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Predicting Biomolecular Properties And Interactions Using Numerical, Statistical And Machine Learning Methods, Elyssa Sliheet

Mathematics Theses and Dissertations

We investigate machine learning and electrostatic methods to predict biophysical properties of proteins, such as solvation energy and protein ligand binding affinity, for the purpose of drug discovery/development. We focus on the Poisson-Boltzmann model and various high performance computing considerations such as parallelization schemes.

Imperfect Immunity And The Stability Of A Modified Kermack-Mckendrick Model, Kaylee Sims

Honors Theses

The classic Kermack-McKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified Kermack-McKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with real-world case data, with its most glaring failure being exponential dampening of the height of each disease case peak due …

Computing Well-Structured Subgraphs In Geometric Intersection Graphs., Satyabrata Jana Dr.

Doctoral Theses

For a set of geometric objects, the associative geometric intersection graph is the graph with a vertex for each object and an edge between two vertices if and only if the corresponding objects intersect. Geometric intersection graphs are very important due to their theoretical properties and applicability. Based on the different geometric objects, several types of geometric intersection graphs are defined. Given a graph G, an induced (either vertex or edge) subgraph H ⊆ G is said to be an well-structured subgraph if H satisfies certain properties among the vertices in H. This thesis studies some well-structured subgraphs finding problems …

Periodic Fast Multipole Method, Ruqi Pei

Dissertations

Applications in electrostatics, magnetostatics, fluid mechanics, and elasticity often involve sources contained in a unit cell C, centered at the origin, on which periodic boundary condition are imposed. The free-space Green’s functions for many classical partial differential equations (PDE), such as the modified Helmholtz equation, are well-known. Among the existing schemes for imposing the periodicity, three common approaches are: direct discretization of the governing PDE including boundary conditions to yield a large sparse linear system of equations, spectral methods which solve the governing PDE using Fourier analysis, and the method of images based on tiling the plane with copies of …

Essays In Multidimensional Mechanism Design., Kolagani Paramahamsa Dr.

Doctoral Theses

This thesis analyzes three problems where a monopolistic seller is selling to an agent with multidimensional private information. While our understanding of such problems is comprehensive if the agent's private information is one-dimensional, problems with multidimensional private information are known to be ubiquitous but analytically notorious. The three chapters in this thesis make progress in understanding optimal mechanism design in such multidimensional screening problems. In the first problem, the seller is selling an object to an agent who exhibits behavioral preferences, in a departure from the standard rational models. Behavioral preferences arise because the agent is budget constrained and needs …

Project-Based Learning In Non-Traditional Settings In Engineering Education, Mary Foss

Electronic Theses and Dissertations

The purpose of this study is to examine the effectiveness of utilizing the principles of Project-based learning (PJBL) in nontraditional settings in engineering education. There is ample literature related to the usage of PJBL techniques in engineering education but there are also challenges with incorporating PJBL within the curriculum. It is the aim of this dissertation to build upon this understanding of the advantages and limitations of PJBL in engineering education and identify areas within the existing body of knowledge in which more research is needed. This dissertation divides this topic into 4 sub-topics. The first sub-topic explores how PJBL …

Improvements And Analysis Of Challenging Numerical Simulations Of Binary Black Holes, Nicole Rosato

Theses

We explore different gauge choices in the moving puncture formulation in order to improve the accuracy of a linear momentum measure evaluated on the horizon of the remnant black hole produced by the merger of a binary. In particular, motivated by the study of gauges in which the damping term in the shift m eta takes on a constant value, we design a gauge via a variable shift parameter m eta(r(t)). This parameter takes a low value asymptotically, 1/m, and then takes on a value of approximately 2 at the final hole horizon. This eta then follows the remnant black …

On The Efficient Evaluation Of The Azimuthal Fourier Components Of The Green's Function For Helmholtz's Equation In Cylindrical Coordinates, James Michael Garritano

Yale Graduate School of Arts and Sciences Dissertations

In this dissertation, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green’s function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green’s function is essential for solvers for electromagnetic scattering from bodies of revolution (e.g., radar cross sections, antennas). Current algorithms to evaluate this modal Green’s function become computationally intractable when the source and target are close or when the wavenumber is large. Furthermore, most of the state of the art methods cannot easily be parallelized. In this work, we present an algorithm for evaluating the modal Green’s function …

