, a state ideal for efficient information processing. A key experimental observation of this type of criticality is neuronal avalanches—scale-free cascades of neuronal activity—which have been documented both in vitro (in neuronal cultures and acute brain slices) and in vivo (in the brains of awake animals). Recent advancements in experimental techniques, such as multi-photon imaging and genetically encoded fluorescent markers, allow for the measurement of activity in living organisms with unparalleled single-cell resolution. Despite these advances, significant challenges remain when only a fraction of neurons can be recorded with sufficient resolution, leading to inaccurate estimations of power-law relationships in size, duration, and scaling of neuronal avalanches. We demonstrate that by analyzing simulated critical neuronal networks alongside real 2-photon imaging data, temporal coarse-graining can recover the critical value of the mean size vs. duration scaling of neuronal avalanches, allowing for more accurate estimations of critical brain dynamics even from subsampled data. Finally, we bridge the gap between machine learning and neuroscience by exploring the concept of excitatory-inhibitory balance, a crucial feature of neuronal networks in the brain, within the framework of reservoir computing. We emphasize the stabilizing role of inhibition in reservoir computers (RCs), mirroring its function in the brain. We propose a novel inhibitory adaptation mechanism that allows RCs to autonomously adjust inhibitory connections to achieve a specific firing rate target, motivated by the firing rate homeostasis observed in biological neurons. Overall, this dissertation strives to deepen the ongoing collaboration between neuroscience and machine learning, fostering advancements that will benefit both fields.Item BUILDING KINETIC MODELS FOR COMPLEX SYSTEMS WITH ARBITRARY MEMORIES(2022) Tsai, Sun-Ting; Tiwary, Pratyush; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Analyzing time series from complex dynamical systems in nature is a common yet challenging task in scientific computation since these time series are usually high-dimensional. To apply our physics intuitions to these dynamical systems often requires projecting these time series to certain low-dimensional degrees of freedom, which often introduces complicated memory effect. A simplest and classic example can be a 2-dimensional coupled differential equation. When one only looks at one of the Cartesian coordinates, one loses the predictability to predict what will happen next given the current 1-dimensional coordinate. The well-known solution is to describe the solution using the eigenvector, and the coupled equation is decoupled into a constant and a 1-dimensional memoryless equation. However, it can be imagined in a more complicated system we may have to look back to more time steps in the past, and it can be impossible to obtain a simple 1-dimensional eigenvector. In this work, we examine such memory effect within time series generated from Langevin dynamics, Molecular Dynamics (MD) simulations, and some experimental time series. We also develop computational methods to minimize and model such memory effects using statistical mechanics and machine learning. In recent years, MD simulation has become a powerful tool to model complex molecular dynamics in physics, chemistry, material science, biology, and many other fields. However, rare events such as droplet formation, nucleation, and protein conformational changes are hard to sample using MD simulations since they happen on the timescales far away from what all-atom MD simulation can reach. This makes MD simulation less useful for studying the mechanism of rare event kinetics. Therefore, it is a common practice to perform enhanced sampling techniques to help sample rare events, which requires performing dimensionality reduction from atomic coordinates to a low-dimensional representation that has a minimal memory effect. In the first part of this study, we focus on reducing the memory effect by capturing slow degrees of freedom using a set of low-dimensional reaction coordinates (RCs). The RCs are a low-dimensional surrogate of the eigenvector in the example of coupled equations. When describing the system using RCs, other dimensions become constant except fast randomly fluctuating noise. These RCs can then be used to help reproducing correct kinetic connectivity between metastable states using enhanced sampling methods such as metadynamics. We demonstrate the utility of our method by applying them to the droplet formation from the gaseous phase of Lennard-Jones particles and the conformational changes of a small peptide Ace-Ala3-Nme. The second part of the study aims at modeling another type of memory coming from intrinsic long-term dependency induced by ignored fast degrees of freedom wherein we utilize one of the fundamental machine learning techniques called the recurrent neural network to model non-Markovianity within time-series generated from MD simulations. This method has been shown to work not only on the molecular model of alanine dipeptide but also on experimental time series taken from single-molecule force spectroscopy. At the end of this second part, we also improve this method to extrapolate physics that the neural network had never seen in the training dataset by incorporating static or dynamical constraints on the path ensemble it generates.Item CONTROL AND CHARACTERIZATION OF OPEN QUANTUM SYSTEMS(2020) Seif Tabrizi, Seyed Alireza; Hafezi, Mohammad M.H.