David Anderson
Van Vleck Visiting Assistant Professor (postdoc)
Department of Mathematics
University of Wisconsin-Madison
617 Van Vleck Hall
480 Lincoln Drive
Madison, WI 53706-1388
Telephone: (608) 263-4943
Fax: (608) 263-8891
E-mail: anderson at math dot wisc dot edu Fall 2008 Teaching: Math 331 Introduction to probability and Markov chain models.
Education

Ph.D. in Mathematics, Duke University, Durham, N.C., 2005.
     Advisors: Michael C. Reed and Jonathan C. Mattingly.

M.A. in Mathematics, Duke University, Durham, N.C., 2001.

B.A. in Mathematics, University of Virginia, Charlottesville, Va., 2000.

Research Interests: My work lies at the interface of probability and biology. More explicitly, my research interests include:
  1. Understanding how network structure affects the stationary behavior of biochemical systems.
    • If the dynamics of a system are modeled deterministically, I consider how network structure affects the existence and stability of equilibria, and how it affects other dynamical properties such as persistence.

    • If the dynamics of a system are modeled stochastically, I consider the role that network structure plays in the existence and form of a stationary distribution (the stochastic analog of a fixed point).

  2. Simulation methods for stochastically modeled biochemical systems.
    • Interest in understanding the dynamics of stochastically modeled biological systems has grown rapidly over the last decade. Simulation methods for such systems can be improved (both in terms of efficiency and stability) by taking advantage of different representations for the models. For example, using a random time change representation has lead to improvements in both exact and approximate (tau-leaping) simulation methods.

  3. Using stochastic forcing to study the emergent properties of biochemical reaction systems that are modeled discretely, via a diffusion approximation, or absolutely continuously (or a combination of the three). This is typically referred to as fluctuation theory.

  4. Simulation methods for stochastic differential equations.

  5. Analyzing biochemical systems with multiple scales.

Curriculum Vitae

Publications
  1. David F. Anderson and Jonathan C. Mattingly, A weakly second-order method for the simulation of stochastic differential equations, in preparation.

  2. David F. Anderson, Arnab Ganguly, and Thomas G. Kurtz, Error Analysis of the tau-leap simulation method for stochastically modeled chemical reaction systems, in preparation.

  3. David F. Anderson, Gheorghe Craciun, and Thomas G. Kurtz, Product-form stationary distributions for deficiency zero chemical reaction networks, Submitted, [arxiv (updated Aug. 10, 2008)] .

  4. David F. Anderson and Gheorghe Craciun, Reduced reaction networks and persistence of chemical systems, in preparation.

  5. David F. Anderson, Global asymptotic stability for a class of nonlinear chemical equations, SIAM J. Appl. Math, vol. 68, issue 5, pgs. 1464 - 1476, May 2008 (arxiv).

  6. David F. Anderson, Incorporating postleap checks in tau-leaping, Journal of Chemical Physics, vol. 128, issue 5, February, 2008, pg. 054103.

  7. David F. Anderson, A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays, Journal of Chemical Physics, vol. 127, issue 21, December 2007, pg. 214107.

  8. David F. Anderson and Jonathan C. Mattingly, Propagation of Fluctuations in Biochemical Reaction Systems, II: Nonlinear Chains, IET Systems Biology, vol. 1, issue 6, November 2007, pgs. 313-325.

  9. David F. Anderson, Jonathan C. Mattingly, H. Frederik Nijhout, Michael Reed, Propagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks, Bulletin of Mathematical Biology, vol. 69, no. 6, August 2007, pgs. 1791-1813.

  10. H. Frederik Nijhout, Michael C. Reed, David F. Anderson, Jonathan C. Mattingly, S. Jill James, and Cornelia M. Ulrich, Long-Range Allosteric Interactions between the Folate and Methionine Cycles Stabilize DNA Methylation Reaction Rate, Epigenetics, vol. 1, no. 2, April/May 2006, pg. 81-87 .

  11. David F. Anderson, Stochastic Perturbations of Biochemical Reaction Systems, PhD Thesis, 2005.