Evolution Of Influenza H3n2: A Random Walk In High Dimensions, 2017 Emory University

#### Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, 2017 Linfield College

#### Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, Grant Cates

*Senior Theses*

Understanding how water molecules behave in isolation is vital to understand many fundamental processes in nature. To that end, scientists have begun studying crystals in which single water molecules become trapped in regularly occurring cavities in the crystal structure. As part of that investigation, numerical models used to investigate the dynamics of isolated water molecules are sought to help bolster our fundamental understanding of how these systems behave. To that end, the efficacy of three computational methods—the Euler Method, the Euler-Aspel Method and the Beeman Method—is compared using a newly defined parameter, called the *predictive stability coefficient ρ ...*

Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, 2017 kgrego12

#### Accuracy And Stability Of Integration Methods For Neutrino Transport In Core Collapse Supernovae, Kyle A. Gregory

*University of Tennessee Honors Thesis Projects*

No abstract provided.

Hawking Radiation And Classical Tunneling: A Numerical Study, 2017 College of William and Mary

#### Hawking Radiation And Classical Tunneling: A Numerical Study, Dmitriy Zhigunov

*Undergraduate Honors Theses*

Unruh [1] demonstrated that black holes have an analogy in acoustics. Under this analogy the acoustic event horizon is defined by the set of points in which the local background flow exceeds the local sound speed. In past work [2], we demonstrated that under a white noise source, the acoustic event horizon will radiate at a thermal spectrum via a classical tunneling process. In this work, I summarize the theory presented in [2] and nondimensionalize it in order to reduce the dynamical equations to one parameter, the coupling coefficient η2. Since η2 is the sole parameter of the system, we ...

Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, 2017 University of Tennessee, Knoxville

#### Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, Joel Anthony Mazer

*Doctoral Dissertations*

In relativistic heavy ion collisions at the Large Hadron Collider (LHC), a hot, dense and strongly interacting medium known as the Quark Gluon Plasma (QGP) is produced. Quarks and gluons from incoming nuclei collide to produce partons at high momenta early in the collisions. By fragmenting into collimated sprays of hadrons, these partons form 'jets'. Within the framework of perturbative Quantum Chromodynamics (pQCD), jet production is well understood in pp collisions. We can use jets measured in pp interactions as a baseline reference for comparing to heavy ion collision systems to detect and study jet quenching. The jet quenching mechanism ...

Plateau Potential Fluctuations And Intrinsic Membrane Noise, 2017 College of William and Mary

#### Plateau Potential Fluctuations And Intrinsic Membrane Noise, Daniel Scott Borrus

*Undergraduate Honors Theses*

This thesis focuses on subthreshold membrane potential fluctuations in the plateau potentials of bistable neurons. Research involved with plateau potentials typically finds one of the resting membrane potentials to be more susceptible to voltage fluctuations. This difference in the amplitude of the membrane potential fluctuations is most often attributed to the voltage-dependent membrane conductance. Occasionally, however, the typically quieter resting membrane potential exhibits larger voltage fluctuations than the expected one. It has been proposed that this increased membrane potential noise is the result of the stochastic gating of the voltage-gated ion channels. In this thesis, we use a simple bistable ...

Surface Energy In Bond-Counting Models On Bravais And Non-Bravais Lattices, 2017 University of Tennessee, Knoxville

#### Surface Energy In Bond-Counting Models On Bravais And Non-Bravais Lattices, Tim Ryan Krumwiede

*Doctoral Dissertations*

Continuum models in computational material science require the choice of a surface energy function, based on properties of the material of interest. This work shows how to use atomistic bond-counting models and crystal geometry to inform this choice. We will examine some of the difficulties that arise in the comparison between these models due to differing types of truncation. New crystal geometry methods are required when considering materials with non-Bravais lattice structure, resulting in a multi-valued surface energy. These methods will then be presented in the context of the two-dimensional material graphene in a way that correctly predicts its equilibrium ...

Efficient Denoising And Sharpening Of Color Images Through Numerical Solution Of Nonlinear Diffusion Equations, 2017 The University of Southern Mississippi

#### Efficient Denoising And Sharpening Of Color Images Through Numerical Solution Of Nonlinear Diffusion Equations, Linh T. Duong

*Honors Theses*

The purpose of this project is to enhance color images through denoising and sharpening, two important branches of image processing, by mathematically modeling the images. Modifications are made to two existing nonlinear diffusion image processing models to adapt them to color images. This is done by treating the red, green, and blue (RGB) channels of color images independently, contrary to the conventional idea that the channels should not be treated independently. A new numerical method is needed to solve our models for high resolution images since current methods are impractical. To produce an efficient method, the solution is represented as ...