Diffusion-Based Approaches To Visualization And Exploration Of High-Dimensional Data, Scott Anthony Gigante

Yale Graduate School of Arts and Sciences Dissertations

In recent years, modern technologies have enabled the collection of exponentially larger quantities of data in the biomedical domain and elsewhere. In particular, the advent of single-cell genomics has allowed for the collection of datasets containing hundreds of thousands of cells measured in tens of thousands of dimensions. This rapid expansion of common datasets beyond the possibility of manual annotation brings forth the need for large-scale exploratory data analysis. In this thesis, we will explore the problem of dimensionality reduction for visualization of high-dimensional datasets. Visualization of high-dimensional data is an essential task in exploratory data analysis, as the low-dimensional …

Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.

Doctoral Theses

No abstract provided.

Domain Restrictions In Strategy-Proof Social Choice., Gopakumar Achuthankutty Dr.

Doctoral Theses

In Chapter 2, we consider domains of admissible preferences with a natural property called top-circularity. Several domains with practical applications such as multidimensional single-peaked domain in [9], union of a single-peaked and a single dipped domain, etc. satisfy top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We show that this result can be applied to the problem of locating a public facility where the planner does not know whether agents derive positive or negative externality from the facility. The union of a single-peaked and a …

Parameter Estimation Of A Cardiac Model Using The Local Ensemble Transform Kalman Filter, Nathan Holt

Theses

Cardiac arrhythmias are irregularities in the electrical activity in the heart; the electrical impulses in the heart become chaotic or disorganized, which can cause a possibly lethal problem to the contraction of the heart. In order to understand the dynamics of arrhythmias and to be able to predict and treat them, numerical models have been developed to capture the dynamics of the electrical impulses in the heart. In a clinical setting, optical mapping technologies — using cameras and voltage-sensitive dyes to capture the electrical impulses propagating across the heart — have been used to capture the dynamics of the electrical …

Investigations And Analysis Of Dynamical And Steady State Properties Of Chemical Reaction Systems, Diego Ortega Hernandez

Master's Theses

In this paper, we investigate results from chemical reaction network theory and a list of techniques to test for the reaction-coordinates dynamical system to have a partial order induced by a positive orthant cone. A successful result from one of these tests guarantees mono-stationarity (and indeed convergence). We also investigate a recently published algorithmic and computational approach to determine whether a reaction network establishes mono- or multi-stationarity. We test new reactions that have not been previously introduced in the literature for mono- or multi-stationarity using this approach. This includes the two-site phosphorylation reaction network and a modified double phosphorylation reaction …

A Multi-Skilled Approach To Property Maintenance Considering Temporal, Spatial And Resource Constraints, Anthony G. Vatterott

Dissertations

With the continued increase in age of the United States housing and building stock, as well as the continued need to maintain properties across the U.S., the need for timely, cost-optimal maintenance is ever more critical. This paper proposes the application of a mathematical model to aid in the scheduling and assignment of construction and maintenance tasks, considering the multi-skilled workforce. The benefit of this approach is to take advantage of the economies of scale that can be developed using cross-functional skilled workers with varying levels of competence and efficiency. This approach schedules and assigns tasks using data from maintenance …

A Numerical Study Of The Van Roosbroeck System For Semiconductors, Alan Ghazarians

Master's Theses

Since the 1950s, semiconductors have played a significant and daily role in our lives, as they are the foundation of our computers, phones, and other electronic devices. Aside from their obvious uses, the equations that govern semiconductors have peaked the interest of mathematicians and numerical analysts. In 1950, van Roosbroeck described the fundamental semiconductor device equations as a system of three nonlinear coupled partial di↵erential equations. The van Roosbroeck system poses a challenge numerically because of its strong nonlinearity and coupled equations. Its diculties lie in simultaneously solving drift-di↵usion equations for electrons and holes and using their solutions to solve …

Lagrangian Coherent Structures: A Climatological Look, Andrew Sven Mccall Jr.

