Other Applied Mathematics Commons^™

A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine

Spora: A Journal of Biomathematics

The large, long-lived, epiphytic bromeliad Tillandsia utriculata is currently listed as state-endangered in Florida due to significant population reduction from predation by an invasive weevil, Metamasius callizona. We have developed a novel demographic model of a population of T. utriculata in Myakka River State Park (MRSP) in Sarasota, Florida using a stage-structured matrix model. Analysis of the model revealed conditions for population viability over a variety of parameter scenarios. Model analysis showed that without weevil predation the minimum germination rate required for population viability is low (4–16%), and that given a viable population at structural equilibrium we would expect …

High-Order Adaptive Synchrosqueezing Transform, Jawaher Alzahrani

Dissertations

The prevalence of the separation of multicomponent non-stationary signals across many elds of research makes this concept an important subject of study. The synchrosqueezing transform (SST) is a particular type of reassignment method. It aims to separate and recover the components of a multicomponent non-stationary signal. The short time Fourier transform (STFT)-based SST (FSST) and the continuous wavelet transform (CWT)based SST (WSST) have been used in engineering and medical data analysis applications. The current study introduces the dierent versions of FSST and WSST to estimate instantaneous frequency (IF) and to recover components. It has a good concentration and reconstruction for …

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri

Spora: A Journal of Biomathematics

Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.

Mathematical Modeling Of Diabetic Foot Ulcers Using Optimal Design And Mixed-Modeling Techniques, Michael Belcher

Mahurin Honors College Capstone Experience/Thesis Projects

A mathematical model for the healing response of diabetic foot ulcers was developed using averaged data (Krishna et al., 2015). The model contains four major factors in the healing of wounds using four separate differential equations with 12 parameters. The four differential equations describe the interactions between matrix metalloproteinases (MMP-1), tissue inhibitors of matrix metalloproteinases (TIMP-1), the extracellular matrix (ECM) of the skin, and the fibroblasts, which produce these proteins. Recently, our research group obtained the individual patient data that comprised the averaged data. The research group has since taken several approaches to analyze the model with the individual …

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data …

Agent-Based Modeling Of Locust Foraging And Social Behavior, Hannah Larson

HMC Senior Theses

Locust swarms contain millions of individuals and are a threat to agriculture on four continents. At low densities, locusts are solitary foragers; however, when crowded, they undergo an epigenetic phase change to a gregarious state in which they are attracted to other locusts. It is believed that this is an evolutionary adaptation that optimizes the seeking of resources. We have developed an agent-based model based on the solitary-gregarious transition and foraging behaviors due to hunger levels. A novel feature of our model is that it treats food resources as a dynamic variable in the environment. We discuss how social interaction …

Association Rules Patterns Discovery From Mixed Data, Welendawa Acharige Charith A. Elson

College of Graduate Studies: Theses & Dissertations

Finding Association Rules has been a popular unsupervised learning technique for dis covering interesting patterns in commercial data for well over two decades. The method seeks groups of data attributes and their values where their probability density of these attributesattherespectivevaluesismaximized. Therearecurrentlywell-establishedmeth ods for tackling this problem for data with categorical (discrete) attributes. However, for the cases of data with continuous variables, the techniques are largely focusing on cate gorizing continuous variables into intervals of interest and then relying on the categorical data methods to address the problem. We address the problem of finding association rules patterns in mixed data by …

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.

