Browsing by Author "Bortz, David Matthew"
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- A parameter sensitivity methodology in the context of HIV delay equation models(North Carolina State University. Center for Research in Scientific Computation, 2002) Banks, Harvey Thomas; Bortz, David Matthew
- Incorporation of variability into the modeling of viral delays in HIV infection dynamics(North Carolina State University. Center for Research in Scientific Computation, 2001) Banks, Harvey Thomas; Bortz, David Matthew; Holte, S. E.
- Inverse problems for a class of measure dependent dynamical systems(North Carolina State University. Center for Research in Scientific Computation, 2004) Banks, Harvey Thomas; Bortz, David Matthew
- Modeling and imaging techniques with potential for application in bioterrorism(North Carolina State University. Center for Research in Scientific Computation, 2003) Banks, Harvey Thomas; Bortz, David Matthew; Pinter, Gabriella A.; Potter, Laura K.
- Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations(2002-09-05) Bortz, David Matthew; H. Thomas Banks, Committee Chair; Marie Davidian, Committee Member; Kazufumi Ito, Committee Member; Hien T. Tran, Committee MemberThis dissertation focuses on developing mathematical and computational tools for use as an aid in understanding the cellular population dynamics of an in vitro HIV experiment. We carefully develop a functional differential equation model which incorporates mathematical mechanisms that account for both the biological delays and the parameter uncertainty inherent in the system. We present the theoretical foundations for our methodology which then allow us to develop a numerical approximation scheme and perform parameter identifications (even on the delay distributions) and sensitivity analyses. We summarize the results of a numerical investigation of the delays followed by the results from the nonlinear least squares inverse problem. We then present a statistical significance argument for the importance of the delay mechanism as well as the results of a sample sensitivity analysis of the system with respect to select parameters.
- Optimizing control of open bay acoustics(North Carolina State University. Center for Research in Scientific Computation, 2000) Cain, A. B.; Rubio, A. D.; Bortz, David Matthew; Banks, Harvey Thomas; Smith, Ralph C.
- Reduced order modeling in control of open cavity acoustics(North Carolina State University. Center for Research in Scientific Computation, 2000) Bortz, David Matthew; Rubio, A. D.; Banks, Harvey Thomas; Cain, A. B.; Smith, Ralph C.
- The simplex gradient and noisy optimization problems(North Carolina State University. Center for Research in Scientific Computation, 1997) Bortz, David Matthew; Kelley, Carl Tim
