Physical Sciences and Mathematics Commons^™

Temporal Feature Selection With Symbolic Regression, Christopher Winter Fusting

Graduate College Dissertations and Theses

Building and discovering useful features when constructing machine learning models is the central task for the machine learning practitioner. Good features are useful not only in increasing the predictive power of a model but also in illuminating the underlying drivers of a target variable. In this research we propose a novel feature learning technique in which Symbolic regression is endowed with a ``Range Terminal'' that allows it to explore functions of the aggregate of variables over time. We test the Range Terminal on a synthetic data set and a real world data in which we predict seasonal greenness using satellite …

Sine, Cosine, And Tangent Table: 0 To 360 Degrees, Paul Royster

Department of Mathematics: Class Notes and Learning Materials

In helping with my high school student's math homework, I was astonished to find no trig tables in the 800-page textbook. I was further astonished to find no printable version online that extended beyond 90°.

While most smartphones will tell you the sine of an angle, they will not necessarily tell you the angle for which the sine is x. And since multiple angles may have the same sine (e.g. 59° and 121°), it seems useful to see the numerical progression of the functions in addition to their graphical representation.

Here is a printable sine-cosine-tangent table for all integer angle …

Code For "Noise-Enhanced Coding In Phasic Neuron Spike Trains", Cheng Ly, Brent D. Doiron

Statistical Sciences and Operations Research Data

This zip file contains Matlab scripts and ode (XPP) files to calculate the statistics of the models in "Noise-Enhanced Coding in Phasic Neuron Spike Trains". This article is published in PLoS ONE.

Daily Traffic Flow Pattern Recognition By Spectral Clustering, Matthew Aven

CMC Senior Theses

This paper explores the potential applications of existing spectral clustering algorithms to real life problems through experiments on existing road traffic data. The analysis begins with an overview of previous unsupervised machine learning techniques and constructs an effective spectral clustering algorithm that demonstrates the analytical power of the method. The paper focuses on the spectral embedding method’s ability to project non-linearly separable, high dimensional data into a more manageable space that allows for accurate clustering. The key step in this method involves solving a normalized eigenvector problem in order to construct an optimal representation of the original data.

While this …

Numerical Simulation Of Viscoelastic Multiphase Flows Using An Improved Two-Phase Flow Solver, Olabanji Shonibare

Dissertations, Master's Theses and Master's Reports

The production of uniformly-sized droplets has numerous applications in various fields including the biotechnology and chemical industries. For example, in the separation of mixtures based on their relative absorbency, an optimal arrangement of monodispersed droplets in columns is desired for an effective separation. However, very few numerical studies on the formation of viscoelastic droplets via cross-flow shear are available, none of which have considered the case when the flow of the continuous phase is Couette. In this work, a new solver capable of automatic mesh refinement is developed for the OpenFOAM CFD toolbox to solve viscoelastic two-phase flow problems. The …

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

Theses and Dissertations--Mechanical Engineering

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model is …

Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …

End-To-End Molecular Communication Channels In Cell Metabolism: An Information Theoretic Study, Zahmeeth Sayed Sakkaff, Jennie L. Catlett, Mikaela Cashman, Massimiliano Pierobon, Nicole R. Buan, Myra B. Cohen, Christine A. Kelley

Department of Biochemistry: Faculty Publications

The opportunity to control and fine-tune the behavior of biological cells is a fascinating possibility for many diverse disciplines, ranging from medicine and ecology, to chemical industry and space exploration. While synthetic biology is providing novel tools to reprogram cell behavior from their genetic code, many challenges need to be solved before it can become a true engineering discipline, such as reliability, safety assurance, reproducibility and stability. This paper aims to understand the limits in the controllability of the behavior of a natural (non-engineered) biological cell. In particular, the focus is on cell metabolism, and its natural regulation mechanisms, and …

Fitting A Linear Regression Model And Forecasting In R In The Presence Of Heteroskedascity With Particular Reference To Advanced Regression Technique Dataset On Kaggle.Com., Samuel Mbah Nde

All Student Theses and Dissertations

Since ancient times, men have built and sold houses. But just how much is a house worth? The challenge is to be able to use information about a house such as its location, and the area on which it is built to predict its price. Such predicted prices can be of great importance to any participant in the real estate business be it an agent, a buyer, seller or a bank to make intelligent decisions and the profit that come with such decisions. Since every company’s success depends on its ability to accurately predict financial outcomes, its profitability will depend …