UVM College of Arts and Sciences College Honors Theses

A relatively new area at the crossroads of fluid and nonlinear dynamics are objects known as Lagrangian Coherent Structures (LCSs). LCSs are mathematically classified to differentiate parts of fluid flows. They, themselves, are the most influential parts of fluids. These objects have the most influence on the fluids around them and they allow for a sense of hierarchy in an otherwise busy environment of endless variables and trajectories. While all particles of fluids have the same dynamics on an individual basis, areas of fluid are not created equal and to be able to detect which parts will be the most …

Visualization And Analysis Of A Numerical Simulation Of Gw150914, Nicole Rosato

Theses

We present a visualization and analysis of a supercomputer simulation displaying the apparent horizons' curvature and radiation emitted from a binary black hole system modeling the LIGO observed signal GW150914. The simulation follows the system from seven orbits prior to merger down to the resultant final Kerr black hole. Apparent horizons are calculated during the simulation with mean curvature data displayed on them. Radiation data was visualized via the real part of the $\Psi_4$ component of the Weyl scalars, which were determined using a numerical quasi-Kinnersley method. We also present a comparative study of the differences in using the quasi-Kinnersley …

Coordination Of Leader-Follower Multi-Agent System With Time-Varying Objective Function, Zalan Mark Fabian

Master's Theses and Capstones

This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the …

Infinite Color Urn Models., Debleena Thacker Dr.

Doctoral Theses

In recent years, there has been a wide variety of work on random reinforcement models of various kinds. Urn models form an important class of random reinforcement models, with numerous applications in engineering and informatics and bioscience. In recent years there have been several works on different kinds of urn models and their generalizations. For occupancy urn models, where one considers recursive addition of balls into finite or infinite number of boxes, there are some works which introduce models with infinitely many colors, typically represented by the boxes.As observed in [51], the earliest mentions of urn models are in the …

Essays On Strategy-Proofness And Implementation., Sonal Yadav Dr.

Doctoral Theses

This thesis comprises of three chapters relating to strategy-proofness and implementation. We provide a brief description of each chapter below.1.1 A Hurwicz Type Result in a Model with Public Good Production We consider a two-good model with an arbitrary number of agents. One of the goods is a public good and the other is a private good. Each agent has an endowment of the private good and the private good can be converted into the public good using a well-behaved production function. A Social Choice Function (SCF) associates an allocation with each admissible preference profile. We impose the following requirements …

"Smoking-Gun" Observables Of Magnetic Reconnection: Spatiotemporal Evolution Of Electron Characteristics Throughout The Diffusion Region, Jason Shuster

Doctoral Dissertations

How does magnetic reconnection happen in a collisionless plasma? Knowledge of electron-scale dynamics is necessary to answer this outstanding question of plasma physics. Based on fully kinetic particle-in-cell (PIC) simulations of symmetric reconnection, the spatiotemporal evolution of velocity distribution functions in and around the electron diffusion region (EDR) elucidates how electrons are accelerated and heated by the cooperating reconnection electric and normal magnetic fields. The discrete, triangular structures characteristic of EDR distributions rotate and gyrotropize in velocity space as electrons remagnetize, forming multicomponent arc and ring structures. Further downstream, exhaust electrons are found to exhibit highly structured, time-dependent anisotropies that …

Design And Evaluation Of A Force Platform-Type Instrument To Measure Rate Change In Mass And Centroid Of An Ablating Body, Travis Paul Trottier

Master's Theses and Capstones

This study pertains to the design and evaluation of a force-platform type instrument comprised of three strain gauge load cells, intended to measure the rate of change in mass and centroid position of an object undergoing rapid ablation by heated flow of air. The strain gauges are affixed to a steel frame, oriented in a triangle beneath a 25 X 20 cm rectangular platform, into which is machined a 9 X 9 regular grid for the purpose of static calibration. An algorithm derived from first principles is used to convert the distribution of the applied load among the strain gauges …

Methods For The Direct Simulation Of Nanoscale Film Breakup And Contact Angles, Kyle Mahady

Dissertations

This thesis investigates direct simulation of fluids with free surfaces and contact lines, with a focus on capturing nanoscale physics in a continuum based computational framework. Free surfaces and contact lines have long presented some of the most challenging problems in computational fluid dynamics. Extensive progress has been made in recent years, and a wide variety of different methods are currently employed for direct simulation in these contexts. The complexity of the full governing equations for such flows poses significant challenges in terms of analytical techniques, and leads to lengthy computational times for direct simulations. For these reasons, reduced models …

