Fall 1999 Mathematical Biology Seminar

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• 22 September at Rice
  John Clark, Professor of Electrical and Computer Engineering, Rice University
  Mathematics of Neuron Modeling
  
  ABSTRACT: This seminar will take a tutorial approach to the discussion of membrane biophysics and electrolyte balance within the individual neuron. Specifically, a Hodgkin-Huxley model will be used to describe membrane dynamics, whereas the cell fluid compartment model will be described using material balances on ions. The nonlinear nature of the differential equations describing the neuron model will be explored using bifurcation theory and numerical simulations. Applications to small neuronal networks will be discussed.
  
  
• 5 November at UH
  Michel Langlais University of Bordeaux II
  Spatially Dependent Epidemic Models
  
  ABSTRACT: The speaker will discuss a discrete model for the propagation of rabies in the red fox population in France. The model will incorporate age dependence, vaccination, sterilization and differentiate between male and females. Spatial effects will also be taken into account.
  
  
• 12 November at Rice
  Thesis Defense
  John Patrick King
  A Microsatellite-Based Statistic for Inferring Patterns of Population Growth: Sampling Properties and Hypothesis Testing
  
  ABSTRACT: DNA sequences sampled from a genetic locus within a population are related by a genealogy. If there is no recombination within the locus, each pair of sequences is descended from some ancestral sequence, one of which is the most recent common ancestor of the entire sample. Past demography shapes this genealogy since the branch lengths depend on the size history of the population. For this reason, observed distributions of allelic types carry information about the population's demographic history. Because of their abundance and relative ease of typing, microsatellites, or short tandem repeats, represent a useful class of loci for the study of demography. This thesis investigates the properties of the imbalance index $\beta$, a microsatellite-based statistic constructed for demographic inference. Simulated data sets are used to explore the sampling properties of $\beta$ and to compare its performance to that of other statistics available in the literature. Tests based on these statistics are applied to samples of microsatellite loci from human populations, and the results are interpreted in light of recent hypotheses concerning the evolution of modern humans.
  
  8:00 a.m. Duncan Hall room 1049
  
  
• 12 November at Rice
  Andrzej Swierniak
  Asymptotic Properties of Microsatellite Repeats Model
  
  
• 3 December at UH
  Jeff Morgan, Professor of Mathematics, Texas A&M University
  Mathematical Biology and the Implicit Function Theorem
  
  ABSTRACT: (Note: This talk is intended primarily for graduate students). Two of the most important problems faced by people studying mathematical models are numerical approximation of steady states and parameter identification. Both of these problems lead to large nonlinear systems of equations that can sometimes be difficult to solve. While there is an abundance of software available to tackle these types of problems, there are often multiple solutions, and many of these can be difficult to find without the aid of a careful strategy. One helpful strategy is to carefully introduce a dummy parameter into the model and use the implicit function theorem. In this talk we discuss the implicit function theorem and demonstrate how it can be used to help solve large nonlinear systems of equations. Applications will be given to the solution of a semilinear cancer model and a parameter identification problem for a system of chemical equations.