Other Applied Mathematics Commons^™

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 …

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Department of Mathematics: Dissertations, Theses, and Student Research

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual …

Multi-Point Flux Approximations Via The O-Method, Christen Leggett

Master's Theses

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients. …

Local Non-Similar Solution Of Powell-Eyring Fluid Flow Over A Vertical Flat Plate, Hemangini Shukla, Hema C. Surati, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

Our objective is to obtain the non-similarity solution of non-Newtonian fluid for Powell-Eyring model by a local non-similarity method. Here, free stream velocity is considered in power-law form (𝑈=𝑥^m). The governing equations are transformed using non-similar transformations and derived equations are treated as ordinary differential equations. Non-similar solutions are obtained for different values of power-law index 𝑚 and stream-wise location 𝜉. Influence of various parameters on velocity and temperature field are presented graphically using MATLAB bvp4c solver.

Inverse Spectral Problems For Spectral Data And Two Spectra Of N By N Tridiagonal Almost-Symmetric Matrices, Bayram Bala, Manaf D. Manafov, Abdullah Kablan

Applications and Applied Mathematics: An International Journal (AAM)

One way to study the spectral properties of Sturm-Liouville operators is difference equations. The coefficients of the second order difference equation which is equivalent Sturm-Liouville equation can be written as a tridiagonal matrix. One investigation area for tridiagonal matrix is finding eigenvalues, eigenvectors and normalized numbers. To determine these datas, we use the solutions of the second order difference equation and this investigation is called direct spectral problem. Furthermore, reconstruction of matrix according to some arguments is called inverse spectral problem. There are many methods to solve inverse spectral problems according to selecting the datas which are generalized spectral function, …

Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising

Electronic Theses and Dissertations

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this …

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

Dissertations

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. …

Planck's And Callendar's Blackbody Radiation Formulas And Their Fitness To Experimental Data, Max Tran

Publications and Research

In this paper, we compare the blackbody radiation density formula obtained with classical physics by Hugh L Callendar and the formula obtained by Max Planck using quantization of energy. We use R and Maxima to analyze their fitness on coordinating experimental data and indicate some limitations with experiments in this area.

Applying Methods Of The Theory Of Heterogeneous Populations To The Problem Of Pathogen Co-Existence, Eric Sarfo Amponsah

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Ecological Model Of West Nile Virus For Classroom Use, Stuart Thiel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Modeling Approach For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Joey Gaudy, Craig Garzella

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Exploring Modeling By Programming: Insights From Numerical Experimentation, Sean Laverty, Brittany E. Bannish

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Reconstruction Using Computational Algebra And Gene Knockouts, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Distribution In Carbon Uptake Across A Global Measurement Network Of Terrestrial Ecosystems, John Zobitz, Madeline Oswood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Simulating Bacterial Growth, Competition, And Resistance With Agent-Based Models And Laboratory Experiments, Anne E. Yust, Davida S. Smyth

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Engaging Undergraduates In Research In Mathematical Biology With Limited Resources, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Pollen Traits To Build A Mathematical Model Of Pollen Competition - A Biologist's Perspective, Rob Swanson, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stayin' Alive In Mathematical Biology: Opportunities, Strategies, And Experiences In Undergraduate Research In Mathematics, Timothy Comar, Hannah Callender Highlander, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analysis Of An Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Study Of Pharmacodynamic Model On Hn, Kamala Dadashova, Ferhan Atici

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model Of Disease Vector Control With Imperfect Treatment, Bismark Oduro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

LSU New Orleans Theses and Dissertations

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

Exploring Delay Dispersal In Us Airport Network, Brandon Sripimonwan, Arun Sathanur

STAR Program Research Presentations

The modeling of delay diffusion in airport networks can potentially help develop strategies to prevent the spread of such delays and disruptions. With this goal, we used the publicly-available historical United States Federal Aviation Administration (FAA) flight data to model the spread of delays in the US airport network. For the major (ASPM-77) airports for January 2017, using a threshold on the volume of flights, we sparsify the network in order to better recognize patterns and cluster structure of the network. We developed a diffusion simulator and greedy optimizer to find the top influential airport nodes that propagate the most …

Smoothness Of Defining Functions And The Diederich-Fornæss Index, Felita Nadia Humes

Graduate Theses and Dissertations

Let Ω ⊂ Cn be a smooth, bounded, pseudoconvex domain, and let M ⊂ ∂Ω be a complex submanifold with rectifiable boundary. In 2017, Harrington studied the equation dM A = α ̃ on M, where α ̃ is D’Angelo’s 1-form and A is real. In this thesis, we will study a non-pseudoconvex example in which M has a non-rectifiable boundary. In spite of the lack of topological obstructions on the boundary, there are no continuous solutions to dM A = α ̃.

Characterizing Majority Rule On Various Discrete Models Of Consensus., Trevor Leach

Electronic Theses and Dissertations

In any social structure, there is often a need to reach decisions, not only within a group but between groups as well, sometimes even urgently so. Each of the individuals constituting these groups has their own preference for the decision to be made. We will discuss the problem of aggregating individual preferences into a collective preference and under what conditions we are required to select a collective majority. In this dissertation we will look at three models of consensus and show the conditions vary based on the model.