Applied Mathematics Commons^™

Rewriting The Rules For Diagnostics: Implications Of Probability And Measure Theory For Sars-Cov-2 Testing, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Inferring Dynamics Of Biological Systems, Tracey G. Oellerich

Biology and Medicine Through Mathematics Conference

No abstract provided.

Probability Distributions Of Active Sensing, Kathleen Hoffman

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Effect Of Prep Uptake And Adherence On The Spread Of Hiv In The Presence Of Casual And Long-Term Partnerships, Sylvia J. Gutowska, Katharine Gurski, Kathleen Hoffman

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Interplay Between Costly Reproduction And Unpredictable Environments Shapes The Stability Of Cooperative Breeding, Glenn Steven Young

Biology and Medicine Through Mathematics Conference

No abstract provided.

Age-Dependent Ventilator-Induced Lung Injury, Quintessa Hay, Christopher Grubb, Rebecca L. Heise, Sarah Minucci, Michael S. Valentine, Jennifer Van Mullekom, Angela M. Reynolds

Biology and Medicine Through Mathematics Conference

No abstract provided.

Understanding The Influence Of Perceptual Noise On Visual Flanker Effects Through Bayesian Model Fitting, Jordan Deakin, Dietmar Heinke

MODVIS Workshop

No abstract provided.

A Novel Chebyshev Wavelet Method For Solving Fractional-Order Optimal Control Problems, Ghodsieh Ghanbari

Theses and Dissertations

This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison …

A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker

Theses and Dissertations

The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …

Large Scale Disease Modeling, Walker Mattox

Master's Theses

In this we study large scale disease modeling. After understanding the mechanics behind the SIR disease model in an ODE sense, we will apply this knowledge to model disease spread in more and more increasing advanced cellular automata. Eventually, some of our cellular automata will include long distance travel. From this discrete data, we can then build an SIR model in the PDE sense to display large scale disease spread.

Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug

Spora: A Journal of Biomathematics

Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year^-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year^-1 reduces hepatitis B by over 90%, …

The Best Linear Approximation To Y= √X On The Interval [0, B] Using The Minimax Error, Hyounkyun Oh

Georgia Journal of Science

This study discusses how to find the best linear approximation y=mx+b to a fundamental function y=sqrt(x) on the interval [0,b], especially using the minimax error in Numerical Analysis. For this aim we employ two mathematical techniques: a) using the MATLAB code, positioning m and n values of the smallest maximum error on a broad range of m, and n value matrix in a rough scale and then repeatedly refining the regions in the smaller scales and b) Finding three-point fitting line to a set of non-colinear three points. We see that both results are successfully obtained and identical …

An Application Of Differential Mathematical Modeling Techniques To Study The Ongoing Rabies Epizootic In China, Christopher Turner

Electronic Theses and Dissertations

Rabies remains a global public health issue with a wide variety of neurological symptoms such as confusion, slight paralysis, hypersalivation, and hydrophobia. Rabies is usually fatal once symptoms appear. Many species are reservoirs for rabies, such as foxes, racoons, and wild dogs, which in turn can transmit the disease to humans, leading to complex transmission chains. There is a long latent period of rabies, between 1 to 3 months after infection, which further complicates control efforts. Mathematical modeling is a valuable tool in the study of infectious disease outbreaks and there have been many models applied to rabies outbreaks. However, …

Generating A Dataset For Comparing Linear Vs. Non-Linear Prediction Methods In Education Research, Jack Mauro, Elena Martinez, Anna Bargagliotti

Honors Thesis

Machine learning is often used to build predictive models by extracting patterns from large data sets. Such techniques are increasingly being utilized to predict outcomes in the social sciences. One such application is predicting student success. Machine learning can be applied to predicting student acceptance and success in academia. Using these tools for education-related data analysis, may enable the evaluation of programs, resources and curriculum. Currently, research is needed to examine application, admissions, and retention data in order to address equity in college computer science programs. However, most student-level data sets contain sensitive data that cannot be made public. To …

Nessie Notation: A New Tool In Sequential Substitution Systems And Graph Theory For Summarizing Concatenations, Colton Davis

