Applied Mathematics Commons^™

A Closer Look At The Death Penalty In The United States, Anna L. Cardell

Research & Creative Achievement Day

The death penalty has always been a source of contention towards most people in the United States – some agree with it, some do not. No matter one's opinion on whether it should be allowed, this poster presentation will give an in-depth analysis and present various visualizations of information regarding the convicted felons that have been sentenced to capital punishment in the United States from 1976-2016. Variables such as gender, age, and race will be explored to create some insight on some of the most infamous killers in United States history. Though looking at the demographics of these individuals and …

Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson

Spora: A Journal of Biomathematics

Silver carp (Hypophthalmichthys molitrix) are planktivorous fish that were originally introduced to the United States for use in fish production ponds and have since escaped these enclosures and are invading the Mississippi River Basin. The silver carp invasion of the Illinois River has a myriad of negative effects on native ecosystems. In this paper, we introduce key dependencies that are likely important in the population dynamics of silver carp: length-dependent egg production and density-dependent growth. Using movement data between two adjacent pools of the Illinois River, we conduct numerical simulations to explore the theoretical effect of harvesting and …

A Mathematical Model For Mosquito Population Dynamics, Christian Evans, Jemal Mohammed-Awel, Andreas Lazari

Georgia Journal of Science

In this study, a deterministic mathematical model for mosquito population dynamics is presented. The use of chemical insecticide to control population is incorporated into the model. It is assumed that there is insecticide sensitive (sensitive-type) and insecticide resistant (resistant-type) mosquitoes in the environment. Conditions for the existence and stability of four equilibria of the model have been established. Numerical simulations are carried out to confirm the analytical results and the implications, in terms of mosquito control in the environment, are discussed.

Topological Data Analysis Of Weight Spaces In Convolutional Neural Networks, Adam Wagenknecht

Dissertations

Convolutional Neural Networks (CNNs) have become one of the most commonly used tools for performing image classification. Unfortunately, as with most machine learning algorithms, CNNs suffer from a lack of interpretability. CNNs are trained by using a training data set and a loss function to tune a set of parameters known as the layer weights. This tuning process is based on the classical method of gradient descent, but it relies on a strong stochastic component, which makes the weight behavior during training difficult to understand. However, since CNNs are governed largely by the weights that make up each of the …

A Predator-Prey Biological Model With Combined Birth Rates, Self-Limitation And Competition Terms, Joon Hyuk Kang, Lucinda Ford

Faculty Publications

The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω in Rⁿ. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive …

Unraveling The Nature Of Nano‑Diamonds And Silica In A Catheterized Tapered Artery: Highlights Into Hydrophilic Traits, Sara I. Abdelsalam, M.M. Bhatti

Basic Science Engineering

No abstract provided.

A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin

Honors College Theses

Fine particulate matter or PM2.5 can be described as a pollution particle that has a diameter of 2.5 micrometers or smaller. These pollution particle values are measured by monitoring sites installed across the United States throughout the year. While these values are helpful, a lot of areas are not accounted for as scientists are not able to measure all of the United States. Some of these unmeasured regions could be reaching high PM2.5 values over time without being aware of it. These high values can be dangerous by causing or worsening health conditions, such as cardiovascular and lung diseases. Within …

Nash Blowups Of Toric Varieties In Prime Characteristic, Daniel Duarte, Jack Jeffries, Luis Núñez-Betancourt

Department of Mathematics: Faculty Publications

We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime characteristic version of the logarithmic Jacobian ideal of a toric variety and prove that its blowup coincides with the Nash blowup of the variety. As a consequence, the Nash blowup of a, not necessarily normal, toric variety of arbitrary dimension in prime characteristic can be described combinatorially.

First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang

LSU Doctoral Dissertations

Nonlinear optimization is a critical branch in applied mathematics and has attracted wide attention due to its popularity in practical applications. In this work, we present two methods which use first-order information to solve two typical classes of nonlinear structured optimization problems.

For a class of unconstrained nonconvex composite optimization problems where the objective is the sum of a smooth but possibly nonconvex function and a convex but possibly nonsmooth function, we propose a unified proximal gradient method with extrapolation, which provides unified treatment to convex and nonconvex problems. The method achieves the best-known convergence rate for first-order methods when …

Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra

Mathematics & Statistics ETDs

Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full …

Finite Element Methods For Elliptic Optimal Control Problems With General Tracking, Seonghee Jeong

LSU Doctoral Dissertations

This dissertation concerns a linear-quadratic elliptic distributed optimal control problem with pointwise state constraints in two spatial dimensions, where the cost function tracks the state at points, curves and regions of a domain.

