Fast Algorithms On Random Matrices And Structured Matrices, 2017 The City University of New York

#### Fast Algorithms On Random Matrices And Structured Matrices, Liang Zhao

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

Randomization of matrix computations has become a hot research area in the big data era. Sampling with randomly generated matrices has enabled fast algorithms to perform well for some most fundamental problems of numerical algebra with probability close to 1. The dissertation develops a set of algorithms with random and structured matrices for the following applications: 1) We prove that using random sparse and structured sampling enables rank-r approximation of the average input matrix having numerical rank r. 2) We prove that Gaussian elimination with no pivoting (GENP) is numerically safe for the average nonsingular and well-conditioned matrix preprocessed with ...

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, 2017 Georgia Institute of Technology

#### High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Large Reaction-Diffusion Model For Cell Polarization In Yeast, 2017 The Ohio State University

#### A Large Reaction-Diffusion Model For Cell Polarization In Yeast, Marissa Renardy

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

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.

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 ...

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.

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 ...

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.

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.

C.V., 2017 Wroclaw University of Technology

Abstract Template Resrb 2017, 2017 Wroclaw University of Technology

#### Abstract Template Resrb 2017, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Order Form Resrb 2017, 2017 Wroclaw University of Technology

#### Order Form Resrb 2017, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

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 ...

Mri-Based Susceptibility Mapping For In-Vivo Iron And Blood Oximetry Measurements, 2017 University of Colorado, Boulder

#### Mri-Based Susceptibility Mapping For In-Vivo Iron And Blood Oximetry Measurements, Hannah Erdevig

*Undergraduate Honors Theses*

MRI is increasingly used in mapping tissue susceptibility to identify cerebral microbleeds associated with traumatic brain injury and pathological iron deposits associated with neurodegenerative diseases such as Parkinson's and Alzheimer's disease [1,2]. Accurate measurement is important for determining oxygen and iron content in blood vessels and tissue in the brain, which are in turn used for noninvasive clinical diagnosis and treatment assessments. Magnetic field distortions with a resolution of a few parts per billion can be measured using MRI phase maps. The field distortion map can then be inverted to obtain a quantitative susceptibility map. The primary ...

Daily Traffic Flow Pattern Recognition By Spectral Clustering, 2017 Claremont McKenna College

#### 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 methodâ€™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 ...

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 ...

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 ...

Long And Short-Range Air Navigation On Spherical Earth, 2017 AAR Aerospace Consulting, LLC

#### Long And Short-Range Air Navigation On Spherical Earth, Nihad E. Daidzic

*International Journal of Aviation, Aeronautics, and Aerospace*

Global range air navigation implies non-stop flight between any two airports on Earth. Such effort would require airplanes with the operational air range of at least 12,500 NM which is about 40-60% longer than anything existing in commercial air transport today. Air transportation economy requires flying shortest distance, which in the case of spherical Earth are Orthodrome arcs. Rhumb-line navigation has little practical use in long-range flights, but has been presented for historical reasons and for comparison. Database of about 50 major international airports from every corner of the world has been designed and used in testing and route ...

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 ...

Modeling And Simulation Of The Peristaltic Flow Of Newtonian And Non-Newtonian Fluids With Application To The Human Body, 2017 Michigan Technological University

#### 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 ...