Student Research

While doing research looking for ways to categorize causal networks generated by Sequential Substitution Systems, I created a new notation to compactly summarize concatenations of integers or strings of integers, including infinite sequences of these, in the same way that sums, products, and unions of sets can be summarized. Using my method, any sequence of integers or strings of integers with a closed-form iterative pattern can be compactly summarized in just one line of mathematical notation, including graphs generated by Sequential Substitution Systems, many Primitive Pythagorean Triplets, and various Lucas sequences including the Fibonacci sequence and the sequence of square …

The Primitive Root Problem: A Problem In Bqp, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Shor’s algorithm proves that the discrete logarithm problem is in BQP. Based on his algorithm, we prove that the primitive root problem, a problem that verifies if some integer g is a primitive root modulo p where p is the largest prime number smaller than 2n for a given n, which is assumed to be harder than the discrete logarithm problem, is in BQP by using an oracle quantum Turing machine.

Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack

Honors College Theses

Various techniques are used to create predictions based on count data. This type of data takes the form of a non-negative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zero-inflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as …

Structure Of Number Theoretic Graphs, Lee Trent

Mathematical Sciences Technical Reports (MSTR)

The tools of graph theory can be used to investigate the structure
imposed on the integers by various relations. Here we investigate two
kinds of graphs. The first, a square product graph, takes for its vertices
the integers 1 through n, and draws edges between numbers whose product
is a square. The second, a square product graph, has the same vertex set,
and draws edges between numbers whose sum is a square.
We investigate the structure of these graphs. For square product
graphs, we provide a rather complete characterization of their structure as
a union of disjoint complete graphs. For …

Electromagnetic Modeling Of A Wind Tunnel Magnetic Suspension And Balance System, Desiree Driver

Mechanical & Aerospace Engineering Theses & Dissertations

Wind tunnels are used to study forces and moments acting on an aerodynamic body. While most results involve some interference from the mechanical supports used to hold the model, a Magnetic Suspension and Balance System (MSBS) is void of these interferences and presents an ideal test scenario. To further investigate the feasibility of dynamic stability testing at supersonic speeds using a MSBS, a preliminary design idea is currently being developed using an existing MSBS in a subsonic wind tunnel. This review focuses on the development of a mathematical model to more accurately portray the capabilities of the 6 inch Massachusetts …

Relaxation Of Variational Principles For Z-Problems In Effective Media Theory, Kenneth Beard

Theses and Dissertations

In this thesis, we consider a class of Z-problems and their associated effective operators on Hilbert spaces which arise in effective media theory, especially within the theory of composites. We provide a unified approach to obtaining solutions of the Z-problem, formulas for the effective operator in terms of generalized Schur complements, and their associated variational principles (e.g., the Dirichlet minimization principle), while allowing for relaxation of the standard hypotheses on positivity and invertibility for the classes of operators usually considered in such problems. The Hilbert space framework developed here is inspired by the methods of orthogonal projections and Hodge decompositions. …

A Central Compact Hybrid-Variable Method With Spectral-Like Resolution, Md Mahmudul Hasan

Open Access Theses & Dissertations

Numerical methods for hyperbolic conservation laws have been a driving force for theresearch in scientific computing and simulation science in the past decades, as many physical, biological, and engineering systems are governed by these equations, such as fluid mechanics, tumor growth, and virtual wind tunnel simulations. Despite the existence of many schemes in the literature, people have never stopped searching for more accurate and efficient methods for these problems. Indeed, the increasing complexity of systems in emerging applications demands better resolution of sub-grid scale phenomenon whereas classical methods usually fail to deliver high-fidelity simulation results of such systems within realistic …

Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen

Graduate Theses and Dissertations

The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in the kernel of the Clifford multiplication. Let X be a simply connected Riemannian spin 4−manifold. Associated to a fixed spin structure on X, we define a Seiberg-Witten-like system of non-linear PDEs using Q and the Hodge-Dirac operator d∗ + d+ after suitable gauge-fixing. The moduli space of solutions M contains (3/2-spinors, purely …

The Impact Of Social Controls And Vaccination On The Spread Of Covid-19 In New Jersey, Ariel J. Bonneau