Nonlinear Waves On A String With Inhomogeneous Properties, Robert Arredondo

Doctoral Dissertations

Nonlinear waves on an infinite string with a rapid change in properties at one location are treated. The string is an idealized version of more complex configurations in both fluids and solids. This idealized version treats the property change as an interface with a discontinuity in properties. Packets of waves are then considered with a reduced model, here a set of nonlinear Schr¨odinger (NLS) equations. The stress and the displacement must both be matched at the interface, resulting in dynamic and kinematic interfacial conditions. The dynamic condition produces an inhomogeneous effect that cannot be treated successfully with separation-of-variables. This inhomogeneity …

A Supercell, Bloch Wave Method For Calculating Low-Energy Electron Reflectivity With Applications To Free-Standing Graphene And Molybdenum Disulfide, John Francis Mcclain

Doctoral Dissertations

This dissertation reports on a novel theoretical and computational framework for calculating low-energy electron reflectivities from crystalline surfaces and its application to two layered systems of two-dimensional materials, graphene and molybdenum disulfide. The framework provides a simple and efficient approach through the matching of a small set of Fourier components of Bloch wave solutions to the Schrodinger Equation in a slab-in-supercell geometry to incoming and outgoing plane waves on both sides of the supercell. The implementation of this method is described in detail for the calculation of reflectivities in the lowest energy range, for which only specular reflection is allowed. …

Porous Medium Convection At Large Rayleigh Number: Studies Of Coherent Structure, Transport, And Reduced Dynamics, Baole Wen

Doctoral Dissertations

Buoyancy-driven convection in fluid-saturated porous media is a key environmental and technological process, with applications ranging from carbon dioxide storage in terrestrial aquifers to the design of compact heat exchangers. Porous medium convection is also a paradigm for forced-dissipative infinite-dimensional dynamical systems, exhibiting spatiotemporally chaotic dynamics if not ``true" turbulence. The objective of this dissertation research is to quantitatively characterize the dynamics and heat transport in two-dimensional horizontal and inclined porous medium convection between isothermal plane parallel boundaries at asymptotically large values of the Rayleigh number $Ra$ by investigating the emergent, quasi-coherent flow. This investigation employs a complement of direct …

Mathematical Analysis Of Energy Harvester Model, Oleksandr Vdovyn

Master's Theses and Capstones

Energy Harvesting from ambient waste energy for the purpose of running low-powered electronics has emerged during last decades. The goal of energy harvesting devices is to provide remote sources of electrical power and/or recharge storage devices such as batteries and capacitors.

The evolution of low-power-consuming electronics have led to and active academic research in energy harvesting. One of the most studied areas is the use of the piezoelectric effect to convert ambient vibration into useful electrical energy. The focus of this study on placed on detailed mathematical analysis of electromechanical models of piezoelectric energy harvester. The area of vibration-based energy …

An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper

Theses and Dissertations

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.

First, we create a …

An Investigation Of Traveling-Wave Electrophoresis Using A Trigonometric Potential, James Vopal

Graduate Theses, Dissertations, and Problem Reports

Traveling-wave electrophoresis, a technique for microfluidic separations in lab-on-achip devices, is investigated using a trigonometric model that naturally incorporates the spatial periodicity of the device. Traveling-wave electrophoresis can be used to separate high-mobility ions from low-mobility ions in forensic and medical applications, with a separation threshold that can be tuned for specific applications by simply choosing the traveling wave frequency. Our simulations predict plateaus in the average ion velocity verses the mobility, plateaus that correspond to Farey fractions and yield Devil's staircases for non-zero discreteness values. The plateaus indicate that ions with different mobilities can travel with the same average …

Discrete Time Dynamic Traffic Assignment Models With Lane Reversals For Evacuation Planning, Yeh-Ern Poh

Graduate Theses, Dissertations, and Problem Reports

In an event of a natural or man-made disaster, an evacuation is likely to be called for to move residents away from potentially hazardous areas. Road congestion and traffic stalling is a common occurrence as residents evacuate towns and cities for safe refuges. Lane reversal, or contra-flow, is a remedy to increase outbound flow capacities from disaster areas which in turn will reduce evacuation time of evacuees during emergency situations. This thesis presents a discrete-time traffic assignment system with lane reversals which incorporates multiple sources and multiple destinations to predict optimal traffic flow at various times throughout the entire planning …