Modeling Community Resource Management: An Agent-Based Approach, Maya M. Lapp

Senior Independent Study Theses

As the human population continues increasing rapidly and climate change accelerates, resource depletion is becoming an international problem. Community-based natural resource management (CBNRM) has been suggested as a method to conserve resources while simultaneously empowering traditionally marginalized communities. Because classical equation-based modeling methods fail to capture the complexity of CBNRM, Agent-Based Modeling (ABM) has emerged as a primary method of modeling these systems. In this investigation, we conduct a sensitivity analysis and thorough evaluation of an existing ABM of community forest management. We then modify the original model by providing a new enforcement mechanism that improves the validity of both …

K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin

CMC Senior Theses

The 2015 article Creating Diversified Portfolios Using Cluster Analysis proposes an algorithm that uses the Sharpe ratio and results from K-means clustering conducted on companies' historical financial ratios to generate stock market portfolios. This project seeks to evaluate the performance of the portfolio-building algorithm during the beginning period of the COVID-19 recession. S&P 500 companies' historical stock price movement and their historical return on assets and asset turnover ratios are used as dissimilarity metrics for K-means clustering. After clustering, stock with the highest Sharpe ratio from each cluster is picked to become a part of the portfolio. The economic and …

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Genetic Algorithms Used For Search And Rescue Of Vulnerable People In An Urban Setting, Shuhad Aljandeel

Graduate Theses, Dissertations, and Problem Reports (ETD)

The main goal of this research is to design and develop a genetic algorithm (GA) for path planning of an Unmanned Aerial Vehicle (UAV) outfitted with a camera to efficiently search for a lost person in an area of interest. The research focuses on scenarios where the lost person is from a vulnerable population, such as someone suffering from Alzheimer or a small child who has wondered off. To solve this problem, a GA for path planning was designed and implemented in Matlab. The area of interest is considered to be a circle that encompasses the distance the person could …

The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane

Dissertations, Master's Theses and Master's Reports

Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L²(M) → X, U : L²(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that

T = Um_σV ^†,

with m_σ : L²(M ) → L²(M ) defined by m_σ(f ) = σf for all f …

Sub-Sampled Matrix Approximations, Joy Azzam

Dissertations, Master's Theses and Master's Reports

Matrix approximations are widely used to accelerate many numerical algorithms. Current methods sample row (or column) spaces to reduce their computational footprint and approximate a matrix A with an appropriate embedding of the data sampled. This work introduces a novel family of randomized iterative algorithms which use significantly less data per iteration than current methods by sampling input and output spaces simultaneously. The data footprint of the algorithms can be tuned (independent of the underlying matrix dimension) to available hardware. Proof is given for the convergence of the algorithms, which are referred to as sub-sampled, in terms of numerically tested …

Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam

College of Graduate Studies: Theses & Dissertations

The automatic character recognition task has been of practical interest for a long time. Nowadays, there are well-established technologies and software to perform character recognition accurately from scanned documents. Although handwritten character recognition from the manuscript image is challenging, the advancement of modern machine learning techniques makes it astonishingly manageable. The problem of accurately recognizing handwritten character remains of high practical interest since a large number of manuscripts are currently not digitized, and hence inaccessible to the public. We create our repository of the datasets by cropping each letter image manually from the manuscript images. The availability of datasets is …

Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins

College of Graduate Studies: Theses & Dissertations

In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …

Modeling The Evolution Of Barrier Islands, Greg Robson

Theses and Dissertations

Barrier islands form off the shore of many coastal areas and serve as the first line of defense, protecting littoral communities against storms. To study the effects that climate change has on barrier islands, we use a cellular model of wind erosion, surface dynamics, beach dynamics, marsh dynamics, and vegetation development. We will show the inhibition of movement when vegetation is present.

Model Selection And Experimental Design Of Biological Networks With Algebraic Geometry, Anyu Zhang

Mathematics Theses and Dissertations

Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.

Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to …

A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen

SMU Data Science Review

Abstract. In this paper, we present a model and methodology for accurately predicting the following quarter’s sales volume of individual products given the previous five years of sales data. Forecasting product demand for a single supplier is complicated by seasonal demand variation, business cycle impacts, and customer churn. We developed a novel prediction using machine learning methodology, based upon a Dense neural network (DNN) model that implicitly considers cyclical demand variation and explicitly considers customer churn while minimizing the least absolute error between predicted demand and actual sales. Using parts sales data for a supplier to the oil and gas …

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also …