Digital Commons Network^™

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 …

Applied Mathematics Laboratory: A Course-Based Research Internship, Mathew Gluck, Alexei Kolesnikov

The Mathematics Enthusiast

The paper describes the Applied Mathematics Laboratory (AML), a course-based model of undergraduate research engagement in applied mathematics at Towson University. We provide historical background of similar programs at other institutions in the US; describe the implementation and the logic model of the AML; include an example of a recent project; and describe the place of the AML in the context of other course-based student research experiences in STEM.

Lecture Note On Delay Differential Equation, Wenfeng Liu

Undergraduate Student Research Internships Conference

Delay differential equation is an important field in applied mathematics since it concerns more situations than the ordinary differential equation. Moreover, it makes the equations more applicable to the object's movement in real life.

My project is the lecture note on the delay differential equation provides a basic introduction to the delay differential equation, its application in real life, improving the ordinary differential equation, the primary method and definition for solving the delay differential equation and the use of the way in the ordinary differential equation to estimate the periodic solution to the delay differential equation.

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 …

Biofilm Viscoelasticity And Nutrient Source Location Control Biofilm Growth Rate, Migration Rate, And Morphology In Shear Flow, Hoa Nguyen, Abraham Ybarra, H. Başağaoğlu, Orrin Shindell

Mathematics Faculty Research

We present a numerical model to simulate the growth and deformation of a viscoelastic biofilm in shear flow under different nutrient conditions. The mechanical interaction between the biofilm and the fluid is computed using the Immersed Boundary Method with viscoelastic parameters determined a priori from measurements reported in the literature. Biofilm growth occurs at the biofilm-fluid interface by a stochastic rule that depends on the local nutrient concentration. We compare the growth, migration, and morphology of viscoelastic biofilms with a common relaxation time of 18 min over the range of elastic moduli 10–1000 Pa in different nearby nutrient source configurations. …

Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics, Jia Li, Yunxiao Liu

Research Collection School Of Economics

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

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 …

Mathematics And Enterprise Innovation, Pingwen Zhang

Bulletin of Chinese Academy of Sciences (Chinese Version)

The innovation and development of China are inseparable from mathematics. The development of applied mathematics, embodied in scientific discovery, national defense construction and enterprise innovation, is mainly driven by national demand. At present, China's economy has entered into a period of innovation driven development. Enterprises, as the main participants of national economic activities, need the support of mathematics for innovation and development. Regarding how to promote enterprise innovation through mathematics, this paper puts forward four aspects that we need to pay attention to and improve on: posing problems, solving problems, reporting results, and evaluating results. At the end, the paper …

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 …

A Mathematical Model Of Pancreatic Cancer Growth And Response To Treatment, Allison Cruikshank

Honors Theses

Pancreatic cancer is one of the leading causes of death due to cancer in the United States. Analyzing the effects of radiation is extremely valuable in determining when a patient is allowed surgical resection, which is, presently, the only potentially curative treatment for pancreatic cancer. This study examines pancreatic tumor growth and shrinkage to predict tumor response and change of resectability for pancreatic cancer patients undergoing radiation therapy. This is done using ordinary differential equations as a mathematical model. Mathematical models have increasingly been applied to various biological systems/processes to analyze the principles involved. In our project, a population dynamical …

Metrics For Performance Quantification Of Adaptive Mesh Refinement, Nicole Beisiegel, Cristóbal E. Castro, Jörn Behrens

Articles

Non-uniform, dynamically adaptive meshes are a useful tool for reducing computational complexities for geophysical simulations that exhibit strongly localised features such as is the case for tsunami, hurricane or typhoon prediction. Using the example of a shallow water solver, this study explores a set of metrics as a tool to distinguish the performance of numerical methods using adaptively refined versus uniform meshes independent of computational architecture or implementation. These metrics allow us to quantify how a numerical simulation benefits from the use of adaptive mesh refinement. The type of meshes we are focusing on are adaptive triangular meshes that are …

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

Doctoral Theses

No abstract provided.

Large Eddy Simulation Of Turbidity Currents In A Narrow Channel With Different Obstacle Configurations, Danial Goodarzi, Kaveh Sookhak Lari, Ehsan Khavasi, Soroush Abolfathi

Research outputs 2014 to 2021

© 2020, The Author(s). Turbidity currents are frequently observed in natural and man-made environments, with the potential of adversely impacting the performance and functionality of hydraulic structures through sedimentation and reduction in storage capacity and an increased erosion. Construction of obstacles upstream of hydraulic structures is a common method of tackling adverse effects of turbidity currents. This paper numerically investigates the impacts of obstacle’s height and geometrical shape on the settling of sediments and hydrodynamics of turbidity currents in a narrow channel. A robust numerical model based on LES method was developed and successfully validated against physical modelling measurements. This …

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

Olusegun Michael Otunuga

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

Mathematics Faculty Research

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …

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 …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

Analysis And Simulation Of Convolution Reverb Using City Tech’S New Auditorium, Tian Leng

Publications and Research

In digital signal processing, convolution reverb can simulate the reverberation of a real acoustic space. The acoustics of different seating areas in an auditorium can vary from each other. To determine the reverberant characteristics of City Tech new building’s auditorium, impulse response (IR) signals are recorded in five key locations of the auditorium.

Directly recorded balloon burst is chosen as the source of impulse source. An omnidirectional and a cardioid microphone with flat frequency response curves are used to record IR signals to 24-bit monophonic wav files. Each IR signal, along with a vocal, is convoluted in MATLAB through both …

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 …

Exact Recovery Of Prototypical Atoms Through Dictionary Initialization, Greg Zanotti, Enrico Au-Yeung

DePaul Discoveries

In dictionary learning, a matrix comprised of signals Y is factorized into the product of two matrices: a matrix of prototypical "atoms" D, and a sparse matrix containing coefficients for atoms in D, called X. Dictionary learning finds applications in signal processing, image recognition, and a number of other fields. Many algorithms for solving the dictionary learning problem follow the alternating minimization paradigm; that is, by alternating solving for D and X. In 2014, Agarwal et al. proposed a dictionary initialization procedure that is used before this alternating minimization process. We show that there is a …

Indicators For Early Assessment Of Palliative Care In Lung Cancer Patients: A Population Study Using Linked Health Data, Maria Kelly, Katie M. O'Brien, Michael Lucey, Kerri Clough-Gorr, Ailish Hannigan

Department of Mathematics Publications

Analysing linked, routinely collected data may be useful to identify characteristics of patients with suspected lung cancer who could benefit from early assessment for palliative care. The aim of this study was to compare characteristics of newly diagnosed lung cancer patients dying within 30 days of diagnosis (short term survivors) with those surviving more than 30 days. To identify indicators for early palliative care assessment we distinguished between characteristics available at diagnosis (age, gender, smoking status, marital status, comorbid disease, admission type, tumour stage and histology) from those available post diagnosis. A second aim was to examine the association between …

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 …