Applied Mathematics Commons^™

Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

Publications and Research

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

An Investigation Of The Effects Of Variable Magnetic Field Gradients On Soot And Co Emissions From Non-Premixed Hydrocarbon Flames, Edison Ekperechukwu Chukwuemeka

LSU Doctoral Dissertations

The interaction of the paramagnetic species in a combustion process with the mag- netic field placed in the vicinity of non-premixed flames affects the characteristics of the non-premixed flames - flame height and flame lift-off height. However, the effect of this magnetic interaction on the pollutants generated by the flame is unknown.

In general, pollutant formation is promoted in most combustion systems due to in- complete combustion of the hydrocarbon due to improper mixing. Since paramagnetic combustion species such as O2, O, OH, etc interacts with magnetic fields and possess a preferential motion direction, imposing magnetic field on non-premixed flames …

A Component-Wise Approach To Smooth Extension Embedding Methods, Vivian Montiforte

Dissertations

Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.

Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods, Eva Lynn Greenman

Dissertations

The solution to a parabolic nonlinear diffusion equation using a Krylov Subspace Spectral method is applied to high resolution color digital images with parallel processing for efficient denoising. The evolution of digital image technology, processing power, and numerical methods must evolve to increase efficiency in order to meet current usage requirements. Much work has been done to perfect the edge detector in Perona-Malik equation variants, while minimizing the effects of artifacts. It is demonstrated that this implementation of a regularized partial differential equation model controls backward diffusion, achieves strong denoising, and minimizes blurring and other ancillary effects. By adaptively tuning …

How To Extend Interval Arithmetic So That Inverse And Division Are Always Defined, Tahea Hossain, Jonathan Rivera, Yash Sharma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life data processing situations, we only know the values of the inputs with interval uncertainty. In such situations, it is necessary to take this interval uncertainty into account when processing data. Most existing methods for dealing with interval uncertainty are based on interval arithmetic, i.e., on the formulas that describe the range of possible values of the result of an arithmetic operation when the inputs are known with interval uncertainty. For most arithmetic operations, this range is also an interval, but for division, the range is sometimes a disjoint union of two semi-infinite intervals. It is therefore desirable …

Optimal Analytical Methods For High Accuracy Cardiac Disease Classification And Treatment Based On Ecg Data, Jianwei Zheng

Computational and Data Sciences (PhD) Dissertations

This work constitutes six projects. In the first project, a newly inaugurated research database for 12-lead electrocardiogram signals was created under the auspices of Chapman University and Shaoxing People's Hospital (Shaoxing Hospital Zhejiang University School of Medicine). This database aims to enable the scientific community in conducting new studies on arrhythmia and other cardiovascular conditions. In the second project, we created a new 12-lead ECG database under the auspices of Chapman University and Ningbo First Hospital of Zhejiang University that aims to provide high quality data enabling detection of the distinctions between idiopathic ventricular arrhythmia from right ventricular outflow tract …

The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker

Electronic Theses and Dissertations

Modeling our atmosphere and determining forecasts using numerical methods has been a challenge since the early 20th Century. Most models use a complex dynamical system of equations that prove difficult to solve by hand as they are chaotic by nature. When computer systems became more widely adopted and available, approximating the solution of these equations, numerically, became easier as computational power increased. This advancement in computing has caused numerous weather models to be created and implemented across the world. However a challenge of approximating these solutions accurately still exists as each model have varying set of equations and variables to …

Extinction Of Species Due To Deterministic And Stochastic Interactions In Food Webs, Claire M. Burke

Theses, Dissertations and Culminating Projects

Previous research on the extinctions that occur in niche model food webs with deterministic and stochastic dynamics has shown that the structure of the food web can play an important role in extinction cascades. In this thesis, other types of synthetic food web models are considered, namely the cascade and generalized cascade models, and the extinction cascades of these food webs are compared with previous findings on the extinction cascades from the niche model. It was found that there are many similarities in the results for all three models, which prompted a closer analysis using food webs with deterministic dynamics. …