An Introduction To The Lebesgue Integral, Ikhlas Adi

All Student Theses and Dissertations

The Riemann integral is the simplest integral to define, and it allows one to integrate every continuous function. It is really important to have a definition of the integral that allows a wider class of functions to be integrated. However, there are many other types of integrals, the most important of which is the Lebesgue integral. The Lebesgue integral allows one to integrate unbounded or discontinuous functions whose Riemann integral does not exist, and it has mathematical properties that the Riemann integral does not. The definition of the Lebesgue integral requires the use of measure theory since picking out a …

Accounting For Locational, Temporal, And Physical Similarity Of Residential Sales In Mass Appraisal Modeling: The Development And Application Of Geographically, Temporally, And Characteristically Weighted Regression, Paul E. Bidanset, Michael Mccord, John R. Lombard, Peadar Davis, William J. Mccluskey

School of Public Service Faculty Publications

Geographically weighted regression (GWR) has been recognized in the assessment community as a viable automated valuation model (AVM) to help overcome, at least in part, modeling hurdles associated with location, such as spatial heterogeneity and spatial autocorrelation of error terms. Although previous researchers have adjusted the GWR weights matrix to also weight by time of sale or by structural similarity of properties in AVMs, the research described in this paper is the first that has done so by all three dimensions (i.e., location, structural similarity, and time of sale) simultaneously. Using 24 years of single-family residential sales in Fairfax, Virginia, …

A Numerical Study Of Construction Of Honey Bee Comb, Pamela Guerrero, Pamela C. Guerrero

Murray State Theses and Dissertations

We use finite difference methods in the treatment of an existing system of partial differential equations that captures the dynamics of parallel honeycomb construction in a bee hive. We conduct an uncertainty analysis by calculating the partial rank correlation coefficient for the parameters to find which are most important to the outcomes of the model. We then use an eFAST method to determine both the individual and total sensitivity index for the parameters. Afterwards we examine our numerical model under varying initial conditions and parameter values, and compare ratios found from local data with the golden mean by fitting images …

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

Global Well-Posedness For The Derivative Nonlinear Schrödinger Equation Through Inverse Scattering, Jiaqi Liu

Theses and Dissertations--Mathematics

We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.

Dynamics Of Gene Networks In Cancer Research, Paul Scott

Electronic Theses and Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

A Markov Decision Process Approach To Adaptive Contact Strategies, Artur Grygorian

Electronic Theses and Dissertations

In the field of survey methodology, optimizing contact strategies helps organizations increase response rates using their allocated budget. Markov Decision Processes (MDP) are widely used to model decision-making strategies in situations where the outcomes have a random component. In this research, we use MDPs and adaptive sampling techniques to construct a strategy that, based on target audience characteristics, suggests the best contact policy. The data we use comes from the First Destination Survey conducted by the Office of Career Services at Georgia Southern University. The constructed model is quite flexible and can be used by other organizations to optimize their …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …

Modeling And Simulation Of The Peristaltic Flow Of Newtonian And Non-Newtonian Fluids With Application To The Human Body, Samer Alokaily

Dissertations, Master's Theses and Master's Reports

Computational models are developed to investigate peristaltic motion in the human gastro-intestinal tract. The peristaltic motion is simulated by means of traveling waves which deform the boundary of the tubes. An axisymmetric tube of uniform diameter is used to model the small intestines, and an axisymmetric conical geometry is developed to model the lower part of the human stomach. The conical geometry represents a simplification of the more complicated three-dimensional models of the human stomach that have been used in other studies. Also, they seeks to reduce computational costs and circumvent difficulties of mesh generation. The computations are performed within …

Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson

Murray State Theses and Dissertations

We translate the RISK board into a graph which undergoes updates as the game advances. The dissection of the game into a network model in discrete time is a novel approach to examining RISK. A review of the existing statistical findings of skirmishes in RISK is provided. The graphical changes are accompanied by an examination of the statistical properties of RISK. The game is modeled as a discrete time dynamic network graph, with the various features of the game modeled as properties of the network at a given time. As the network is computationally intensive to implement, results are produced …

Weighted Networks: Applications From Power Grid Construction To Crowd Control, Thomas Charles Mcandrew

Graduate College Dissertations and Theses

Since their discovery in the 1950's by Erdos and Renyi, network theory (the study of objects and their associations) has blossomed into a full-fledged branch of mathematics.

Due to the network's flexibility, diverse scientific problems can be reformulated as networks and studied using a common set of tools.

I define a network G = (V,E) composed of two parts: (i) the set of objects V, called nodes, and (ii) set of relationships (associations) E, called links, that connect objects in V.