First we explore the elliptic optimal control problem subject to pointwise control constraints. This problem is reduced into a problem that only involves the control. The solution of the reduced problem is characterized by a variational inequality. Then we introduce the elliptic optimal control problem with general tracking and pointwise state constraints. Here we reformulate the optimal control problem into a problem that only involves the state, …

Effects Of Topography On Tornado Paths Using Navier Stokes Equations, Kayleigh Smith

Mathematics Senior Capstone Papers

Tornadoes are relatively common in Louisiana with an average of 55 tornadoes per year. Predicting tornado paths has been extremely challenging due to the many factors that play into the formation of a tornado. According to NASA/ADS topography can have significant influence on tornado direction. The main goal of this research is to analyze tornado patterns and to determine if local topography has an effect on tornadic activity. Navier-Stokes partial differential equations will be used to model the data that is collected from the national weather service and a finite difference method will be used to solve the equations. Data …

Modeling Reverberant Chambers Used In Time-Reversal Cavities Using Time-Frequency Methods, Jordan Savoie

Mathematics Senior Capstone Papers

The signal processing technique of time-reversal is used for various purposes in electro-magnetic interference testing, radar, communication, sonar, and medicine. This paper models the impulse response of a reverberant chamber such as might be used for a time-reversal cavity (TRC) using time-frequency methods. Reverberant chambers have chaotic delaying phase responses that cause the majority of the distortion seen in their impulse response. Time-reversal cancels this, creating a focused signal from a disperse one. Most research modeling the behavior of TRCs is more concerned with their physics, so there is relatively little commented on the form of their signals. Data of …

Project Based Learning, Christopher Imm

Sabbatical Projects

Project-based learning (PBL) is a pedagogy which encourages students to be actively involved in their learning process through gaining information to solve real-world problems with projects. In areas of STEM education, PBL can supplement the traditional classroom lecture, where students have a predominantly passive role in the learning process. Through practical activities, interactive discussions, independent reflection and/or team cooperation, students achieve the desired learning outcomes.

Graphsearchnet: Enhancing Gnns Via Capturing Global Dependencies For Semantic Code Search, Shangqing Liu, Xiaofei Xie, Jjingkai Siow, Lei Ma, Guozhu Meng, Yang Liu

Research Collection School Of Computing and Information Systems

Code search aims to retrieve accurate code snippets based on a natural language query to improve software productivity and quality. With the massive amount of available programs such as (on GitHub or Stack Overflow), identifying and localizing the precise code is critical for the software developers. In addition, Deep learning has recently been widely applied to different code-related scenarios, ., vulnerability detection, source code summarization. However, automated deep code search is still challenging since it requires a high-level semantic mapping between code and natural language queries. Most existing deep learning-based approaches for code search rely on the sequential text ., …

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

CODEE Journal

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans

Mathematics Theses and Dissertations

For decades, it has been observed that broad-beam irradiation of semiconductor surfaces can lead to spontaneous self-organization into highly regular patterns, sometimes at length scales of only a few nanometers. Initial theory was largely based on erosion and redistribution of material occurring on fast time scales, which are able to produce good agreement with certain aspects of surface evolution. However, further experimental and theoretical work eventually led to the realization that numerous effects are active in the irradiated target, including stresses associated with ion-implantation and the accumulation of damage leading to the development of a disordered, amorphous layer atop the …

Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow, Norah Hakami

Mathematics Theses and Dissertations

When employing the immersed interface method (IIM) to simulate a fluid flow around a moving rigid object, the immersed object can be replaced by a virtual fluid enclosed by singular forces on the interface between the real and virtual fluids. These forces represent the impact of the rigid motion on the fluid flow and cause jump discontinuities across the interface in the whole flow field. Then, the IIM resolves the fluid flow on a fixed computational domain by directly incorporating the jump conditions across the interface into numerical schemes. Previous development of the method is limited to simple smooth boundaries. …

A Node Elimination Algorithm For Cubatures Of High-Dimensional Polytopes, Arkadijs Slobodkins

Mathematics Theses and Dissertations

Node elimination is a numerical approach for obtaining cubature rules for the approximation of multivariate integrals over domains in Rⁿ. Beginning with a known cubature, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. In this work, a new node elimination criterion is introduced that is based on linearization of the moment equations. In addition, a penalized iterative solver is introduced that ensures positivity of weights and interiority of nodes. We aim to construct a universal algorithm for convex polytopes that produces efficient cubature rules without any user …

Impact Of Teaching Mathematics With Four Teaching Strategies On Fifth Grade Students’ Learning Of Fractions Addition And Subtraction, Nabil Riziq Al Farra

Dissertations

There are different tools, resources, and materials that mathematics teachers may use to enhance the teaching and learning processes under many types of teaching strategies such as technology (e.g., videos and virtual manipulatives), real objects (e.g., concrete manipulatives), and other teaching strategies are traditional (e.g., lectures). Some of the most important things that a teacher has to consider is the students’ learning needs and how to reach to their minds by different teaching strategies with a variety of resources and assess which are more effective in students’ learning anddevelopment in mathematics.