Applications Of Evidence Theory To High-Consequence Systems Safety, Christina Marie Deffenbaugh

Mathematics & Statistics ETDs

Issues linked to abnormal environments (like high-consequence systems safety, e.g., nuclear weapon components, bridges, apartment buildings, etc.) may have insufficient information to use either classical statistical methods or Bayesian approaches for calculating associated probabilistic risks, so there is often a requirement for another method that can deal with a low-information situation to obtain a risk assessment. Belief/plausibility measures of uncertainty from A. P. Dempster and G. Shafer’s Evidence Theory is one such method. This thesis has two goals. First, a brief discussion on belief/plausibility measures as an application of Evidence Theory will familiarize the audience with its history and how …

Constructing Non-Proxy Small Test Modules For The Complete Intersection Property, Benjamin Briggs, Eloísa Grifo, Josh Pollitz

Department of Mathematics: Faculty Publications

A local ring R is regular if and only if every finitely generated R-module has finite projective dimension. Moreover, the residue field k is a test module: R is regular if and only if k has finite projective dimension. This characterization can be extended to the bounded derived category Df(R), which contains only small objects if and only if R is regular. Recent results of Pollitz, completing work initiated by Dwyer-Greenlees-Iyengar, yield an analogous characterization for complete intersections: R is a complete intersection if and only if every object in Df(R) is proxy small. In this paper, we study a …

Gene Selection And Classification In High-Throughput Biological Data With Integrated Machine Learning Algorithms And Bioinformatics Approaches, Abhijeet R Patil

Open Access Theses & Dissertations

With the rise of high throughput technologies in biomedical research, large volumes of expression profiling, methylation profiling, and RNA-sequencing data are being generated. These high-dimensional data have large number of features with small number of samples, a characteristic called the "curse of dimensionality." The selection of optimal features, which largely affects the performance of classification algorithms in machine learning models, has led to challenging problems in bioinformatics analyses of such high-dimensional datasets. In this work, I focus on the design of two-stage frameworks of feature selection and classification and their applications in multiple sets of colorectal cancer data. The first …

Schur Complement Algebra And Operations With Applications In Multivariate Functions, Realizations, And Representations, Anthony Dean Stefan

Theses and Dissertations

We provide a new approach to the following multidimensional realizability problem: Can an arbitrary square matrix, whose entries are from the field of multivariate rational functions over the complex numbers, be realized as a Schur complement of a linear matrix pencil with symmetries? To answer this problem, we prove the main theorem of M. Bessmertny˘ı,“On realizations of rational matrix functions of several complex variables,” in Vol. 134 of Oper. Theory Adv. Appl., pp. 157-185, Birkh¨auser Verlag, Basel, 2002 and have included additional symmetries as an extension to his results. Furthermore, we were so thorough in our constructive approach that we …

Stability Results For Special Solutions Of Scalar-Field Equations With Variable Coeffcients, Mashael Ibrahiem Alammari

Theses and Dissertations

We study the long-time behavior of general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. In the first part of the dissertation, we take the coefficients to be uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are motivated by the question of how these perturbations of the equation may change the stability properties of kink solutions (one-dimensional topological solitons). We prove existence of a stationary kink solution in our setting, and perform a detailed spectral analysis of the corresponding linearized operator, based on perturbing the linearized operator around the constant-coefficient kink. …

Optimality Of Delaunay Triangulations, Estefania A. Sierra

Theses and Dissertations

In this paper, we begin by defining and examining the properties of a Voronoi diagram and extend it to its dual, the Delaunay triangulations. We explore the algorithms that construct such structures. Furthermore, we define several optimal functionals and criterions on the set of all triangulations of points in Rd that achieve their minimum on the Delaunay triangulation. We found a new result and proved that Delaunay triangulation has lexicographically the least circumradii sequence. We discuss the CircumRadii-Area (CRA) conjecture that the circumradii raised to the power of alpha times the area of the triangulation holds true for all α …

