Physical Sciences and Mathematics Commons^™

Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho

Scripps Senior Theses

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.

R₀ Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, Jon T. Jacobsen, M. A. Lewis

All HMC Faculty Publications and Research

Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R₀ for advection-diffusion-reaction equations and on related measures. We apply the measures to population persistence in rivers under various flow regimes. This work lays …

Study Of Vortex Ring Dynamics In The Nonlinear Schrödinger Equation Utilizing Gpu-Accelerated High-Order Compact Numerical Integrators, Ronald Meyer Caplan

CGU Theses & Dissertations

We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.

Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient …

Two-Subspace Projection Method For Coherent Overdetermined Systems, Deanna Needell, Rachel Ward

CMC Faculty Publications and Research

We present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image processing. The Kaczmarz method is one of the most popular solvers for overdetermined systems of linear equations due to its speed and simplicity. Here we introduce and analyze an extension of the Kaczmarz method which iteratively projects the estimate onto a solution space given from two randomly selected rows. We show that this projection algorithm provides exponential convergence to the solution in expectation. The convergence rate significantly improves upon …

Discrete Event Simulation Of Elevator Systems, Sasi Bharath Desai

CMC Senior Theses

The intent of this paper is to present the reader with a simple comparison of two systems of vertical transportation. Vertical transportation is a a relatively new field and is the subject of much interest in today's world. As buildings get taller and real estate becomes more expensive, the need to find a quick, efficient system with a small footprint becomes important. By performing a simulation and subjecting the two systems under study to similar traffic conditions, one can determine the effectiveness of one system relative to the other. Additionally, we look at the effects of changing various system attributes …

A Fire Simulation Model For Heterogeneous Environments Using The Level Set Method, Shin-En Lo

CGU Theses & Dissertations

Wildfire hazard and its destructive consequences have become a growing issue around the world especially in the context of global warming. An effective and efficient fire simulation model will make it possible to predict the fire spread and assist firefighters in the process of controlling the damage and containing the fire area. Simulating wildfire spread remains challenging due to the complexity of fire behaviors. The raster-based method and the vector-based method are two major approaches that allow one to perform computerized fire spread simulation. In this thesis, we present a scheme we have developed that utilizes a level set method …