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The study of open physical systems concerns finding ways to incorporate the lack of information about the environment into a theory that best describes the behavior of the system. We consider characterizing the environment by using the system as a sensor, mitigating errors, and learning the physics governing systems out of equilibrium with computer algorithms.We characterize long-range correlated errors and crosstalk, which are impor- tant factors that negatively impacts the performance of noisy intermediate-scale quantum (NISQ) computing devices. We propose a compressed sensing method for detecting correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s << n(n − 1)/2, and n is the total number of qubits). Our method uses entangled many-qubit GHZ states, and it can detect long-range correlations whose distribution is completely arbitrary, independent of the geometry of the system. Our method is also highly scalable: it requires only s log n measurement settings, in contrast to the naive O(n2) estimate, and efficient classical postprocessing based on convex optimization. For mitigating the effect of errors, we consider measurements in a quantum computer. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. We experimentally il- lustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms. To learn about physical systems using computer algorithms, we consider the problem of arrow of time. We show that a machine learning algorithm can learn to discern the direction of time’s arrow when provided with a system’s microscopic trajectory as input. Examination of the algorithm’s decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be used to study systems out of equilibrium, and ultimately to uncover physical principles.Item Numerical Studies of Quantum Chaos in Various Dynamical Systems(2020) Rozenbaum, Efim; Galitski, Victor; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We study two classes of quantum phenomena associated with classical chaos in a variety of quantum models: (i) dynamical localization and its extension and generalization to interacting few- and many-body systems and (ii) quantum exponential divergences in high-order correlators and other diagnostics of quantum chaos. Dynamical localization (DL) is a subtle phenomenon related to Anderson localization. It hinges on quantum interference and is typically destroyed in presence of interactions. DL often manifests as a failure of a driven system to heat up, violating the foundations of statistical physics. Kicked rotor (KR) is a prototypical chaotic classical model that exhibits linear energy growth with time. The quantum kicked rotor (QKR) features DL instead: its energy saturates. Multiple attempts of many-body generalizations faced difficulties in preserving DL. Recently, DL was shown in a special integrable many-body model. We study non-integrable models of few- and many-body QKR-like systems and provide direct evidence that DL can persist there. In addition, we show how a novel related concept of localization landscape can be applied to study transport in rippled channels. Out-of-time-ordered correlator (OTOC) was proposed as an indicator of quantum chaos, since in the semiclassical limit, this correlator's possible exponential growth rate (CGR) resembles the classical Lyapunov exponent (LE). We show that the CGR in QKR is related, but distinct from the LE in KR. We also show a singularity in the OTOC at the Ehrenfest time tᴱ due to a delay in the onset of quantum interference. Next, we study scaling of OTOC beyond tᴱ. We then explore how the OTOC-based approach to quantum chaos relates to the random-matrix-theoretical description by introducing an operator we dub the Lyapunovian. Its level statistics is calculated for quantum stadium billiard, a seminal model of quantum chaos, and aligns perfectly with the Wigner-Dyson surmise. In the semiclassical limit, the Lyapunovian reduces to the matrix of uncorrelated finite-time Lyapunov exponents, connecting the CGR at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference. Finally, we consider quantum polygonal billiards: their classical counterparts are non-chaotic. We show exponential growth of the OTOCs in these systems, sharply contrasted with the classical behavior even before quantum interference develops.Item A Deep Dive into the Distribution Function: Understanding Phase Space Dynamics with Continuum Vlasov-Maxwell Simulations(2020) Juno, James; Dorland, William; TenBarge, Jason; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly collisional plasma is challenging. The equation system of relevance, the Vlasov--Maxwell--Fokker--Planck (VM-FP) system of equations, is difficult to numerically integrate, and traditional methods such as the particle-in-cell method introduce counting noise into the distribution function. In this thesis, we present a new algorithm for the discretization of VM-FP system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin (DG) finite element method for the spatial discretization and a third order strong-stability preserving Runge--Kutta for the time discretization, we obtain an accurate solution for the plasma's distribution function in space and time. We both prove the numerical method retains key physical properties of the VM-FP system, such as the conservation of energy and the second law of thermodynamics, and demonstrate these properties numerically. These results are contextualized in the history of the DG method. We discuss the importance of the algorithm being alias-free, a necessary condition for deriving stable DG schemes of kinetic equations so as to retain the implicit conservation relations embedded in the particle distribution function, and the computational favorable implementation using a modal, orthonormal basis in comparison to traditional DG methods applied in computational fluid dynamics. A diverse array of simulations are performed which exploit the advantages of our approach over competing numerical methods. We demonstrate how the high fidelity representation of the distribution function, combined with novel diagnostics, permits detailed analysis of the energization mechanisms in fundamental plasma processes such as collisionless shocks. Likewise, we show the undesirable effect particle noise can have on both solution quality, and ease of analysis, with a study of kinetic instabilities with both our continuum VM-FP method and a particle-in-cell method. Our VM-FP solver is implemented in the Gkyell framework, a modular framework for the solution to a variety