Discovering Kepler’S Third Law From Planetary Data, Boyan Kostadinov, Satyanand Singh

Publications and Research

In this data-inspired project, we illustrate how Kepler’s Third Law of Planetary Motion can be discovered from fitting a power model to real planetary data obtained from NASA, using regression modeling. The power model can be linearized, thus we can use linear regression to fit the model parameters to the data, but we also show how a non-linear regression can be implemented, using the R programming language. Our work also illustrates how the linear least squares used for fitting the power model can be implemented in Desmos, which could serve as the computational foundation for this project at a lower …

Predicting Suboptimal Care In Insured Nebraskans With Known And Suspected Chronic Conditions., Avery Wallace

Capstone Experience: Master of Public Health

Health insurance companies have a goal of improving population health for their members (people who the company insures). As a health insurance company, [Company] has ample data on the health of its members that can be utilized to improve the health, and by extension lives of the people they insure. Although [Company] does not deliver care, they communicate with their members and physicians to identify ways to improve the health of the member. Of specific interest are members with known chronic conditions who are receiving suboptimal care, as well as members who have undiagnosed chronic conditions. Two chronic conditions were …

Optimal Control Of Algae Biofilm Growth In Wastewater Treatment Using Computational Mathematical Models, Gerald Benjamin Jones

Undergraduate Honors Capstone Projects

Microalgal biofilms are comprised of a syntrophic consortium of microalgae and other microorganisms embedded within an extracellular matrix. Despite significant processes in the application of microalgal biofilms in wastewater treatment, mechanistic understanding and optimization of microalgal biomass yield and productivity under environmental constraints is still lacking. This paper identifies theoretical insights on this challenging biological problem by leveraging novel mathematical and computational tools. In particular, through a computational mathematical model to advance the understanding of microalgal biofilm growth kinetics under environmental constraints through a systematic parameter study. Moreover, design of algae biofilm reactors for optimal biomass yield and productivity in …

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …

The Brezis-Nirenberg Problem For The Generalized Kirchhoff Equation, Erisa Hasani

Theses and Dissertations

We study a class of critical Kirchhoff problems with a general nonlocal term. The main difficulty here is the absence of a closed-form formula for the compactness threshold. First we obtain a variational characterization of this threshold level. Then we prove a series of existence and multiplicity results based on this variational characterization.

Parallel Computation Of Action Potentials In The Hodgkin-Huxley Model Via The Parareal Algorithm, Eric Boerman, Khanh Pham, Katie Peltier

Mathematics Student Work

The Hodgkin-Huxley model is a system of differential equations that describe the membrane voltage of an axon as it fires the basic signal of the nervous system: the action potential. When charge-carrying ions such as sodium, potassium, and others are enabled to cross a selectively permeable membrane, the resulting current propagates along the length of the axon as a wave of altered ionic potential. However, the degree to which the membrane is permeable to sodium and potassium is itself gated by voltage; therefore, voltage depends on permeability and permeability depends on voltage. This interdependent cellular system is expressed as a …

Solving The Heat Equation With Interfaces, Michael Bauer, Rex Llewellyn, Shauna Frank

Mathematics Student Work

When modeling systems made up of two materials with different thermodynamic properties, a physical interface can be introduced to account for the border where the materials meet. This interface separates our model’s standard grid into two regions, each with its unique physical properties. At these interfaces, boundary conditions can be imposed to represent the difference in heat and in heat flux between the different materials so that their interaction may be modeled accurately. Because standard finite difference methods are inadequate to deal with interfaces, a Matched Interface and Boundary (MIB) technique is investigated in this work to solve the heat …

Analysis Of An Integral Metric On Hyperspaces, Darren Schmidt

Undergraduate Research Conference at Missouri S&T

In this paper, we will be investigating how to compute the integral distance defined by Dr. Insall and Dr. Charatonik, and we will analyze the results from this computation. We develop a way to compute the integral distance by using Monte-Carlo Integration, and we analyze the time complexity and the error that results from this method of computation. We also investigate when this distance function is a metric, and how this metric compares to some other common metrics.

