Applied Mathematics Commons^™

Local Binary Pattern Based Algorithms For The Discrimination And Detection Of Crops And Weeds With Similar Morphologies, Vi Nguyen Thanh Le

Theses: Doctorates and Masters

In cultivated agricultural fields, weeds are unwanted species that compete with the crop plants for nutrients, water, sunlight and soil, thus constraining their growth. Applying new real-time weed detection and spraying technologies to agriculture would enhance current farming practices, leading to higher crop yields and lower production costs. Various weed detection methods have been developed for Site-Specific Weed Management (SSWM) aimed at maximising the crop yield through efficient control of weeds. Blanket application of herbicide chemicals is currently the most popular weed eradication practice in weed management and weed invasion. However, the excessive use of herbicides has a detrimental impact …

Zero-Inflated Longitudinal Mixture Model For Stochastic Radiographic Lung Compositional Change Following Radiotherapy Of Lung Cancer, Viviana A. Rodríguez Romero

Theses and Dissertations

Compositional data (CD) is mostly analyzed as relative data, using ratios of components, and log-ratio transformations to be able to use known multivariable statistical methods. Therefore, CD where some components equal zero represent a problem. Furthermore, when the data is measured longitudinally, observations are spatially related and appear to come from a mixture population, the analysis becomes highly complex. For this matter, a two-part model was proposed to deal with structural zeros in longitudinal CD using a mixed-effects model. Furthermore, the model has been extended to the case where the non-zero components of the vector might a two component mixture …

An Application Of A Binary-Integer Programming Process To The Faculty-Course Assignment Problem, Charles Graves

Murray State Theses and Dissertations

Have you ever wondered why you have a certain class or professor at a certain time during the week? Creating a faculty-course schedule is a complicated and time- consuming process. In this thesis, we will examine two binary-integer programming models to generate the faculty-course schedule with various unique course preparations for the Department of Mathematics and Statistics at Murray State University. The first model will present a traditional, on-campus course schedule, and the second will present an online, asynchronous learning course schedule.

Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman

Mathematics Faculty Publications

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …

Editorial: Recent Trends In Computational Fluid Dynamics, M. M. Bhatti, M. Marin, A. Zeeshan, Sara I. Abdelsalam

Basic Science Engineering

No abstract provided.

Toward Automated Region Detection & Parcellation Of Rat Brain Tissue Images, Alexandro Arnal

Open Access Theses & Dissertations

People who analyze images of biological tissue often rely on segmentation of structures as a preliminary step. In particular, laboratories studying the rat brain manually delineate brain regions to position scientific findings on a brain atlas to propose hypotheses about the rat brain, and ultimately, the human brain. Our work intersects with the preliminary step of delineating regions in images of brain tissue via computational methods.

We investigate pixel-wise classification or segmentation of brain regions using ten histological images of brain tissue sections stained for Nissl substance, and two deep learning models: U-Net and Tile2Vec. Our goal is to assess …

Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze

Articles

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and …

Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda

Theses, Dissertations and Culminating Projects

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, …

Increasing Performance Of Classifiers For Ssvep-Based Brain-Computer Interfaces Using Extension Methods, Ethan Douglas Webster

Legacy Theses & Dissertations (2009 - 2024)

Brain-computer interfaces (BCI) provide an alternative communication method that does not require standard physical mediums (speech, typing, etc.). These systems have been implemented to provide additional communication and control options for people with certain motor disabilities. Classification is an important part of BCI systems and consists of inferring user commands from brain activity. Supervised classification methods often achieve higher accuracy, but unsupervised classification methods are useful when training is not practical for the user. This thesis focuses on unsupervised classification algorithms used for a BCI speller application and presents extensions for two existing classifiers that improve classification accuracy and thus …

Maxwell's Equations And Yang-Mills Equations In Complex Variables : New Perspectives, Sachin Munshi

Legacy Theses & Dissertations (2009 - 2024)

Maxwell's equations, named after James C. Maxwell, are a U(1) gauge theory describing the interactions between electric and magnetic fields. They lie at the heart of classical electromagnetism and electrodynamics. Yang-Mills equations, named after C. N. Yang and Robert Mills, generalize Maxwell's equations and are associated with a non-abelian gauge theory called Yang-Mills theory. Yang-Mills theory unified the electroweak interaction with the strong interaction (QCD), and it is the foundation of the Standard Model in particle physics.

Unitary And Symmetric Structure In Deep Neural Networks, Kehelwala Dewage Gayan Maduranga

Theses and Dissertations--Mathematics

Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well-known difficulty in using RNNs is the vanishing or exploding gradient problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogonal or unitary recurrent weight matrix. One such architecture is the scaled Cayley orthogonal recurrent neural network (scoRNN), which parameterizes the orthogonal recurrent weight matrix through a scaled Cayley transform. This parametrization contains a diagonal scaling matrix consisting of positive or negative one entries that can not be optimized by gradient descent. Thus the …

Orthogonal Recurrent Neural Networks And Batch Normalization In Deep Neural Networks, Kyle Eric Helfrich

Theses and Dissertations--Mathematics

Despite the recent success of various machine learning techniques, there are still numerous obstacles that must be overcome. One obstacle is known as the vanishing/exploding gradient problem. This problem refers to gradients that either become zero or unbounded. This is a well known problem that commonly occurs in Recurrent Neural Networks (RNNs). In this work we describe how this problem can be mitigated, establish three different architectures that are designed to avoid this issue, and derive update schemes for each architecture. Another portion of this work focuses on the often used technique of batch normalization. Although found to be successful …