of equation systems in plasma physics and fluid dynamics.Item Simulations of Accretion Mechanisms and Observational Signatures of Black Hole Accretion Disks(2019) Smith, Megan; McKinney, Jonathan C; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Black holes have been a subject of fascination since they were first theorized about over a century ago. There are many questions about them left unanswered. One of these questions is how matter is accreted onto these objects when the plasma around them is rotating in an accretion disk. An answer to this question is likely to be found in the magnetohydrodynamic processes that occur in the plasma, which require highly sophisticated numerical simulations to explore. In this thesis, I describe an analysis of one magnetohydrodynamic instability found in these simulations as well as the observational signatures it produces, which might be recognized in observations of these systems. For the remainder of this thesis, I will discuss the formation and evolution of a formal near-peer mentoring program for women in the University of Maryland physics department. Mentoring programs have been shown to have a number of benefits for both mentors and mentees. Primary among them is an increased sense of belonging and science identity, which is linked to increased retention. Given the so-called "leaky pipeline" problem of women leaving physics, a field where they are already underrepresented, efforts to improve retention are vital and peer mentoring is one way to do this.Item SUBMONOLAYER ADSORBATES: THEORETICAL STUDIES OF TRANSIENT MOBILITY AND SYMMETRY-BREAKING(2019) Morales Cifuentes, Josue Ricardo; Einstein, Theodore L.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Weakly bound submonolayer adsorbates provide important insight into fundamental descriptions of physics that would otherwise be masked, or even suppressed, by strong effects such as chemical binding. We focus on two surface effects: transient mobility at the microscopic scale, and symmetry-breaking at the atomic one. We present a novel island nucleation and growth model that explicitly includes, at the microscopic scale, the behavior of transient (ballistic) monomers. At a deposition rate F , monomers are assumed to be in a hot precursor state before thermalizing. In the limiting regimes of fast (diffusive) and slow (ballistic) thermalization, we recover the expected scaling of the island density, N : N ∝ F^α. We construct effective growth exponents, α eff , and activation energies to properly characterize the transitional regions between these limiting regimes. Through these constructs, we describe a rich and complex structure of metastable limiting regimes, asymptotic behavior and energetically driven transitions. Application to N (F, T ) ofrecent organic-molecule deposition experiments yields excellent fits. We have also studied, at the atomic scale, an effective potential mechanism that breaks the intrinsic two-fold sublattice (hexagonal) symmetry of (honeycomb) graphene using DFT calculations (VASP ver 5.3.3). We choose the specific system of CF3Cl adsorbates on single layer graphene, to benefit from experimental results obtained locally. Using ab initio van der Waals density functionals, we discover a physisorbed phase with binding energies of about 280 meV. For low coverages, sublattice symmetry-breaking effects are responsible for gap openings of 4 meV; contrastingly, in large coverages, it is the formation of ordered overlayers that opens gaps nearly 5 times as large, of roughly 18 meV. We discover that in both cases, differentiation of graphene’s two sublattices induces symmetry-breaking by means of adsorbate interactions that favor large ordered regions, coverage itself is insignificant. For CF3Cl adsorbates on bilayer graphene, symmetry-breaking effects caused by the formation of graphene-like overlayers, and not sublattice differentiation, opened gaps of 25 meV, the largest in our study.Item LARGE-SCALE NEURAL NETWORK MODELING: FROM NEURONAL MICROCIRCUITS TO WHOLE-BRAIN COMPLEX NETWORK DYNAMICS(2018) Liu, Qin; Anlage, Steven; Horwitz, Barry; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Neural networks mediate human cognitive functions, such as sensory processing, memory, attention, etc. Computational modeling has been proved as a powerful tool to test hypothesis of network mechanisms underlying cognitive functions, and to understand better human neuroimaging data. The dissertation presents a large-scale neural network modeling study of human brain visual/auditory processing and how this process interacts with memory and attention. We first modeled visual and auditory objects processing and short-term memory with local microcircuits and a large-scale recurrent network. We proposed a biologically realistic network implementation of storing multiple items in short-term memory. We then realized the effect that people involuntarily switch attention to salient distractors and are difficult to distract when attending to salient stimuli, by incorporating exogenous and endogenous attention modules. The integrated model could perform a number of cognitive tasks utilizing different cognitive functions by only changing a task-specification parameter. Based on the performance and simulated imaging results of these tasks, we proposed hypothesis for the neural mechanism beneath several important phenomena, which may be tested experimentally in the future. Theory of complex network has been applied in the analysis of neuroimaging data, as it provides a topological abstraction of the human brain. We constructed functional connectivity networks for various simulated experimental conditions. A number of important network properties were studied, including the scale-free property, the global efficiency, modular structure, and explored their relations with task complexity. We showed that these network properties and their dynamics of our simulated networks matched empirical studies, which verifies the validity and importance of our modeling work in testing neural network hypothesis.