Construct Linear Quasi-Interpolants On Infinite Intervals, Johara Farah Albaliwi

Dissertations

In solving the data interpolation problem, which is fundamental in data analysis, we typically deal with the data samples spread in a finite interval [a, b], which results in the operations involving finite-dimensional matrices. There are many interesting results developed under this framework. However, when the data samples are given from an infinite interval [a, ∞) (for certain special types of real-world applications), many existing results would not work anymore due to the special properties of the infinite data samples. A new framework should be established to support the infinite data samples.

In this dissertation, we develop a special tool …

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 …

Compact Dupin Hypersurfaces, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface M in Rⁿ is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if the number of distinct principal curvatures is constant on M, i.e., each continuous principal curvature function has constant multiplicity on M. These conditions are preserved by stereographic projection, so this theory is essentially the same for hypersurfaces in Rⁿ or Sⁿ . The theory of compact proper Dupin hypersurfaces in Sⁿ is closely related to the theory of isoparametric hypersurfaces in S^{n …}

Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai

Mathematical Sciences Spring Lecture Series

There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …

Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai

Mathematical Sciences Spring Lecture Series

We consider solving system of nonlinear algebraic equations arising from the discretization of partial differential equations. Inexact Newton is a popular technique for such problems. When the nonlinearities in the system are well-balanced, Newton's method works well, but when a small number of nonlinear functions in the system are much more nonlinear than the others, Newton may converge slowly or even stagnate. In such a situation, we introduce some nonlinear preconditioners to balance the nonlinearities in the system. The preconditioners are often constructed using a combination of some domain decomposition methods and nonlinear elimination methods. For the nonlinearly preconditioned problem, …

Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis

Spora: A Journal of Biomathematics

Though clinicians can now collect detailed information about a variety of tumor characteristics as a tumor evolves, it remains difficult to predict the efficacy of a given treatment prior to administration. Additionally, the process of data collection may be invasive and expensive. Thus, the creation of a framework for predicting patient response to treatment using only information collected prior to the start of treatment could be invaluable. In this study, we employ ordinary differential equation models for tumor growth and utilize synthetic data from a cellular automaton model for calibration. We investigate which parameters have the most influence upon treatment …

Kleptoparasitic Hawk-Dove Games, Isabella H. Evans-Riester, Chasity T. Kay, Karina L. Ortiz-Suarez, Jan Rychtář, Dewey Taylor

Spora: A Journal of Biomathematics

The Hawk-Dove game is a classical game-theoretical model of potentially aggressive animal conflicts. In this paper, we apply game theory to a population of foraging animals that may engage in stealing food from one another. We assume that the population is composed of two types of individuals, Hawks and Doves. Hawks try to escalate encounters into aggressive contests while Doves engage in non-aggressive displays between themselves or concede to aggressive Hawks. The fitness of each type depends upon various natural parameters, such as food density, the mean handling time of a food item, as well as the mean times of …

Netsci High: Bringing Agency To Diverse Teens Through The Science Of Connected Systems, Stephen M. Uzzo, Catherine B. Cramer, Hiroki Sayama, Russell Faux

Northeast Journal of Complex Systems (NEJCS)

This paper follows NetSci High, a decade-long initiative to inspire teams of teenage researchers to develop, execute and disseminate original research in network science. The project introduced high school students to the computer-based analysis of networks, and instilled in the participants the habits of mind to deepen inquiry in connected systems and statistics, and to sustain interest in continuing to study and pursue careers in fields involving network analysis. Goals of NetSci High ranged from proximal learning outcomes (e.g., increasing high school student competencies in computing and improving student attitudes toward computing) to highly distal (e.g., preparing students for 21st …