Filtered-Dynamic-Inversion Control For Unknown Minimum-Phase Systems With Unknown Relative Degree, Sumit Suryakant Kamat

Theses and Dissertations--Mechanical and Aerospace Engineering

We present filtered-dynamic-inversion (FDI) control for unknown linear time-invariant systems that are multi-input multi-output and minimum phase with unknown-but-bounded relative degree. This FDI controller requires limited model information, specifically, knowledge of an upper bound on the relative degree and knowledge of the first nonzero Markov parameter. The FDI controller is a single-parameter high-parameter-stabilizing controller that is robust to uncertainty in the relative degree. We characterize the stability of the closed-loop system. We present numerical examples, where the FDI controller is implemented in feedback with mathematical and physical systems. The numerical examples demonstrate that the FDI controller for unknown relative degree …

Three Point Boundary Value Problems For Ordinary Differential Equations, Uniqueness Implies Existence, Paul W. Eloe, Johnny Henderson, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We consider a family of three point n − 2, 1, 1 conjugate boundary value problems for nth order nonlinear ordinary differential equations and obtain conditions in terms of uniqueness of solutions imply existence of solutions. A standard hypothesis that has proved effective in uniqueness implies existence type results is to assume uniqueness of solutions of a large family of n−point boundary value problems. Here, we replace that standard hypothesis with one in which we assume uniqueness of solutions of large families of two and three point boundary value problems. We then close the paper with verifiable conditions on the …

Description Of Income And Substitution Effects Using Slutsky Identity, Julius N. Esunge, Dali Magrakvelidze

Mathematics Articles

In the paper we describe how income and price changes affect consumer's decision making using the Slutsky Identity. We also investigate economical meaning of curve turn-movements of consumer's budget. For analyzing the changes of consumer's choice we are using two step movements (turn, then parallel movement) of budget curve.

Pulsatile Flow Through Idealized Renal Tubules: Fluid-Structure Interaction And Dynamic Pathologies, Niksa Praljak, Shawn D. Ryan, Andrew Resnick

Mathematics and Statistics Faculty Publications

Kidney tubules are lined with flow-sensing structures, yet information about the flow itself is not easily obtained. We aim to generate a multiscale biomechanical model for analyzing fluid flow and fluid-structure interactions within an elastic kidney tubule when the driving pressure is pulsatile. We developed a two-dimensional macroscopic mathematical model of a single fluid-filled tubule corresponding to a distal nephron segment and determined both flow dynamics and wall strains over a range of driving frequencies and wall compliances using finite-element analysis. The results presented here demonstrate good agreement with available analytical solutions and form a foundation for future inclusion of …

Artificial Neural Network Models For Pattern Discovery From Ecg Time Series, Mehakpreet Kaur

College of Graduate Studies: Theses & Dissertations

Artificial Neural Network (ANN) models have recently become de facto models for deep learning with a wide range of applications spanning from scientific fields such as computer vision, physics, biology, medicine to social life (suggesting preferred movies, shopping lists, etc.). Due to advancements in computer technology and the increased practice of Artificial Intelligence (AI) in medicine and biological research, ANNs have been extensively applied not only to provide quick information about diseases, but also to make diagnostics accurate and cost-effective. We propose an ANN-based model to analyze a patient's electrocardiogram (ECG) data and produce accurate diagnostics regarding possible heart diseases …

Swimming Of Motile Gyrotactic Microorganisms And Nanoparticles In Blood Flow Through Anisotropically Tapered Arteries, M. M. Bhatti, M. Marin, A. Zeeshan, R. Ellahi, Sara I. Abdelsalam

Basic Science Engineering

In the present article, we have presented a theoretical study on the swimming of migratory gyrotactic microorganisms in a non-Newtonian blood-based nanofluid via an anisotropically narrowing artery. Sutterby fluid model is used in order to understand the rheology of the blood as a non-Newtonian fluid model. This fluid pattern has the ability to show Newtonian and non-Newtonian features. The mathematical formulation is performed via continuity, temperature, motile microorganism, momentum, and concentration equation. The series solutions are obtained using the perturbation scheme up to the third-order approximation. The resulting solutions are discussed with the help of graphs for all the leading …

Decoupled Finite Element Methods For General Steady Two-Dimensional Boussinesq Equations, Lioba Boveleth

Masters Theses

"This work presents two kinds of decoupled finite element methods for the steady natural convection problem in two dimensions. Firstly, the standard Galerkin finite element method is derived in detail stating algorithms needed for the realization in MATLAB. A numerical example verifies the error convergence. Secondly, using iteration, the Boussinesq equations are decoupled into the Navier-Stokes equations and a parabolic problem. The resulting problems are solved either in parallel or sequentially. Finally, the same numerical example as before is used to confirm the convergence and analyze the methods in terms of iteration performance. In addition to a higher flexibility and …

The Application Of Machine Learning Models In The Concussion Diagnosis Process, Sujit Subhash

Masters Theses

“Concussions represent a growing health concern and are challenging to diagnose and manage. Roughly four million concussions are diagnosed every year in the United States. Although research into the application of advanced metrics such as neuroimages and blood biomarkers has shown promise, they are yet to be implemented at a clinical level due to cost and reliability concerns. Therefore, concussion diagnosis is still reliant on clinical evaluations of symptoms, balance, and neurocognitive status and function. The lack of a universal threshold on these assessments makes the diagnosis process entirely reliant on a physician’s interpretation of these assessment scores. This study …