Keith E. Howard

Born: ; place: Macon Georgia

  B.S. (1995) Morehouse College; B.ChE. (1995) Georgia Tech; M.S. (1997) Vanderbilt University

Ph.D. (2000) Vanderbilt University
thesis: advisor Glenn F. Webb

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Area: Mathematical Biology (Cell Population Dynamics), Chaotic Semigroups of Operators

"My area of study in mathematics is Hypercyclic and Chaotic Semigroups of Operators. This area of semigroups deals with the density of certain semigroup mappings within particular Banach spaces. This is an important discipline due in part to the strong connection of semigroups solutions to the Abstract Cauchy Problem, (ACP). There are many physical phenomena that can be modeled through the (ACP), particularly within the area of Mathematical Biology. "

"I am particularly interested in the study of models of cell population dynamics. Here we attempt to connect the processes that occur at the individual cell level to overall population changes that can be observed. By modeling cellular systems using the (ACP) we are able to find and analyze solutions that describe the corresponding system. Of significant interest is the long-term or asymptotic behavior of these solutions, which serve to describe the long-term behavior of a particular population. Typically some form of stability in its asymptotic behavior characterizes a healthy system. Certain abnormal or unhealthy systems can be characterized by their lack of stability. One type of instability that can be which can be represented is hypercyclic or chaotic behavior. Research in area has been fruitful in describing the mechanics of certain blood diseases, such as aplastic anemia and certain types of leukemia."


A Size Structured Model of Cell Dwarfism, accepted for publication in Discrete and Continuous Dynamical Systems, Series B

An Abnormal Size and Maturity Model of Cell Population Dynamics, (Submitted for publication)


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