Theses, Dissertations and Culminating Projects

The emergence of the novel coronavirus (SARS-CoV-2) in late 2019 has led to a global pandemic (COVID-19) which continues to cause enormous public health and economic challenges around the world. It is therefore important to improve our understanding of the outbreak and spread of COVID-19 as well as to investigate how one might contain or stop the spread of COVID-19 via different control measures. In this thesis, we consider a COVID-19 model based on an SEIR compartmental model. The model includes susceptible, vaccinated, exposed, pre-symptomatic, symptomatic infectious, asymptomatic infectious, hospitalized, recovered, and deceased compartments, each of which is sub-divided into …

Modeling The Dynamics Of Excitable Cells, Asja Alić

Theses, Dissertations and Culminating Projects

We consider an electrical parallel conductance membrane model which is an extension of the classical Hodgkin-Huxley neuronal model of excitability. This extended model describes the formation of the resting membrane potential and conductance, and the formation of action potentials in nodose A-type excitable cells. The model consists of a set of nonlinear ordinary differential equations which are numerically solved using the Python programming language. The results show that the model is capable of accurately describing experimental results including resting membrane potential and conductance, duration and form of action potentials, amplitude of the spike, oscillations, and activitydependent changes in [Ca^{2+ …}

Forecasting Electricity Load In New Jersey With Artificial Neural Networks, Erik W. Raab

Theses, Dissertations and Culminating Projects

Load forecasting is an important tool for both the energy and environmental sectors. It has progressed hand-in-hand with machine learning innovation, where recurrent neural networks, a type of artificial neural network, is primarily used. This thesis compares progressively complex, feed-forward artificial neural networks using a mix of weather and temporal data. We demonstrate that electrical load in New Jersey can be reliably predicted using memory-less algorithms with minimal predictors drawn from preexisting public data sources. The methods used in this thesis could be used to build competitive load forecasting models in other states, and if included in diverse model ensembles, …

State Estimation—Beyond Gaussian Filtering, Haozhan Meng

LSU New Orleans Theses and Dissertations

This dissertation considers the state estimation problems with symmetric Gaussian/asymmetric skew-Gaussian assumption under linear/nonlinear systems. It consists of three parts. The first part proposes a new recursive finite-dimensional exact density filter based on the linear skew-Gaussian system. The second part adopts a skew-symmetric representation (SSR) of distribution for nonlinear skew-Gaussian estimation. The third part gives an optimized Gauss-Hermite quadrature (GHQ) rule for numerical integration with respect to Gaussian integrals and applies it to nonlinear Gaussian filters.

We first develop a linear system model driven by skew-Gaussian processes and present the exact filter for the posterior density with fixed dimensional recursive …

A Novel Data Lineage Model For Critical Infrastructure And A Solution To A Special Case Of The Temporal Graph Reachability Problem, Ian Moncur

Graduate Theses and Dissertations

Rapid and accurate damage assessment is crucial to minimize downtime in critical infrastructure. Dependency on modern technology requires fast and consistent techniques to prevent damage from spreading while also minimizing the impact of damage on system users. One technique to assist in assessment is data lineage, which involves tracing a history of dependencies for data items. The goal of this thesis is to present one novel model and an algorithm that uses data lineage with the goal of being fast and accurate. In function this model operates as a directed graph, with the vertices being data items and edges representing …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …

Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero

Theses and Dissertations

General adversarial networks (GANs) are a form of machine learning that includes two neural networks competing in a zero-sum game. One network produces artificial, while the other tries to distinguish artificial data from real. The Wasserstein general adversarial network with gradient penalty (WGAN-GP) variant of this technique is used to produce solutions for ordinary and partial differential equations.

Evaluating The Behaviour Of Centrally Perforated Unreinforced Masonry Walls: Applications Of Numerical Analysis, Machine Learning, And Stochastic Methods, Mohsen Khaleghi, Javid Salimi, Visar Farhangi, Mohammad Javad Moradi, Moses Karakouzian

Civil and Environmental Engineering and Construction Faculty Research

The presence of openings greatly affects the response of unreinforced masonry (URM) walls. This topic greatly attracts the attention of many researchers. Perforated unreinforced masonry (PURM) walls under in-plane loads through the truss discretization method (TDM) along with several machine learning approaches such as Multilayer perceptron (MLP), Group of Method Data Handling (GMDH), and Radial basis function (RBF) are described in this paper. A new method named Multi-pier (MP) that is fast and accurate, is used to determine the behavior of PURM walls. The results of the MP method are expressed as a ratio of lateral load-bearing capacity and initial …