Electrodynamical Modeling For Light Transport Simulation, 2017 East Tennessee State University

#### Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders

*Undergraduate Honors Theses*

Modernity in the computer graphics community is characterized by a burgeoning interest in physically based rendering techniques. That is to say that mathematical reasoning from first principles is widely preferred to ad hoc, approximate reasoning in blind pursuit of photorealism. Thereby, the purpose of our research is to investigate the efficacy of explicit electrodynamical modeling by means of the generalized Jones vector given by Azzam [1] and the generalized Jones matrix given by Ortega-Quijano & Arce-Diego [2] in the context of stochastic light transport simulation for computer graphics. To augment the status quo path tracing framework with such a modeling technique ...

Application Of Symplectic Integration On A Dynamical System, 2017 East Tennessee State University

#### Application Of Symplectic Integration On A Dynamical System, William Frazier

*Electronic Theses and Dissertations*

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic ...

Models Of Nation-Building Via Systems Of Differential Equations, 2017 Cedarville University

#### Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker

*The Research and Scholarship Symposium*

Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.

Testing The Consistency Of Nested Logit Models With Utility Maximization, 2017 Iowa State University

#### Testing The Consistency Of Nested Logit Models With Utility Maximization, Joseph A. Herriges, Catherine L. Kling

*Catherine Kling*

The Nested Multinomial Logit (NMNL) model is used extensively in modeling consumer choices among discrete alternatives when the number of alternatives is large. Unfortunately, applied researchers often find that estimated NMNL models fail to meet the Daly-ZacharyMcFadden (DZM) sufficient conditions for consistency with stochastic utility maximization. Borsch-Supan (1990) provides a relaxed set of conditions to test for consistency. While these conditions are increasingly cited, they are seldom tested. This paper corrects and extends BorschSupan's Theorem 2, providing simple necessary conditions on first, second, and third derivatives of choice probabilities and a graph oft he bounds they place on dissimilarity ...

Steady State Probabilities In Relation To Eigenvalues, 2017 Liberty University

#### Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

*The Kabod*

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.

A Numerical Study Of Construction Of Honey Bee Comb, 2017 Murray State University

#### 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 ...

Information Metrics For Predictive Modeling And Machine Learning, 2017 University of Massachusetts Amherst

#### Information Metrics For Predictive Modeling And Machine Learning, Kostantinos Gourgoulias

*Doctoral Dissertations*

The ever-increasing complexity of the models used in predictive modeling and data science and their use for prediction and inference has made the development of tools for uncertainty quantification and model selection especially important. In this work, we seek to understand the various trade-offs associated with the simulation of stochastic systems. Some trade-offs are computational, e.g., execution time of an algorithm versus accuracy of simulation. Others are analytical: whether or not we are able to find tractable substitutes for quantities of interest, e.g., distributions, ergodic averages, etc.

The first two chapters of this thesis deal with the study ...

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., 2017 Governors State University

#### 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*

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 ...

Analysis Of Variability In Crop Yield For Industrial Hemp On Two Farms In Virginia, 2017 James Madison University

#### Analysis Of Variability In Crop Yield For Industrial Hemp On Two Farms In Virginia, Nicholas S. Gentile, Evan M. Hylton, Justin Ngo

*Senior Honors Projects, 2010-current*

Although the cultivation of Cannabis sativa was substantially halted in the United States with the Marihuana Tax Act of 1937, Canada reintroduced licenses for industrial hemp research and commercial production by the mid 1990’s. This led to a resurgence of interest in exploring the potential for this industry across North America, and by 2016, permits were granted to grow industrial hemp in Virginia. The ultimate goal of this project is to explore the agricultural feasibility of growing industrial hemp on small and medium sized farms in Virginia, and integrating small-farm production with a potential supply chain for three key ...

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, 2017 University of Kentucky

#### 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 ...

Paving The Randomized Gauss-Seidel, 2017 Scripps College

#### Paving The Randomized Gauss-Seidel, Wei Wu

*Scripps Senior Theses*

The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix A ...

Dynamics Of Gene Networks In Cancer Research, 2017 Georgia Southern University

#### Dynamics Of Gene Networks In Cancer Research, Paul Scott

*Electronic Theses & 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 ...