Physical Sciences and Mathematics Commons^™

Analyzing Multistationarity In A Model Of A Dual Phosphorylation Network, Killian Kearney Anderson

Graduate Research Theses & Dissertations

Otero-Muras, Banga, and Alonso in [18] state biological reaction systems exhibit multistationarity, a system with at least two positive steady states. According to Otero-Muras,Banga, and Alonso in [18], initial conditions within the system, however, dictate the number of stable states in that system. Furthermore, multistationarity is an important componenet present in biological reaction systems that manage cellular responses [18]. Signal pathways regulating cell maturation, cell replication, and cell death rely on such systems [18]. Given the importance of multistationarity in biological reaction systems, it is necessary to construct a mathematical model, one in which multistationarity will be configured. More importantly, …

Computational Analysis Of The Sir Mathematical Model For The Dengue Fever, Joseph Phillip Diaz

Theses and Dissertations

Dengue fever is a disease affecting people in more than 100 countries. Here we consider a host and vector model for the transmission of dengue fever. This SIR model consists of three compartments of susceptible, infective and removed for host (human) and two compartments of susceptible and infective for vector (dengue mosquitos). These five compartments yield five coupled nonlinear ordinary differential equations (ODEs). After non-dimensionalization, we have a system of three nonlinear ODEs. Reproductive number and two equilibrium points are calculated for various cases. Simulation is carried out for susceptible, infective and removed and the results are presented in graphical …

Explicit Equations Of Non-Hyperelliptic Genus 3 Curves With Real Multiplication By Q(ζ7+ζ7-1), Dun Liang

LSU Doctoral Dissertations

This thesis is devoted to proving the following:

For all (u₁, u₂, u₃, u₄) in a Zariski dense open subset of C⁴ there is a genus 3 curve X(u₁, u₂, u₃, u₄) with the following properties:

1. X(u₁, u₂, u₃, u₄) is not hyperelliptic.
2. End(Jac((X(u₁, u₂, u₃, u₄))) ⊗Q contains the real cubic field Q(ζ₇+ζ₇^-1) where ζ₇ is …

Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell

Mark R Segal

We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The proposed solution represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed in Meng and Rubin (1991) that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize a result from Green (1990) that provides an expression for the Jacobian of the mapping induced by the EM algorithm applied to a penalized …