The purpose of this study is to investigate the …

Extremal Absorbing Sets In Low-Density Parity-Check Codes, Emily Mcmillon, Allison Beemer, Christine A. Kelley

Department of Mathematics: Faculty Publications

Absorbing sets are combinatorial structures in the Tanner graphs of low-density parity-check (LDPC) codes that have been shown to inhibit the high signal-to-noise ratio performance of iterative decoders over many communication channels. Absorbing sets of minimum size are the most likely to cause errors, and thus have been the focus of much research. In this paper, we determine the sizes of absorbing sets that can occur in general and left-regular LDPC code graphs, with emphasis on the range of b for a given a for which an (a, b)-absorbing set may exist. We identify certain cases of extremal …

Data-Driven Learning Algorithm Via Densely-Defined Multiplication Operators And Occupation Kernels., John Kyei

USF Tampa Graduate Theses and Dissertations

Consider a nonautonomous nonlinear evolution $\dot{x}=f(x,t,\mu)$, where the vector $x(t) \in \mathbb{R}^n$ represents the state of the dynamical system at time $t$, $\mu$ contains system parameters, and $f(\cdot)$ represents a dynamic constraint. In most practical applications, the nonlinear dynamic constraint $f$ is unknown analytically. The problem of approximating $f$ directly from data measurements generated by the system is a main goal of this manuscript. In the postulates of the Nonlinear Autoregressive (NAR) framework, we show that the problem of approximating $f$ can be studied through symbols of densely defined multiplication operators over a Reproducing Kernel Hilbert Spaces (RKHS). In this …

Mathematical Modeling And Inverse Problems In Applications, Thanh T. Nguyen

College of Science & Mathematics Departmental Research

Mathematical models, based on ordinary or partial differential equations, are widely used to describe physical/chemical/biological processes and can be found in several applications: nondestructive testing, subsurface imaging, defense, medicine, environmental sciences, etc.

Using Physics-Informed Neural Networks For Multigrid In Time Coarse Grid Equations, Jonathan P. Gutierrez

Mathematics & Statistics ETDs

For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as …

Problem Of The Week: A Student-Led Initiative To Bring Mathematics To A Broader Audience, Jordan M. Sahs, Brad Horner

UNO Student Research and Creative Activity Fair

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy …

Infinite-Dimensional Stochastic Transforms And Reproducing Kernel Hilbert Space, Myung-Sin Song, Palle Jorgensen, James Feng Tian

SIUE Faculty Research, Scholarship, and Creative Activity

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general setting of Gaussian processes. Our results serve to unify existing tools from infinite-dimensional analysis.

Formal Conjugacy Growth In Graph Products I, Laura Ciobanu,, Susan Hermiller, Valentin Mercier

Department of Mathematics: Faculty Publications

In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.

Chatgpt As Metamorphosis Designer For The Future Of Artificial Intelligence (Ai): A Conceptual Investigation, Amarjit Kumar Singh (Library Assistant), Dr. Pankaj Mathur (Deputy Librarian)

Library Philosophy and Practice (e-journal)

Abstract

Purpose: The purpose of this research paper is to explore ChatGPT’s potential as an innovative designer tool for the future development of artificial intelligence. Specifically, this conceptual investigation aims to analyze ChatGPT’s capabilities as a tool for designing and developing near about human intelligent systems for futuristic used and developed in the field of Artificial Intelligence (AI). Also with the helps of this paper, researchers are analyzed the strengths and weaknesses of ChatGPT as a tool, and identify possible areas for improvement in its development and implementation. This investigation focused on the various features and functions of ChatGPT that …

Kegg_Pull: A Software Package For The Restful Access And Pulling From The Kyoto Encyclopedia Of Gene And Genomes, Erik D. Huckvale, Hunter N. B. Moseley

Markey Cancer Center Faculty Publications

Background: The Kyoto Encyclopedia of Genes and Genomes (KEGG) provides organized genomic, biomolecular, and metabolic information and knowledge that is reasonably current and highly useful for a wide range of analyses and modeling. KEGG follows the principles of data stewardship to be findable, accessible, interoperable, and reusable (FAIR) by providing RESTful access to their database entries via their web-accessible KEGG API. However, the overall FAIRness of KEGG is often limited by the library and software package support available in a given programming language. While R library support for KEGG is fairly strong, Python library support has been lacking. Moreover, there …

Evolution Of Coronal Magnetic Field Parameters During X5.4 Solar Flare, Seth H. Garland, Benjamin F. Akers, Vasyl B. Yurchyshyn, Robert D. Loper, Daniel J. Emmons

Faculty Publications

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz| ≥ 300 G, areas of flare brightening seen …