We can extend the classic network of nodes and links by describing the intensity of these associations with weights. …

Adrc Based Control Of Nonlinear Dynamical System With Multiple Sources Of Disturbance And Multiple Inputs, Chan Mi Park

Electronic Theses and Dissertations

In this thesis, we study the stability of Active Disturbance Rejection Control (ADRC) applied to controlling the Lorenz system. The Lorenz system is a nonlinear dynamical system that we attempt to control. In fact, the system is used to model convection flow such as that found in thermosyphons, electric circuits, and lasers. We are stabilizing the Lorenz system along with a few disturbances. Thus, to stabilize this chaotic system, a robust controller is required. The ADRC system is known as as effective method to stabilize a dynamical system. With the help of the Extended State Observer (ESO), the system can …

Applications Of Flow Network Models In Finance, Angel J. Woods

Electronic Theses and Dissertations

In this thesis we explore the applications of flow networks in practical problems in finance. After introducing basic definitions and background information, we first survey some known applications of flow networks in theoretical mathematics. We also briefly comment on their potential applications in the setting of financial flow networks. We then construct networks from practical financial flows and present the construction, reasoning, and known applications. Lastly, we show a design of financial flow networks that takes time into consideration and discuss its applications.

An Application Of Time Series Methods To Investigate Eu Dairy Commodity Price Dynamics, Dennis Bergmann

Theses

Fundamental changes to the common agricultural policy (CAP) have led to greater market orientation which in turn has resulted in significantly changed price dynamics of EU dairy prices. These changed dynamics include sharply increased price variability of EU farm gate milk prices as well EU dairy commodity prices such as butter and Skimmed Milk Powder (SMP). In addition it was expected that EU dairy prices will align to Word dairy prices. This alignment of prices would also see an alignment of volatility levels which were significantly higher for World dairy prices than EU dairy prices. The aim of this thesis …

Dynamics And Clustering In Locust Hopper Bands, Jialun Zhang

HMC Senior Theses

In recent years, technological advances in animal tracking have renewed interests in collective animal behavior, and in particular, locust swarms. These swarms pose a major threat to agriculture in northern Africa, the Middle East, and other regions. In their early life stages, locusts move in hopper bands, which are huge aggregations traveling on the ground. Our main goal is to understand the underlying mechanisms for the emergence and organization of these bands. We construct an agent-based model that tracks individual locusts and a continuum model that tracks the evolution of locust density. Both these models are motivated by experimental observations …

Kinetic Monte Carlo Methods For Computing First Capture Time Distributions In Models Of Diffusive Absorption, Daniel Schmidt

HMC Senior Theses

In this paper, we consider the capture dynamics of a particle undergoing a random walk above a sheet of absorbing traps. In particular, we seek to characterize the distribution in time from when the particle is released to when it is absorbed. This problem is motivated by the study of lymphocytes in the human blood stream; for a particle near the surface of a lymphocyte, how long will it take for the particle to be captured? We model this problem as a diffusive process with a mixture of reflecting and absorbing boundary conditions. The model is analyzed from two approaches. …

Pattern Recognition In Stock Data, Kathryn Dover

HMC Senior Theses

Finding patterns in high dimensional data can be difficult because it cannot be easily visualized. There are many different machine learning methods to fit data in order to predict and classify future data but there is typically a large expense on having the machine learn the fit for a certain part of a dataset. We propose a geometric way of defining different patterns in data that is invariant under size and rotation. Using a Gaussian Process, we find that pattern within stock datasets and make predictions from it.

Incorporating The Centers For Disease Control And Prevention Into Vaccine Pricing Models, Dina Sinclair

HMC Senior Theses

The American vaccine pricing market has many actors, making it a complex system to model. Because of this, previous papers have chosen to model only vaccine manufacturers while leaving out the government. However, the government is also an important actor in the market, since it buys over half of vaccines produced. In this work, we aim to introduce the government into vaccine pricing models to better recommend pricing strategies to the Centers for Disease Control and Prevention.

Interaction Graphs Derived From Activation Functions And Their Application To Gene Regulation, Simon Joyce

Graduate Dissertations and Theses

Interaction graphs are graphic representations of complex networks of mutually interacting components. Their main application is in the field of gene regulatory networks, where they are used to visualize how the expression levels of genes activate or inhibit the expression levels of other genes.

First we develop a natural transformation of activation functions and their derived interaction graphs, called conjugation, that is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.

We then discuss the question of what restrictions, if …

Multi-Scale Cardiovascular Flow Analysis By An Integrated Meshless-Lumped Parameter Model, Leonardo A. Bueno, Eduardo A. Divo, Alain J. Kassab

Publications

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage …

Direct Sampling Methods For Inverse Scattering Problems, Ala Mahmood Nahar Al Zaalig

Dissertations, Master's Theses and Master's Reports

Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on R^d, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer.

In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, …